Patent Application
20110016124
The present invention relates generally to compression/decompression of data. More particularly, it relates to defining a digital spectrum of a data file, such as a compressed file, in order to determine properties that can be compared to other files. In this manner, file similarity, file adjacency and file grouping, to name a few, can be determined. Grouped files with overlapped members are further partitioned to achieve optimization.
Recent data suggests that nearly eighty-five percent of all data is found in computing files and growing annually at around sixty percent. One reason for the growth is that regulatory compliance acts, statutes, etc., (e.g., Sarbanes-Oxley, HIPAA, PCI) force companies to keep file data in an accessible state for extended periods of time. However, block level operations in computers are too lowly to apply any meaningful interpretation of this stored data beyond taking snapshots and block de-duplication. While other business intelligence products have been introduced to provide capabilities greater than block-level operations, they have been generally limited to structured database analysis. They are much less meaningful when acting upon data stored in unstructured environments.
Unfortunately, entities the world over have paid enormous sums of money to create and store their data, but cannot find much of it later in instances where it is haphazardly arranged or arranged less than intuitively. Not only would locating this information bring back value, but being able to observe patterns in it might also prove valuable despite its usefulness being presently unknown. However, entities cannot expend so much time and effort in finding this data that it outweighs its usefulness. Notwithstanding this, there are still other scenarios, such as government compliance, litigation, audits, etc., that dictate certain data/information be found and produced, regardless of its cost in time, money and effort. Thus, a clear need is identified in the art to better find, organize and identify digital data, especially data left in unstructured states.
In search engine technology, large amounts of unrelated and unstructured digital data can be quickly gathered. However, most engines do little to organize the data other than give a hierarchical presentation. Also, when the engine finds duplicate versions of data, it offers few to no options on eliminating the replication or migrating/relocating redundancies. Thus, a further need in the art exists to overcome the drawbacks of search engines.
When it comes to large amounts of data, whether structured or not, compression techniques have been devised to preserve storage capacity, reduce bandwidth during transmission, etc. With modern compression algorithms, however, they simply exist to scrunch large blocks of data into smaller blocks according to their advertised compression ratios. As is known, some do it without data loss (lossless) while others do it “lossy.” None do it, unfortunately, with a view toward recognizing similarities in the data itself.
From biology, it is known that highly similar species have highly similar DNA strings. In the computing context, consider two word processing files relating to stored baseball statistics. In a first file, words might appear for a baseball batter, such as “batting average,” “on base percentage.” and “slugging percentage.” while a second file might have words for a baseball pitcher, such as “strikeouts,” “walks,” and “earned runs.” Conversely, a third file wholly unrelated to baseball, statistics or sports, may have words such as “environmental protection.” “furniture,” or whatever comes to mind. It would be exceptionally useful if, during times of compression, or upon later manipulation by an algorithm if “mapping” could recognize the similarity in subject matter in the first two files, although not exact to one another, and provide options to a user. Appreciating that the “words” in the example files are represented in the computing context as binary bits (1's or 0's), which occurs by converting the English alphabet into a series of 1's and 0's through application of ASCII encoding techniques, it would be further useful if the compression algorithm could first recognize the similarity in subject matter of the first two files at the level of raw bit data. The reason for this is that not all files have words and instead might represent pictures (e.g., .jpeg) or spread sheets of numbers.
Appreciating that certain products already exist in the above-identified market space, clarity on the need in the art is as follows. One, present day “keyword matching” is limited to select set of words that have been pulled from a document into an index for matching to the same exact words elsewhere. Two, “Grep” is a modern day technique that searches one or more input files for lines containing an identical match to a specified pattern. Three, “Beyond Compare,” and similar algorithms, are line-by-line comparisons of multiple documents that highlight differences between them. Four, block level data de-duplication has no application in compliance contexts, data relocation, or business intelligence.
The need in the art, on the other hand, needs to serve advanced notions of identifying new business intelligence, conducting operations on completely unstructured or haphazard data, and organizing it, providing new useful options to users, providing new user views, providing new encryption products, and identifying highly similar data, to name a few. As a byproduct, solving this need will create new opportunities in minimizing transmission bandwidth and storage capacity, among other things. Naturally, any improvements along such lines should contemplate good engineering practices, such as stability, ease of implementation, unobtrusiveness, etc.
The foregoing and other problems are solved by applying the principles and teachings associated with optimized partitions for grouping and differentiating files of data. Broadly, embodiments of the invention identify self-organizing, emergent patterns in data sets without any keyword, semantic, or metadata processing. Among certain advantages is that: the strongest possible memberships are determined given the input of groups of overlapping members; the smallest number of groups are defined while still allowing members to be in more than one group (not forcing mutually exclusive groups); observable, new, clear, and distinct groups are created from less distinct and less clear “fuzzy” overlapping groups; and a specific algorithm is presented for determining the weight of each member in the fuzzy overlapping groups and the number of fuzzy overlapping groups to determine a strength for every possible new partition of groups created from the members of the fuzzy overlapping groups in order to mathematically (objectively) determine the optimal set of groups (partitioning of the original groups).
In representative embodiments, methods and apparatus teach a digital spectrum of a compressed file. The digital spectrum is used to map a file's position in multi-dimensional space. This position relative to another file's position reveals closest neighbors. Certain of the closest neighbors are grouped together to define a set. Overlapping members in the groups may be further differentiated from one another by partitioning. An optimized partition of set S of N overlapping groups yields a maximum strength for groups and members in that partition. The optimized partition includes relative strengths of every individual member in every possible partition and weighting functions applied to the relative strengths and to subgroups of files within the partitions.
Using semi formal mathematical notation, the strength T=SP(P) of a partition P is given as: SP(Partition)=Σ SGS(GSi)*WGS(GSi), for all groups GSi in the partition and where SGS(GS)=Σ SM(Mj)*WM(Mj), for all members Mj in the groups and where SM(Member)=(Number of total groups having that member)/(total numbers of groups); and where WGS( ) is the relative strength of this set of groups compared with the total number of original groups and WM( ) is the relative strength of this member compared with the total number of members in all the groups of this set of groups. Specifically WGS(GS)=this number of groups/number of all original groups and WM(M)=(1.0)/(total number of members in this set of groups).
In a computing context, files are stored on one or more computing devices. As representatively encoded, they have pluralities of symbols representing an underlying data stream of original bits of data. These symbols define the multi-dimensional space in which file positions are examined relative to one another. Distances between the files in this space and matrix sorts of the distances are still other embodiments that are ultimately used to facilitate file grouping/differentiating, and then the partitioning.
Executable instructions loaded on one or more computing devices for undertaking the foregoing are also contemplated as are computer program products available as a download or on a computer readable medium. The computer program products are also available for installation on a network appliance or an individual computing device.
These and other embodiments of the present invention will be set forth in the description which follows, and in part will become apparent to those of ordinary skill in the art by reference to the following description of the invention and referenced drawings or by practice of the invention. The claims, however, indicate the particularities of the invention.
The accompanying drawings incorporated in and forming a part of the specification, illustrate several aspects of the present invention, and together with the description serve to explain the principles of the invention. In the drawings:
b are data streams, tree diagrams and tables in accordance with the present invention relating to decompression of a compressed file;
FIGS. 94-98A-B are definitions and diagrams in accordance with the present invention showing a “digital spectrum” embodiment of an encoded file, including grouping of files; and
In the following detailed description of the illustrated embodiments, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration, specific embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention and like numerals represent like details in the various figures. Also, it is to be understood that other embodiments may be utilized and that process, mechanical, electrical, arrangement, software and/or other changes may be made without departing from the scope of the present invention. In accordance with the present invention, methods and apparatus are hereinafter described for optimizing data compression of digital data.
In a representative embodiment, compression occurs by finding highly occurring patterns in data streams, and replacing them with newly defined symbols that require less space to store than the original patterns. The goal is to eliminate as much redundancy from the digital data as possible. The end result has been shown by the inventor to achieve greater compression ratios on certain tested files than algorithms heretofore known.
In information theory, it is well understood that collections of data contain significant amounts of redundant information. Some redundancies are easily recognized, while others are difficult to observe. A familiar example of redundancy in the English language is the ordered pair of letters QU. When Q appears in written text, the reader anticipates and expects the letter U to follow, such as in the words queen, quick, acquit, and square. The letter U is mostly redundant information when it follows Q. Replacing a recurring pattern of adjacent characters with a single symbol can reduce the amount of space that it takes to store that information. For example, the ordered pair of letters QU can be replaced with a single memorable symbol when the text is stored. For this example, the small Greek letter alpha (α) is selected as the symbol, but any could be chosen that does not otherwise appear in the text under consideration. The resultant compressed text is one letter shorter for each occurrence of QU that is replaced with the single symbol (α). e.g., “αeen,” “αick,” “acαit,” and “sαare.” Such is also stored with a definition of the symbol alpha (α) in order to enable the original data to be restored. Later, the compressed text can be expanded by replacing the symbol with the original letters QU. There is no information loss. Also, this process can be repeated many times over to achieve further compression.
With reference to
Redundancy is the superfluous repetition of information. As demonstrated in the QU example above, adjacent characters in written text often form expected patterns that are easily detected. In contrast, digital data is stored as a series of bits where each bit can have only one of two values: off (represented as a zero (0)) and on (represented as a one (1)). Redundancies in digital data, such as long sequences of zeros or ones, are easily seen with the human eye. However, patterns are not obvious in highly complex digital data. The invention's methods and procedures identify these redundancies in stored information so that even highly complex data can be compressed. In turn, the techniques can be used to reduce, optimize, or eliminate redundancy by substituting the redundant information with symbols that take less space to store than the original information. When it is used to eliminate redundancy, the method might originally return compressed data that is larger than the original. This can occur because information about the symbols and how the symbols are encoded for storage must also be stored so that the data can be decompressed later. For example, compression of the word “queen” above resulted in the compressed word “αeen.” But a dictionary having the relationship QU=α also needed to be stored with the word “αeen”, which makes a “first pass” through the compression technique increase in size, not decrease. Eventually, however, further “passes” will stop increasing and decrease so rapidly, despite the presence of an ever-growing dictionary size, that compression ratios will be shown to greatly advance the state of the art. By automating the techniques with computer processors and computing software, compression will also occur exceptionally rapidly. In addition, the techniques herein will be shown to losslessly compress the data.
The following compression method iteratively substitutes symbols for highly occurring tuples in a data stream. An example of this process is provided later in the document.
The compression procedure will be performed on digital data. Each stored bit has a value of binary 0 or binary 1. This series of bits is referred to as the original digital data.
The original digital data is examined at the bit level. The series of bits is conceptually converted to a stream of characters, referred to as the data strewn that represents the original data. The symbols 0 and 1 are used to represent the respective raw bit values in the new data stream. These symbols are considered to be atomic because all subsequently defined symbols represent tuples that are based on 0 and 1.
A dictionary is used to document the alphabet of symbols that are used in the data stream. Initially, the alphabet consists solely of the symbols 0 and 1.
The following tasks are performed iteratively on the data stream:
From
In the following example and with any data stream of digital data that can be compressed according to the techniques herein, two symbols (0 and 1) occur in the alphabet and are possibly the only symbols in the entire data stream. By examining them as “tuples,” the combination of the 0 and 1 as ordered pairs of adjoining characters reveals only four possible outcomes, i.e., a tuple represented by “00,” a tuple represented by “01,” a tuple represented by “10,” and a tuple represented by “11.”
With reference to
With
The process begins by examining the adjacent characters in position one and two of the data stream. Together, the pair of characters forms a tuple. Advance by one character in the stream and examine the characters in positions two and three. By incrementing through the data stream one character at a time, every combination of two adjacent characters in the data stream is examined and tallied against one of the tuples.
Sequences of repeated symbols create a special case that must be considered when tallying tuples. That is, when a symbol is repeated three or more times, skilled artisans might identify instances of a tuple that cannot exist because the symbols in the tuple belong to other instances of the same tuple. The number of actual tuples in this case is the number of times the symbol repeats divided by two.
For example, consider the data stream 14 in table 16 (
After the entire data stream has been examined, the final counts for each tuple are compared to determine which tuple occurs most frequently. In tabular form, the 0 followed by a 1 (tuple 0>1) occurs the most and is referenced at element 19 in table 22,
In the situation of a tie between two or more tuples, skilled artisans must choose between one of the tuples. For this, experimentation has revealed that choosing the tuple that contains the most complex characters usually results in the most efficient compression. If all tuples are equally complex, skilled artisans can choose any one of the tied tuples and define it as the most highly occurring.
The complexity of a tuple is determined by imagining that the symbols form the sides of a right triangle, and the complexity is a measure of the length of the hypotenuse of that triangle. Of course, the hypotenuse is related to the sum of the squares of the sides, as defined by the Pythagorean Theorem,
The tuple with the longest hypotenuse is considered the most complex tuple, and is the winner in the situation of a tie between the highest numbers of occurring tuples. The reason for this is that less-complex tuples in the situation of a tie are most likely to be resolved in subsequent passes in the decreasing order of their hypotenuse length. Should a tie in hypotenuse length occur, or a tie in complexity, evidence appears to suggest it does not make a difference which tuple is chosen as the most highly occurring.
For example, suppose that tuples 3>7, 4>4 and 1>5 each occur 356 times when counted (in a same pass). To determine the complexity of each tuple, use the tuple symbols as the two sides of a right triangle and calculate the hypotenuse,
Skilled artisans can also use the tuple array to visualize the hypotenuse by drawing lines in the columns and rows from the array origin to the tuple entry in the array, as shown in table 24 in
As before, a symbol stands for the two adjacent characters that form the tuple and skilled artisans select any new symbol they want provided it is not possibly found in the data stream elsewhere. Also, since the symbol and its definition are added to the alphabet, e.g., if “α=QU,” a dictionary grows by one new symbol in each pass through the data, as will be seen. A good example of a new symbol for use in the invention is a numerical character, sequentially selected, because numbers provide an unlimited source of unique symbols. In addition, reaching an optimized compression goal might take thousands (or even tens of thousands) of passes through the data stream and redundant symbols must be avoided relative to previous passes and future passes.
Replacing the Tuple with the New Symbol
Upon examining the data stream to find all occurrences of the highest occurring tuple, skilled artisans simply substitute the newly defined or newly created symbol for each occurrence of that tuple. Intuitively, substituting a single symbol for two characters compresses the data stream by one character for each occurrence of the tuple that is replaced.
To accomplish this, counting occurs for how many times that each of the symbols in the current alphabet occurs in the data stream. They then use the symbol count to apply an encoding scheme, such as a path-weighted Huffman coding scheme, to the alphabet. Huffman trees should be within the purview of the artisan's skill set.
The encoding assigns bits to each symbol in the current alphabet that actually appears in the data stream. That is, symbols with a count of zero occurrences are not encoded in the tree. Also, symbols might go “extinct” in the data stream as they are entirely consumed by yet more complex symbols, as will be seen. As a result, the Huffman code tree is rebuilt every time a new symbol is added to the dictionary. This means that the Huffman code for a given symbol can change with every pass. The encoded length of the data stream usually decreases with each pass.
The compressed file size is the total amount of space that it takes to store the Huffman-encoded data stream plus the information about the compression, such as information about the file, the dictionary, and the Huffman encoding tree. The compression information must be saved along with other information so that the encoded data can be decompressed later.
To accomplish this, artisans count the number of times that each symbol appears in the data stream. They also count the number of bits in the symbol's Huffman code to find its bit length. They then multiply the bit length by the symbol count to calculate the total bits needed to store all occurrences of the symbol. This is then repeated for each symbol. Thereafter, the total bit counts for all symbols are added to determine how many bits are needed to store only the compressed data. To determine the compressed file size, add the total bit count for the data to the number of bits required for the related compression information (the dictionary and the symbol-encoding information).
Determining Whether the Compression Goal has been Achieved
Substituting a tuple with a single symbol reduces the total number of characters in a data stream by one for each instance of a tuple that is replaced by a symbol. That is, for each instance, two existing characters are replaced with one new character. In a given pass, each instance of the tuple is replaced by a new symbol. There are three observed results:
By repeating the compression procedure a sufficient number of times, any series of characters can eventually be reduced to a single character. That “super-symbol” character conveys the entire meaning of the original text. However, the information about the symbols and encoding that is used to reach that final symbol is needed to restore the original data later. As the number of total characters in the text decreases with each repetition of the procedure, the number of symbols increases by one. With each new symbol, the size of the dictionary and the size of the Huffman tree increase, while the size of the data decreases relative to the number of instances of the tuple it replaces. It is possible that the information about the symbol takes more space to store than the original data it replaces. In order for the compressed file size to become smaller than the original data stream size, the text size must decrease faster than the size increases for the dictionary and the Huffman encoding information.
The question at hand is then, what is the optimal number of substitutions (new symbols) to make, and how should those substitutions be determined?
For each pass through the data stream, the encoded length of the text decreases, while the size of the dictionary and the Huffman tree increases. It has been observed that the compressed file size will reach a minimal value, and then increase. The increase occurs at some point because so few tuple replacements are done that the decrease in text size no longer outweighs the increase in size of the dictionary and Huffman tree.
The size of the compressed file does not decrease smoothly or steadily downward. As the compression process proceeds, the size might plateau or temporarily increase. In order to determine the true (global) minimum, it is necessary to continue some number of iterations past the each new (local) minimum point. This true minimal value represents the optimal compression for the data stream using this method.
Through experimentation, three conditions have been found that can be used to decide when to terminate the compression procedure: asymptotic reduction, observed low, and single character. Each method is described below. Other terminating conditions might be determined through further experimentation.
An asymptotic reduction is a concession to processing efficiency, rather than a completion of the procedure. When compressing larger files (100 kilobytes (KB) or greater), after several thousand passes, each additional pass produces only a very small additional compression. The compressed size is still trending downward, but at such a slow rate that additional compute time is not warranted.
Based on experimental results, the process is terminated if at least 1000 passes have been done, and less than 1% of additional data stream compression has occurred in the last 1000 passes. The previously noted minimum is therefore used as the optimum compressed file.
A reasonable number of passes have been performed on the data and in the last reasonable number of passes a new minimum encoded file size has not been detected. It appears that further passes only result in a larger encoded file size.
Based on experimental results, the process is terminated if at least 1000 passes have been done, and in the last 10% of the passes, a new low has not been established. The previously noted minimum is then used as the optimum compressed file.
The data stream has been reduced to exactly one character. This case occurs if the file is made up of data that can easily reduce to a single symbol, such a file filled with a repeating pattern. In cases like this, compression methods other than this one might result in smaller compressed file sizes.
The representative embodiment of the invention uses Huffman trees to encode the data stream that has been progressively shortened by tuple replacement, and balanced against the growth of the resultant Huffman tree and dictionary representation.
The average length of a Huffman encoded symbol depends upon two factors:
The average encoded symbol length grows in a somewhat stepwise fashion as more symbols are added to the dictionary. Because the Huffman tree is a binary tree, increases naturally occur as the number of symbols passes each level of the power of 2 (2, 4, 8, 16, 32, 64, etc.). At these points, the average number of bits needed to represent any given symbol normally increases by 1 bit, even though the number of characters that need to be encoded decreases. Subsequent compression passes usually overcome this temporary jump in encoded data stream length.
The second factor that affects the efficiency of Huffman coding is the distribution of the frequency of symbol use. If one symbol is used significantly more than any other, it can be assigned a shorter encoding representation, which results in a shorter encoded length overall, and results in maximum compression. The more frequently a symbol occurs, the shorter the encoded stream that replaces it. The less frequently a symbol occurs, the longer the encoded stream that replaces it.
If all symbols occur at approximately equal frequencies, the number of symbols has the greater effect than does the size of the encoded data stream. Supporting evidence is that maximum compression occurs when minimum redundancy occurs, that is, when the data appears random. This state of randomness occurs when every symbol occurs at the same frequency as any other symbol, and there is no discernable ordering to the symbols.
The method and procedure described in this document attempt to create a state of randomness in the data stream. By replacing highly occurring tuples with new symbols, eventually the frequency of all symbols present in the data stream becomes roughly equal. Similarly, the frequency of all tuples is also approximately equal. These two criteria (equal occurrence of every symbol and equal occurrence of ordered symbol groupings) is the definition of random data. Random data means no redundancy. No redundancy means maximum compression.
This method and procedure derives optimal compression from a combination of the two factors. It reduces the number of characters in the data stream by creating new symbols to replace highly occurring tuples. The frequency distribution of symbol occurrence in the data stream tends to equalize as oft occurring symbols are eliminated during tuple replacement. This has the effect of flattening the Huffman tree, minimizing average path lengths, and therefore, minimizing encoded data stream length. The number of newly created symbols is held to a minimum by measuring the increase in dictionary size against the decrease in encoded data stream size.
To demonstrate the compression procedure, a small data file contains the following simple ASCII characters:
aaaaaaaaaaaaaaaaaaaaaaaaaaabaaabaaaaaaaababbbbbb
Each character is stored as a sequence of eight bits that correlates to the ASCII code assigned to the character. The bit values for each character are:
a=01100001
b=01100010
The digital data that represents the file is the original data that we use for our compression procedure. Later, we want to decompress the compressed file to get back to the original data without data loss.
The digital data that represents the file is a series of bits, where each bit has a value of 0 or 1. We want to abstract the view of the bits by conceptually replacing them with symbols to form a sequential stream of characters, referred to as a data stream.
For our sample digital data, we create two new symbols called 0 and 1 to represent the raw bit values of 0 and 1, respectively. These two symbols form our initial alphabet, so we place them in the dictionary 26,
The data stream 30 in
Also, the characters in data stream 30 are separated with a space for user readability, but the space is not considered, just the characters. The space would not occur in computer memory either.
The data stream 30 of
For the initial pass, the original data stream and alphabet that were created in “Preparing the Data Stream” are obtained.
An easy way to identify all possible combinations of the characters in our current alphabet (at this time having 0 and 1) is to create a tuple array (table 35,
For example, the table 35 shows the tuple array for characters 0 and 1. In the cell for column 0 and row 0, the tuple is the ordered pair of 0 followed by 0. The shorthand notation of the tuple in the first cell is “0>0”. In the cell for column 0 and row 1, the tuple is 0 followed by 1, or “0>1”. In the cell for column 1 and row 0, the tuple is “1>0”. In the cell for column 1 and row 1, the tuple is “1>1” (As skilled artisans will appreciate, most initial dictionaries and original tuple arrays will be identical to these. The reason is that computing data streams will all begin with a stream of 1's and 0's having two symbols only.)
After completion of the tuple array, we are ready to look for the tuples in the data stream 30,
For example, the first two characters in our sample data stream are 0 followed by 1. This matches the tuple 0>1 so we count that as one instance of the tuple. We step forward one character. The characters in positions two and three are 1 followed by 1, which matches the tuple 1>1. We count it as one instance of the 1>1 tuple. We consider the sequences of three or more zeros in the data stream (e.g., 01100001 . . . ) to determine the actual number of tuples for the 0>0 tuple. We repeat this process to the end of the data set with the count results in table 40,
Now that we have gathered statistics for how many times each tuple appears in the data stream 30, we compare the total counts for each tuple to determine which pattern is the most highly occurring. The tuple that occurs most frequently is a tie between a 1 followed by 0 (1>0), which occurs 96 times, and a 0 followed by 1 (0>1), which also occurs 96 times. As discussed above, skilled artisans then choose the most complex tuple and do so according to Pythagorean's Theorem. The sum of the squares for each tuple is the same, which is 1 (1+0) and 1 (0+1). Because they have the same complexity, it does not matter which one is chosen as the highest occurring. In this example, we will choose tuple 1>0.
We also count the number of instances of each of the symbols in the current alphabet as seen in table 41,
In this next pass, we replace the most highly occurring tuple from the previous pass with a new symbol, and then we determine whether we have achieved our compression goal.
We replace the most highly occurring tuple from the previous pass with a new symbol and add it to the alphabet. Continuing the example, we add a new symbol 2 to the dictionary and define it with the tuple defined as 1 followed by 0 (1>0). It is added to the dictionary 26′ as seen in
Replacing the Triple with the New Symbol
In the original data stream 30, every instance of the tuple 1>0 is now replaced with the new, single symbol. In our example data stream 30,
After we compress the data stream by using the new symbol, we use a path-weighted Huffman coding scheme to assign bits to each symbol in the current alphabet.
To do this, we again count the number of instances of each of the symbols in the current alphabet (now having “0,” “1” and “2.”) The total symbol count in the data stream is 288 symbols as seen in table 41′,
Next, we use the counts to build a Huffman binary code tree. 1) List the symbols from highest count to lowest count. 2) Combine the counts for the two least frequently occurring symbols in the dictionary. This creates a node that has the value of the sum of the two counts. 3) Continue combining the two lowest counts in this manner until there is only one symbol remaining. This generates a Huffman binary code tree.
Finally, label the code tree paths with zeros (0s) and ones (1s). The Huffman coding scheme assigns shorter code words to the more frequent symbols, which helps reduce the size length of the encoded data. The Huffman code for a symbol is defined as the string of values associated with each path transition from the root to the symbol terminal node.
With reference to
In this compression procedure, we will re-build a Huffman code tree every time we add a symbol to the current dictionary. This means that the Huffman code for a given symbol can change with every compression pass.
From the Huffman tree, we use its code to evaluate the amount of space needed to store the compressed data as seen in table 52,
To know whether we achieved optimal compression, we must consider the total amount of space that it takes to store the compressed data plus the information about the compression that we need to store in order to decompress the data later. We also must store information about the file, the dictionary, and the Huffman tree. The table 57 in
Determining Whether the Compression Goal has been Achieved
Finally, we compare the original number of bits (384,
In early passes, however, we expect to see that the substitution requires more space than the original data because of the effect of carrying a dictionary, adding symbols, and building a tree. On the other hand, skilled artisans should observe an eventual reduction in the amount of space needed as the compression process continues. Namely, as the size of the data set decreases by the symbol replacement method, the size grows for the symbol dictionary and the Huffman tree information that we need for decompressing the data.
In this pass, we replace the most highly occurring tuple from the previous pass (pass 1) with still another new symbol, and then we determine whether we have achieved our compression goal.
As a result of the new symbol, the tuple array is expanded by adding the symbol that was created in the previous pass. Continuing our example, we add 2 as a first symbol and last symbol, and enter the tuples in the new cells of table 35′
As before, the tuple array identifies the tuples that we look for and tally in our revised alphabet. As seen in table 40′,
We define still another new symbol “3” to represent the most highly occurring tuple 2>0, and add it to the dictionary 26″,
Replacing the Tuple with the New Symbol
In the data stream 30′.
As demonstrated above, we count the number of symbols in the data stream, and use the count to build a Huffman tree and code for the current alphabet. The total symbol count has been reduced from 288 to 234 (e.g., 88+48+40+58, but not including the EOF marker) as seen in table 41″,
We need to evaluate whether our substitution reduces the amount of space that it takes to store the data. As described above, we calculate the total bits needed (507) as in table 52′,
In table 57′,
Determining Whether the Compression Goal has been Achieved
Finally, we compare the original number of bits (384) to the current number of bits (545=507+38) that are needed for this compression pass. We find that it takes 141% or 1.41 times as many bits to store the compressed data as it took to store the original data. Compression is still not achieved and the amount of data in this technique is growing larger rather than smaller in comparison to the previous pass requiring 132%.
In this pass, we replace the most highly occurring tuple from the previous pass with a new symbol, and then we determine whether we have achieved our compression goal.
We expand the tuple array 35″,
The tuple array identifies the tuples that we look for and tally in our revised alphabet. In table 40″,
We define a new symbol 4 to represent the most highly occurring tuple 1>3, and add it to the dictionary 26′″,
Replacing the Tuple with the New Symbol
In the data stream, we replace every instance of the most highly occurring tuple from the earlier data stream with the new single symbol. We replace the 48 instances of the 1>3 tuple with the symbol 4 and new data stream 30-4 is obtained,
We count the number of symbols in the data stream, and use the count to build a Huffman tree and code for the current alphabet as seen in table 41′″,
We need to evaluate whether our substitution reduces the amount of space that it takes to store the data. As seen in table 52″,
In table 57″,
Determining Whether the Compression Goal has been Achieved
Finally, we compare the original number of bits (384) to the current number of bits (382) that are needed for this compression pass. We find that it takes 0.99 times as many bits to store the compressed data as it took to store the original data. Compression is achieved.
In this pass, we replace the most highly occurring tuple from the previous pass with a new symbol, and then we determine whether we have achieved our compression goal.
We expand the tuple array 35′″,
The tuple array identifies the tuples that we look for and tally in our revised alphabet. In table 40′″,
We define a new symbol 5 to represent the 4>0 tuple, and add it to the dictionary 26-4,
Replacing the Tuple with the New Symbol
In the data stream, we replace every instance of the most highly occurring tuple with the new single symbol. We replace the 48 instances of the 40 tuple in data stream 30-4,
As demonstrated above, we count the number of symbols in the data stream, and use the count to build a Huffman tree and code for the current alphabet. There is no Huffman code assigned to the symbol 1 and the symbol 4 because there are no instances of these symbols in the compressed data in this pass. The total symbol count has been reduced from 184 to 136 (e.g., 40+0+40+8+0+48, but not including the EOF marker) as seen in table 41-4,
We need to evaluate whether our substitution reduces the amount of space that it takes to store the data. As seen in table 52′″,
As seen in table 57′″,
Determining Whether the Compression Goal has been Achieved
Finally, we compare the original number of bits (384) to the current number of bits (331) that are needed for this compression pass as seen in table 58′″,
In this pass, we replace the most highly occurring tuple from the previous pass with a new symbol, and then we determine whether we have achieved our compression goal.
We expand the tuple array by adding the symbol that was created in the previous pass. We add the symbol 5 as a first symbol and last symbol, and enter the tuples in the new cells as seen in table 35-4,
The tuple array identifies the tuples that we look for and tally in our revised alphabet as seen in table 40-4,
We define a new symbol 6 to represent the most highly occurring tuple 2>5, and add it to the dictionary for the alphabet that was developed in the previous passes as seen in table 26-5,
Replacing the Tuple with the New Symbol
In the data stream, we replace every instance of the most highly occurring tuple with the new single symbol. We replace the 39 instances of the 2>5 tuple in data stream 30-5,
As demonstrated above, we count the number of symbols in the data stream, and use the count to build a Huffman tree and code for the current alphabet as seen in table 41-5,
We need to evaluate whether our substitution reduces the amount of space that it takes to store the data. As seen in table 52-4,
As seen in table 57-4,
Determining Whether the Compression Goal has been Achieved
Finally, we compare the original number of bits (384) to the current number of bits (246, or 187+59) that are needed for this compression pass as seen in table 58-4,
In this pass, we replace the most highly occurring tuple from the previous pass with a new symbol, and then we determine whether we have achieved our compression goal.
We expand the tuple array 35-5 by adding the symbol that was created in the previous pass as seen in
The tuple array identifies the tuples that we look for and tally in our revised alphabet. (Total Symbol Count=97) The tuple that occurs most frequently is the symbol 0 followed by symbol 6 (0>6). It occurs 39 times as seen in table 40-5,
We define a new symbol 7 to represent the 0>6 tuple, and add it to the dictionary for the alphabet that was developed in the previous passes as seen in table 26-6,
Replacing the Tuple with the New Symbol
In the data stream, we replace every instance of the most highly occurring tuple with the new single symbol. We replace the 39 instances of the 0>6 tuple in data stream 30-6,
As demonstrated above, we count the number of symbols in the data stream, and use the count to build a Huffman tree and code for the current alphabet as seen in table 41-6,
Because all the symbols 1, 4, and 6 have been removed from the data stream, there is no reason to express them in the encoding scheme of the Huffman tree 50′,
We need to evaluate whether our substitution reduces the amount of space that it takes to store the data. As seen in table 52-5,
As seen in table 57-5,
Determining Whether the Compression Goal has been Achieved
Finally, we compare the original number of bits (384) to the current number of bits (166, or 95+71) that are needed for this compression pass as seen in table 58-5,
Skilled artisans will also notice that overhead has been growing in size while the total number of bits is still decreasing. We repeat the procedure to determine if this is the optimum compressed file size. We compare the compression size for each subsequent pass to the first occurring lowest compressed file size. The chart 60,
With reference to table 61,
The information needed to decompress a file is usually written at the front of a compressed file, as well as to a separate dictionary only file. The compressed file contains information about the file, a coded representation of the Huffman tree that was used to compress the data, the dictionary of symbols that was created during the compression process, and the compressed data. The goal is to store the information and data in as few bits as possible.
This section describes a method and procedure for storing information in the compressed file.
The first four bits in the file are reserved for the version number of the file format, called the file type. This field allows flexibility for future versions of the software that might be used to write the encoded data to the storage media. The file type indicates which version of the software was used when we saved the file in order to allow the file to be decompressed later.
Four bits allows for up to 16 versions of the software. That is, binary numbers from 0000 to 1111 represent version numbers from 0 to 15. Currently, this field contains binary 0000.
The second four bits in the file are reserved for the maximum symbol width. This is the number of bits that it takes to store in binary form the largest symbol value. The actual value stored is four less than the number of bits required to store the largest symbol value in the compressed data. When we read the value, we add four to the stored number to get the actual maximum symbol width. This technique allows symbol values up to 20 bits. In practical terms, the value 2̂20 (2 raised to the 20th power) means that about 1 million symbols can be used for encoding.
For example, if symbols 0-2000 might appear in the compressed file, the largest symbol ID (2000) would fit in a field containing 11 bits. Hence, a decimal 7 (binary 0111) would be stored in this field.
In the compression example, the maximum symbol width is the end-of-file symbol 8, which takes four bits in binary (1000). We subtract four, and store a value of 0000. When we decompress the data, we add four to zero to find the maximum symbol width of four bits. The symbol width is used to read the Huffman tree that immediately follows in the coded data stream.
We must store the path information for each symbol that appears in the Huffman tree and its value. To do this, we convert the symbol's digital value to binary. Each symbol will be stored in the same number of bits, as determined by the symbol with the largest digital value and stored as the just read “symbol width”.
In the example, the largest symbol in the dictionary in the Huffman encoded tree is the end-of-file symbol 8. The binary form of 8 is 1000, which takes 4 bits. We will store each of the symbol values in 4 bits.
To store a path, we will walk the Huffman tree in a method known as a pre-fix order recursive parse, where we visit each node of the tree in a known order. For each node in the tree one bit is stored. The value of the bit indicates if the node has children (1) or if it is a leaf with no children (0). If it is a leaf, we also store the symbol value. We start at the root and follow the left branch down first. We visit each node only once. When we return to the root, we follow the right branch down, and repeat the process for the right branch.
In the following example, the Huffman encoded tree is redrawn as 50-2 to illustrate the prefix-order parse, where nodes with children are labeled as 1, and leaf nodes are labeled as 0 as seen in
The discovered paths and symbols are stored in the binary form in the order in which they are discovered in this method of parsing. Write the following bit string to the file, where the bits displayed in bold/underline represent the path, and the value of the 0 node are displayed without bold/underline. The spaces are added for readability; they are not written to media.
110 0101 110 0000 10 1000 0 0010 0 0011 0 0111
The dictionary information is stored as sequential first/last definitions, starting with the two symbols that define the symbol 2. We can observe the following characteristics of the dictionary:
Because the symbol represents a tuple made up of lower-level symbols, we will increase the bit width at the next higher symbol value; that is, at 3, 5, 9, and 17, instead of at 2, 4, 8, and 16.
We use this information to minimize the amount of space needed to store the dictionary. We store the binary values for the tuple in the order of first and last, and use only the number of bits needed for the values.
Three dictionary instances have special meanings. The 0 and 1 symbols represent the atomic symbols of data binary 0 binary 1, respectively. The last structure in the array represents the end-of-file (EOF) symbol, which does not have any component pieces. The EOF symbol is always assigned a value that is one number higher than the last symbol found in the data stream.
Continuing our compression example, the table 63,
Write the following bit string to the file. The spaces are added for readability; they are not written to media.
10 1000 0111 100000 010101 000110
To store the encoded data, we replace the symbol with its matching Huffman code and write the bits to the media. At the end of the encoded bit string, we write the EOF symbol. In our example, the final compressed symbol string is seen again as 30-7,
The Huffman code for the optimal compression is shown in table 67,
As we step through the data stream, we replace the symbol with the Huffman coded bits as seen at string 68,
The compressed bit string for the data, without spaces is:
010000111111111111111111111111111011001110110011111111011001011000110001 10001100011000101101010
As summarized in the diagram 69,
In the example, the bits 70 of
The process of decompression unpacks the data front the beginning of the file 69,
Read the first four bits of the file to determine the file format version.
Read the next four bits in the file, and then add four to the value to determine the maximum symbol width. This value is needed to read the Huffman tree information.
Reconstruct the Huffman tree. Each 1 bit represents a node with two children. Each 0 bit represents a leaf node, and it is immediately followed by the symbol value. Read the number of bits for the symbol using the maximum symbol width.
In the example, the stored string for Huffman is:
11001011100000101000000100001100111
With reference to
To reconstruct the dictionary from file 69, read the values for the pairs of tuples and populate the table. The values of 0 and 1 are known, so they are automatically included. The bits are read in groups based on the number of bits per symbol at that level as seen in table 72,
In our example, the following bits were stored in the file:
1010000111101000010101000110
We read the numbers in pairs, according to the bits per symbol, where the pairs represent the numbers that define symbols in the dictionary:
We convert each binary number to a decimal number:
We identify the decimal values as the tuple definitions for the symbols:
We populate the dictionary with these definitions as seen in table 73,
We use the tuples that are defined in the re-constructed dictionary to build the Huffman decode tree. Let's decode the example dictionary to demonstrate the process. The diagram 74 in
Start with symbols 0 and 1. These are the atomic elements, so there is no related tuple. The symbol 0 is a left branch from the root. The symbol 1 is a right branch. (Left and right are relative to the node as you are facing the diagram—that is, on your left and on your right.) The atomic elements are each represented by a single bit, so the binary path and the original path are the same. Record the original bits 0 and 1 in the decode table.
Symbol 2 is defined as the tuple 1>0 (symbol 1 followed by symbol 0). In the decode tree, go to the node for symbol 1, then add a path that represents symbol 0. That is, add a left branch at node 1. The terminating node is the symbol 2. Traverse the path from the root to the leaf to read the branch paths of left (L) and right (R). Replace each left branch with a 0 and each right path with a 1 to view the binary forum of the path as LR, or binary 10.
Symbol 3 is defined as the tuple 2>0. In the decode tree, go to the node for symbol 2, then add a path that represents symbol 0. That is, add a left branch at node 2. The terminating node is the symbol 3. Traverse the path from the root to the leaf to read the branch path of RLL. Replace each left branch with a 0 and each right path with a 1 to view the binary form of the path as 100.
Symbol 4 is defined as the tuple 1>3. In the decode tree, go to the node for symbol 1, then add a path that represents symbol 3. From the root to the node for symbol 3, the path is RLL. At symbol 1, add the RLL path. The terminating node is symbol 4. Traverse the path from the root to the leaf to read the path of RRLL, which translates to the binary format of 1100.
Symbol 5 is defined as the tuple 4>0. In the decode tree, go to the node for symbol 4, then add a path that represents symbol 0. At symbol 4, add the L path. The terminating node is symbol 5. Traverse the path from the root to the leaf to read the path of RRLLL, which translates to the binary format of 11000.
Symbol 6 is defined as the tuple 2>5. In the decode tree, go to the node for symbol 2, then add a path that represents symbol 5. From the root to the node for symbol 5, the path is RRLLL. The terminating node is symbol 6. Traverse the path from the root to the leaf to read the path of RLRRLLL, which translates to the binary format of 1011000.
Symbol 7 is defined as the tuple 0>6. In the decode tree, go to the node for symbol 0, then add a path that represents symbol 6. From the root to the node for symbol 6, the path is RLRRLLL. The terminating node is symbol 7. Traverse the path from the root to the leaf to read the path of LRLRRLLL, which translates to the binary format of 01011000.
To decompress the data, we need the reconstructed Huffman tree and the decode table that maps the symbols to their original bits as seen at 75,
The compressed file data bits are:
0100001111111111111111111111111101100111011001111111101100101000110001 10001100011000101101010
For example, the first four bits of encoded data 0100 takes us to symbol 0 in the Huffman tree, as illustrated in the diagram 76,
In the diagram 77 in
In the diagram 78,
The next symbol we discover is with bits 011. We follow these bits in the Huffman tree in diagram 79,
We continue the decoding and replacement process to discover the symbol 2 near the end of the stream with bits 01011, as illustrated in diagram 80,
The final unique sequence of bits that we discover is the end-of-file sequence of 01010, as illustrated in diagram 81,
Altogether, the unpacking of compressed bits recovers the original bits of the original data stream in the order of diagram 82 spread across two
With reference to
An intervening Xen or other hypervisor layer 150, also known as a “virtual machine monitor,” or virtualization manager, serves as a virtual interface to the hardware and virtualizes the hardware. It is also the lowest and most privileged layer and performs scheduling control between the virtual machines as they task the resources of the hardware platform, e.g., memory, processor, storage, network (N) (by way of network interface cards, for example), etc. The hypervisor also manages conflicts, among other things, caused by operating system access to privileged machine instructions. The hypervisor can also be type 1 (native) or type 2 (hosted). According to various partitions, the operating systems, applications, application data, boot data, or other data, executable instructions, etc., of the machines are virtually stored on the resources of the hardware platform. Alternatively, the computing system environment is not a virtual environment at all, but a more traditional environment lacking a hypervisor, and partitioned virtual domains. Also, the environment could include dedicated services or those hosted on other devices.
In any embodiment, the representative computing device 120 is arranged to communicate 180 with one or more other computing devices or networks. In this regard, the devices may use wired, wireless or combined connections to other devices/networks and may be direct or indirect connections. If direct, they typify connections within physical or network proximity (e.g., intranet). If indirect, they typify connections such as those found with the internet, satellites, radio transmissions, or the like. The connections may also be local area networks (LAN), wide area networks (WAN), metro area networks (MAN), etc., that are presented by way of example and not limitation. The topology is also any of a variety, such as ring, star, bridged, cascaded, meshed, or other known or hereinafter invented arrangement.
In still other embodiments, skilled artisans will appreciate that enterprises can implement some or all of the foregoing with humans, such as system administrators, computing devices, executable code, or combinations thereof. In turn, methods and apparatus of the invention further contemplate computer executable instructions, e.g., code or software, as part of computer program products on readable media, e.g., disks for insertion in a drive of a computing device 120, or available as downloads or direct use from an upstream computing device. When described in the context of such computer program products, it is denoted that items thereof, such as modules, routines, programs, objects, components, data structures, etc., perform particular tasks or implement particular abstract data types within various structures of the computing system which cause a certain function or group of function, and such are well known in the art.
While the foregoing produces a well-compressed output file, e.g.,
The definitions from
Broadly, the “fast approximation” hereafter 1) greatly reduces the processing time needed to compress a file using the techniques above, and 2) creates and uses a decode tree to identify the most complex possible pattern from an input bit stream that matches previously defined patterns. Similar to earlier embodiments, this encoding method requires repetitive computation that can be automated by computer software. The following discusses the logical processes involved.
Instead of using the iterative process of discovery of the optimal set of symbols, above, the following uses the symbols that were previously created for another file that contains patterns significantly similar to those of the file under consideration. In a high-level flow, the process involves the following tasks:
The objective of the fast approximation method is to take advantage of the key information in an optimally compressed file that was created by using the techniques above. In its uncompressed form of original data, the compressed file should contain data patterns that are significantly similar to the patterns in the current file under consideration for compression. The effectiveness of the resultant compression depends on how similar a related tile's patterns are to the original file's patterns. The way a skilled artisan recognizes a similar file is that similar bit patterns are found in the originally compressed and new file yet to be compressed. It can be theorized a priori that files are likely similar if they have similar formatting (e.g., text, audio, image, powerpoint, spreadsheet, etc), topic content, tools used to create the files, file type, etc. Conclusive evidence of similar bit patterns is that similar compression ratios will occur on both files (i.e. original file compresses to 35% of original size, while target file also compresses to about 35% of original size). It should be noted that similar file sizes are not a requisite for similar patterns being present in both files.
With reference to
From the key information 200, read and unpack the File Type, Maximum Symbol Width, Huffman Tree, and Dictionary fields.
Create a pattern decode tree using the symbol dictionary retrieved from the key information. Each symbol represents a bit pattern from the original data stream. We determine what those bits are by building a decode tree, and then parsing the tree to read the bit patterns for each symbol.
We use the tuples that are defined in the re-constructed dictionary to build the decode tree. The pattern decode tree is formed as a tree that begins at the root and branches downward. A terminal node represents a symbol ID value. A transition node is a placeholder for a bit that leads to terminal nodes.
Read the bit stream of the current file one bit at a time. As the data stream is parsed from left to right, the paths in the decode tree are traversed to detect patterns in the data that match symbols in the original dictionary.
Starting from the root of the pattern decode tree, use the value of each input bit to determine the descent path thru the pattern decode tree. A “0” indicates a path down and to the left, while a “1” indicates a path down and to the right. Continue descending through the decode tree until there is no more descent path available. This can occur because a branch left is indicated with no left branch available, or a branch right is indicated with no right branch available.
When the end of the descent path is reached, one of the following occurs:
Return to the root of the decode tree and continue with the next bit in the data stream to find the next symbol.
Repeat this process until all of the bits in the stream have been matched to patterns in the decode tree. When done, there exists a list of all of the symbols that occur in the bit stream and the frequency of occurrence for each symbol.
Use the frequency information to create a Huffman encoding tree for the symbols that occur in the current file. Include the end-of-file (EOF) symbol when constructing the tree and determining the code.
Use the Huffman tree for the current file to encode its data. The information needed to decompress the file is written at the front of the compressed file, as well as to a separate dictionary only file. The compressed file contains:
This example uses the key information 200 from a previously created but related compressed file to approximate the symbols needed to compress a different file.
With reference to table 202,
Construct the Decode Tree from the Dictionary
With reference to
Start with symbols 0 and 1. These are the atomic elements, by definition, so there is no related tuple as in the dictionary of
Symbol 2 is defined from the dictionary as the tuple 1>0 (symbol 1 followed by symbol 0). In the decode tree 212, go to the node for symbol 1 (which is transition node 205 followed by a right path R and ending in a terminal node 206, or arrow 214), then add a path that represents symbol 0 (which is transition node 205 followed by a left path L and ending in a terminal node 206, or path 216). That is, you add a left branch at node 1. The terminating node 220 is the symbol 2. Traverse the path from the root to the leaf to read the branch paths of right (R) and left (L). Replace each left branch with a 0 and each right path with a 1 to view the binary form of the path as RL, or binary 10 as in decode table 210.
Symbol 3 is defined as the tuple 2>0. In its decode tree 230, it is the same as the decode tree for symbol 2, which is decode tree 212, followed by the “0.” Particularly, in tree 230, go to the node for symbol 2, then add a path that represents symbol 0. That is, you add a left branch (e.g., arrow 216) at node 2. The terminating node is the symbol 3. Traverse the path from the root to the leaf to read the branch path of RLL. Replace each left branch with a 0 and each right path with a 1 to view the binary format of 100 as in the decode table.
Similarly, the other symbols are defined with decode trees building on the decode trees for other symbols. In particular, they are as follows:
Symbol 4 from the dictionary is defined as the tuple 1>3. In its decode tree, go to the node for symbol 1, then add a path that represents symbol 3. From the root to the node for symbol 3, the path is RLL. At symbol 1, add the RLL path. The terminating node is symbol 4. Traverse the path from the root to the leaf to read the path of RRLL, which translates to the binary format of 1100 as in the decode table.
Symbol 5 is defined as the tuple 4>0. In its decode tree, go to the node for symbol 4, then add a path that represents symbol 0. At symbol 4, add the L path. The terminating node is symbol 5. Traverse the path from the root to the leaf to read the path of RRLLL, which translates to the binary format of 11000.
Symbol 6 is defined as the tuple 5>3. In its decode tree, go to the node for symbol 5, then add a path that represents symbol 3. The terminating node is symbol 6. Traverse the path from the root to the leaf to read the path of RRLLLRLL, which translates to the binary format of 11000100.
Symbol 7 is defined from the dictionary as the tuple 5>0. In its decode tree, go to the node for symbol 5, then add a path that represents symbol 0. From the root to the node for symbol 5, the path is RRLLL. Add a left branch. The terminating node is symbol 7. Traverse the path from the root to the leaf to read the path of RRLLLL, which translates to the binary format of 110000.
Finally, symbol 8 is defined in the dictionary as the tuple 7>2. In its decode tree, go to the node for symbol 7, then add a path that represents symbol 2. From the root to the node for symbol 7, the path is RRLLLL. Add a RL path for symbol 2. The terminating node is symbol 8. Traverse the path from the root to the leaf to read the path of RRLLLLRL, which translates to the binary format of 11000010.
The final decode tree for all symbols put together in a single tree is element 240,
For this example, the sample or “current file” to be compressed is similar to the one earlier compressed who's key information 200.
011000010110001001100001011000100110000101100001011000100110000101100010 011000010110000101100010011000010110001001100001011000100110000101100010 011000100110001001100010011000100110000101100001011000100110000101100010 0110000101100010
We step through the stream one bit at a time to match patterns in the stream to the known symbols from the dictionary 200,
Return to the root node of the Decode Tree, and begin looking for the next symbol again starting with the last unused input stream hit, e.g., the bit “1” at position 255,
“0868688686886868686666688686852.”
From here, the frequency of occurrence of each of the symbols in the new bit stream is counted. For example, the symbols “0” and “2” are each found occurring once at the beginning and end of the new bit stream. Similarly, the symbol “5” is counted once just before the symbol “2.” Each of the symbols “6” and “8” are counted fourteen times in the middle of the new bit stream for a total of thirty-one symbols. Its result is shown in table 275,
From the symbol “counts” in
To construct the tree 280, list first the symbols from highest count to lowest count. In this example, the symbol “8” and symbol “6” tied with a count of fourteen and are each listed highest on the tree. On the other hand, the least counted symbols were each of symbol “0,” “2,” “5,” and the EOF. Combine the counts for the two least frequently occurring symbols in the dictionary. This creates a node that has the value of the sum of the two counts. In this example, the EOF and 0 are combined into a single node 281 as are the symbols 2 and 5 at node 283. Together, all four of these symbols combine into a node 285. Continue combining the two lowest counts in this manner until there is only one symbol remaining. This generates a Huffman binary code tree.
Label the code tree paths with zeros (0s) and ones (1s). To encode a symbol, parse from the root to the symbol. Each left and down path represents a 0 in the Huffman code. Each right and down path represents a 1 in the Huffman code. The Huffman coding scheme assigns shorter code words to the more frequent symbols, which helps reduce the size length of the encoded data. The Huffman code for a symbol is defined as the string of values associated with each path transition from the root to the symbol terminal node.
With reference to
The diagram in
1001 0 11 0 11 0 0 11 0 11 0 0 11 0 11 0 0 11 11 11 11 11 0 0 11 0 11 0 1011 1010 1000
Spaces are shown between the coded bits for readability; the spaces are not written to media. Also, the code for the EOF symbol (1000) is placed at the end of the encoded data and shown in underline.
With reference to
In still another alternate embodiment, the following describes technology to identify a file by its contents. It is defined, in one sense, as providing a tile's “digital spectrum.” The spectrum, in turn, is used to define a file's position in an N-dimensional universe. This universe provides a basis by which a file's position determines similarity, adjacency, differentiation and grouping relative to other files. Ultimately, similar files can originate many new compression features, such as the “fast approximations” described above. The terminology defined in
The set of values that digitally identities the file, referred to as the file's digital spectrum, consists of several pieces of information found in two scalar values and two vectors.
The scalar values are:
The symbol frequency vector can be thought of as a series of coordinates in an N-dimensional universe where N is the number of symbols defined in the alphabet of the dictionary, and the counts represent the distance from the origin along the related coordinate axis. The vector describes the file's informational position in the N-dimension universe. The meaning of each dimension is defined by the meaning of its respective symbol.
The origin of N-dimensional space is an ordered vector with a value of 0 for each coordinate:
FO=(0, 0, 0, 0, 0, 0, 0, 0, . . . , 0).
The magnitude of the frequency vector is calculated relative to the origin. An azimuth in each dimension can also be determined using ordinary trigonometry, which may be used at a later time. By using Pythagorean geometry, the distance from the origin to any point Fx in the N-dimensional space can be calculated, i.e.:
D
ox=square root(((F0x−F0o)̂2)+((F1x−F1o)̂2)+((F2x−F2o)̂2)+((F3x−F3o)̂2)+ . . . +((FNx−FNo)̂2))
Substituting the 0 at each coordinate for the values at the origin, the simplified equation is:
D
ox=square root((F0x)̂2)+(F1x)̂2)+(F2x)̂2)+(F3x)̂2)+ . . . +(FNx)̂2))
As an example, imagine that a file has 10 possible symbols and the frequency vector for the file is:
Since this vector also describes the file's informational position in this 10-dimension universe, its distance from the origin can be calculated using the geometry outlined. Namely,
D
ox=square root(((3−0)̂2)+((5−0)̂2)+((6−0)̂2)+((6−0)̂2)+((1−0)̂2)+((0−0)̂2)+((7−0)̂2)+((19−0)̂2)+((3−0)̂2)+((6−0)̂2)+((22−0)̂2))
Dox=31.78.
To create a digital spectrum for a file under current consideration, we begin with the key information 200,
The key information actually selected for the characteristic digital spectrum is considered to be a “well-suited key.” A “well-suited key” is a key best derived from original data that is substantially similar to the current data in a current file or source file to be examined. The key might even be the actual compression key for the source file under consideration. However, to eventually use the digital spectrum information for the purpose of file comparisons and grouping, it is necessary to use a key that is not optimal for any specific file, but that can be used to define the N-dimensional symbol universe in which all the files of interest are positioned and compared. The more closely a key matches a majority of the files to be examined, the more meaningful it is during subsequent comparisons.
The well-suited key can be used to derive the digital spectrum information for the characteristic file that we use to define the N-dimensional universe in which we will analyze the digital spectra of other files. From above, the following information is known about the characteristic digital spectrum of the file:
Using the key information and digital spectrum of the characteristic file, execute the process described in the fast approximation embodiment for a current, related file of interest, but with the following changes:
The digital spectrum of a file can be used to catalog a file's position in an N-dimensional space. This position in space, or digital spectrum, can be used to compute “distances” between file positions, and hence similarity, e.g., the closer the distance, the closer the similarity. The notion of a digital spectrum may eventually lead to the notion of a self-cataloging capability of digital files, or other.
To demonstrate the foregoing embodiment, the digital spectrum will be determined for a small data file that contains the following simple ASCII characters:
aaaaaaaaaaaaaaaaaaaaaaaaaaabaaabaaaaaaaababbbbbb (eqn. 100)
Each character is stored as a sequence of eight bits that correlates to the ASCII code assigned to the character. The bit values for each character are:
a=01100001 (eqn. 101)
b=01100010 (eqn. 102)
By substituting the bits of equations 101 and 102 for the “a” and “b” characters in equation 100, a data stream 30 results as seen in
After performing an optimal compression of the data by using the process defined above in early embodiments, the symbols remaining in the data stream 30-7 are seen in
0 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3 5 7 7 7 3 5 7 7 7 7 7 7 7 7 3 5 7 3 5 3 5 3 5 3 5 3 5 2 (eqn. 103)
With reference to
With reference to table 310,
In turn, the scalar values to be used in the tile's digital spectrum are:
The vectors to be used in the file's digital spectrum are:
The digital spectrum information can be used to calculate various useful characteristics regarding the file from which it was derived, as well as its relationship to other spectra, and the files from which the other spectra were derived. As an example, the frequency spectrum F(x) shown above, may be thought to describe a file's informational position in an 8-dimension universe, where the meaning of each dimension is defined by the meaning of its respective symbols.
Since the origin of the 8-dimensional space is an ordered vector with a value of 0 at each symbol position, e.g., F(0)=(0, 0, 0, 0, 0, 0, 0, 0), the informational position in 8-dimensional space can be defined as an azimuth and distance from the origin. The magnitude of the position vector is calculated using Pythagorean geometry. Dist(x,0)=sqrt (((F(x,0)−F(00)̂2)+ . . . (F(x,7)−F(0,7)̂2)). Simplified, this magnitude becomes Dist(x,0)=sqrt((F(x,0)̂2+F(x,2)̂2+F(x,3)̂2 . . . F(x,7)̂2)). Using the values above in Fx, the magnitude of the Dist(x,0)=40.84, or Dx0=square root (((1)̂2)+((0)̂2)+((1)̂2)+((8)̂2)+((0)̂2)+((9)̂2)+((0)̂2)+((39)̂2))=square root (1+0+1+64+0+81+0+1521)=40.84. Azimuth of the vector can be computed using basic trigonometry.
Using information found in the digital spectra of a group of files, an analysis can be done to determine similarity, or not, of two or more subject files. Information from the digital spectrum is used to create an information statistic for a file. Statistics found to be pertinent in doing this analysis include at least:
S1) Frequency of occurrence of each possible symbol (FREQ)
S2) Normalized frequency of occurrence of each possible symbol (NORM FREQ)
S3) Informational content of occurrence of each symbol (INFO)
S4) Normalized information content of occurrence of each symbol (NORM INFO)
For ease of reference, statistic S1 can be called FREQ for frequency, statistic S2 can be called NORM FREQ for normalized frequency, statistic S1 can be called INFO for informational content, and statistic S4 can be called NORM INFO for normalized informational content. A further discussion is given below for each of these statistical values.
As a first example, a digital spectra of three files, F1, F2, and F3 is given with respect to a common set of “N” symbols, e.g., symbols 1, symbol 2 and symbol 3. Each file is processed looking for the number of times each symbol is found in the file. The frequency of each symbol as it is found in each file is recorded along with a total number of symbols in each file. For this example, their respective spectra are:
Using a relevant pattern-derived statistic (possibly including S1, S2, S3, or S4 above), a vector of values is calculated for the N symbol definitions that may occur in each file. A position in N-dimensional space is determined using this vector, where the distance along each axis in N-space is determined by the statistic describing its corresponding symbol.
Specifically in this example, we will use statistic S1 (FREQ) and we have three (3) common symbols that we are using to compare these files and so a 3-dimensional space is determined. Each file is then defined as a position in this 3-dimensional space using a vector of magnitude 3 for each file. The first value in each vector is the frequency of symbol 1 in that file, the second value is the frequency of symbol 2, and the third value is the frequency of symbol 3.
With reference to
A matrix is created with the statistic chosen to represent each file. A matrix using the symbol frequency as the statistic looks like the following:
Using Pythagorean arithmetic, the distance (D) between the positions of any two files (Fx, Fy) is calculated as
In the example above, the distance between the position of F1 and F2 is
Similarly, the distance between F1 and F3 is found by
A matrix of distances between all possible files is built. In the above example this matrix would look like this:
It can be seen graphically in
Each row of the matrix is then sorted, such that the lowest distance value is on the left, and the highest value is on the right. During the sort process, care is taken to keep the File ID associated with each value. The intent is to determine an ordered distance list with each file as a reference. The above matrix would sort to this:
Using this sorted matrix, the same conclusions that were previously reached by visual examination can now be determined mathematically. Exclude column 1, wherein it is obvious that the closest file to a given file is itself (or a distance value of 0.00). Column 2 now shows that the closest neighbor to F1 is F2, the closest neighbor to F2 is F1, and the closest neighbor the F3 is F1.
Of course, this concept can be expanded to hundreds, thousands, or millions or more of files and hundreds, thousands, or millions or more of symbols. While the matrices and vectors are larger and might take more time to process, the math and basic algorithms are the same. For example, consider a situation in which there exist 10,000 files and 2,000 symbols.
Each file would have a vector of length 2000. The statistic chosen to represent the value of each symbol definition with respect to each file is calculated and placed in the vector representing that file. An information position in 2000-space (N-2000) is determined by using the value in each vector position to represent the penetration along the axis of each of the 2000 dimensions. This procedure is done for each file in the analysis. With the statistic value matrix created, the distances between each file position are calculated using the above distance formula. A matrix that has 10,000 by 10,000 cells is created, for the 10,000 files under examination. The content of each cell is the calculated distance between the two files identified by the row and column of the matrix. The initial distance matrix would be 10,000×10,000 with the diagonal values all being 0. The sorted matrix would also be 10,000 by 10,000 with the first column being all zeros.
In a smaller example, say ten files, the foregoing can be much more easily demonstrated using actual tables represented as text tables in this document. An initial matrix containing the distance information of ten files might look like this.
The distances in each row are then sorted such that an ordered list of distances, relative to each file, is obtained. The file identity relation associated with each distance is preserved during the sort. The resulting matrix now looks like this:
Using the information in columns 1 and 2 a relationship graph can be created of closest neighbor files. From the above matrix, skilled artisans will note the following:
F1's nearest neighbor is F3. Create a group, G1, assign these two files to that group.
F2's nearest neighbor is F8. Create a group, G2, assign these two files to that group.
F3 has already been assigned, its nearest neighbor is F1, and they belong to group G1.
F4's nearest neighbor is F2, which already belongs to G2. Assign F4 to G2 as well.
F5's nearest neighbor is F1, which already belongs to G1. Assign F5 to G1 as well.
F6's nearest neighbor is F8, which already belongs to G2. Assign F6 to G2 as well.
F7's nearest neighbor is F2, which already belongs to G2. Assign F7 to G2 also.
F8's has already been assigned, It's nearest neighbor is F2, and they belong to G2.
F9's nearest neighbor is F8, which already belongs to G2. Assign F9 to G2 also.
F10's nearest neighbor is F8 which already belongs to G2. Assign F10 to G2 also.
The above “nearest neighbor” logic leads to the conclusion that two groups (G1 and G2) of files exist. Group G1 contains F1, F3, F5, while Group G2 contains F2, F4, F6, F7, F8, F9, and F10.
An algorithm for determining groups based on adjacent neighbors is given in
With reference to
In order to find relationships or groupings of files in alternate embodiments of the invention, the following proposes an embodiment of relevancy groups for arbitrary sets of data files having rightly sized and rightly numbered files. In turn, underlying data of the files is partitioned into meaningful groups without any prior classification schemes or metadata analysis. There is no defining a number of groups before grouping begins and criteria for ascertaining functions for stopping grouping is revealed.
With reference to
Generically, skilled artisans create these matrixes as array “distances” that are N×N in an (N) multi-dimensional space. Each Rowi in the table represents file Fi, each Colk in the table represents file Fk, and cell at Rowi and Colk in represents the distance from Fi to Fk. The values in the matrix are generically floating point values, depending on the algorithm used to generate the vectors in the N-dimensional symbol universe. Sometimes they range from 0.0 to 1.0 inclusive, or sometimes they range from 1.0 to some MAX value. Either embodiment is acceptable for use with the following grouping algorithm.
The “sorted” array is also N×N where each row is sorted from the closest file (itself) to its furthest neighbor. In this case, each Rowi in the table still represents Fi, but each Colk now represents the Kth closest file and thus each cell at Rowi and Colk has a value J that represents Fi. This means that the value J is in the cell at Rowi and Colk then Fj is the Kth closest file to Fi.
Hereafter, the minimum and maximum distances between any two files in the “distances” matrix are calculated. In the ongoing example of
Next, a stepping mechanism is created that moves a tolerance value in rounds between the min and max values in some regular fashion. In one embodiment, this could be a linear progress with (step+1) iterations using a formula like (min+((max−min)/round)*(round−1)) for each round in step+1 rounds. Alternatively, this could be a log or exponential type function that moves much more slowly for “close” values and much more quickly for large values. The latter type of progress is much more useful in N-dimensional symbol universes where some nodes are very far away from a cluster of nodes that are close together. Whatever the stepping function, the tolerance value grows.
A tolerance is calculated (increasing with each round) and a group of members (e.g., files) is determined for each row in the “Distances” matrix 450. Only those files that are closer than or equal to the tolerance value are included in that relevancy group for that file for that round. For example, consider Row 1 for file F1 in the Distances matrix 450 which has ten steps of movement through the minimum and maximum values (from 0.0 to 70.0) with the tolerance value growing in linear fashion starting at 0.0 and moving to 70.0 by a tolerance of 7.0 at each step for 11 (steps+1) rounds. The result is seen in
Other rows would follow similar patterns. For any row, skilled artisans should observe that a relevancy group grows in members as the tolerances (grow larger as it approaches the MAX value. At each round, any groups that are subsets of any other groups are deleted since they add no more information to the set of relevancy groups. Also, at round 1 there are one-hundred separate groups with each file being in its own dedicated group (or one member per one group). This is expected since the tolerance is 0.0 and the group does not include any other files other than the file itself since no other files are “closer” than the file itself. Unfortunately, this set of one-hundred groups with one file is not interesting from a “relevancy groups” point of view since the number of relevancy groups is the same as the number of individual files. The inventors refer to this situation as “isolation” and it represents one end of the spectrum defining relevancy groups, e.g., one file per group and the number of groups equals the original number of files, in this case 100.
In the middle of grouping, at Roundx there are some number of groups such that the number of groups is more than one, but less than the total possible numbers of groups, or, 1<=NumberGroups(Roundx)<=100.
In the last round, round 11 or round (steps+1), there is only one group remaining and it includes all files as members. This is due to the fact that the tolerance has now reached the maximum value of any distance in the Distances matrix. So, all files are within that closeness to any other file and each group for each row now includes all files such that every group for every row is a subset of each other and they all contain all files. Thus, at round 1, there were 100 groups, each with one member. At the last round, round 11, there is only 1 group with 100 files in the group. The inventors call the latter “chaos” or “total integration” and it is at the other end of the spectrum defining relevancy groups. It is opposite the spectrum where “isolation” occurs. Also, this single group of 100 files is also not interesting from a “relevancy groups” point of view since all files are integrated into a chaotic mess of only one relevancy group.
As a result, the inventors have valuably identified a situation as to when the tolerance should stop growing and at which round the grouping should stop so that the resultant relevancy group is rightly sized with the right number of groups. The inventors seek to avoid isolation (or limited grouping) or total integration (or chaos) since neither of these extremes provides optimization. To answer the question of when a correct number of groups occur, the inventors have experimented with various types of actual files and data sets. To date, these include: 100 fairly random text, PDF, MS Office, and Open Office documents; 250 fairly random ASCII short stories; 65 JPG files (with various levels of compression and color); 75 audio files; and various patent files.
Hereafter, the embodiments of the invention identify at least three situations in which a stopping function is optimized for stopping the adding of members to a relevancy group. With reference to
With reference to graph 510,
All of these plots 512, 514, 516, 518, and 520 were obtained from real data sets (101 files with different symbol counting algorithms) and they show the number of groups at each round for 100 rounds. From the beginning, the plots have 101 groups, while at the end they have but one group. In between, the plots reveal different information. In any situation, however, the generic response is to determine the numbers of groups per round, step 530,
In the example of the plotted curve 512,
In a second approach to applying a stopping, function, stopping can occur at a time when there is no overlapping,
Instead of having these overlapping groups,
{1, 2, 3}
{1, 2, 3, 4}
{4, 5}
{6, 7, 8}
{8, 9}
a re-defining of the groups reveals
{1, 2, 3, 4, 5}
{6, 7, 8, 9}
In this case, the number of groups reduces much more quickly than in case 1 above and so it is impractical to use a metric like a 10% decrease in a steep “Reverse S” curve or a 10% increase in “local minimum” curves. The stopping point for this type of grouping algorithm, then, would be based on a much larger percent. It is recommended that stopping occur at the round where only ⅓ (33%) of the original number of groups is obtained. These groups are often more broad and not tightly clustered groups, but the inventors have found that they are good groups for making a first level segmentation decision. More fine-grained group divisions could then be done amongst each 1st level group, e.g., taking another third of the first third, and so on.
In a third approach to stopping, a function examines the size of each group and “dismisses a group” when it becomes fairly meaningless. Representatively,
Among certain advantages of the foregoing stopping approaches is that a right number and right sized relevancy group for an arbitrary set of data files is readily determined. These relevancy groups are then used to partition the data into meaningful groups without any prior classification or metadata analysis. This also occurs according to the following: without any pre-defined or pre-declared conditions about the number or size of the groups; by organizing relevance groups into human understandable relevance relationships without any human intervention; and by optimally combining related files into relevance groups up to a point but not passing the point where the relevance groups become too broad to be useful.
In still other embodiments, pluralities of files grouped together into relevancy groups may have overlapping members which causes some ambiguity. In these cases, these overlapping relevancy groups may be further differentiated from one another into more clearly defined relevancy groups. For example, consider the following set S of four (4) groups where there are overlapping members in the groups:
S={A, B, C, D} where
In this example, member 1 is in groups A, C, and D; member 2 is in groups A, B, and C; member 3 is in groups A and B; and member 4 is only in group D. The question arises around the best partition of S into new relevancy groups that show some aggregation into the strongest possible groups with the least amount of overlap within those groups. The problem in doing that is evident in this example. Specifically, member 4 seems to be related to member 1 because of D. However, member 1 also seems to be related to member 2 because of groups A and C. Of note is that the relationship of member 1 to member 4 seems weaker than the relationship of member 1 to member 2 because the declaration that member 1 is related to member 4 occurs only once (in group D) while the declaration that member 1 is related to member 2 occurs twice (in groups A and C). The question that the inventors were faced with in experimental data similar to this example was how to improve the relevancy groups while considering the notion that some members might be more strongly related to each other than to other members. Specifically in this example, member 1 might have a stronger relevancy bonding with member 2 than it does with member 4. In addition to and simultaneously with that information, the inventors were also faced with the strong or weak relevancy bonding relationships of member 1 with member 3, member 3 with member 2, member 3 with member 4, and so on. It became clear that all of the information declared in the set S must be considered and used to define a partition of S into new relevancy groups that shows the strongest possible relevancy grouping strength with the least amount of overlap. In this example, if members 1 and 2 and 4 were placed in the same relevancy group would that be stronger or weaker (given only the data defined in set S) than if member 4 were not placed in the same relevancy group as members 1 and 2. Even more to the point, would a partition of S into [{1, 2, 3}, {1, 4}] be stronger than a partition of S into [{1, 2, 3, 4}].
This invention teaches a new method for using only information in the set S of overlapping groups to define a new partition of that set into the strongest possible relevancy groups with the least amount of overlap among members of those groups. This is achieved using only the relevancy information contained in that original set—using no other a priori external information or any other pre-determined or semantic information about that set. This method can thus be used across any data set regardless of semantic content or domain of interest specific knowledge.
First we define the new method in general terms and then we will move back to our specific earlier example to show the application of the new method on that set. The new method finds an optimized partition of any set S of N overlapping groups that yields the maximum strength for relevancy groups and members in that partition. Using semi-formal notation: the best partition P of S has strength T where T=SP(P) and T is greater than all other T′ where T′=SP(P′) and P′ is some other partition of S. Alternatively stated, there should be a partition P of S into groups such that Order(P)=J; 1<=J<=N; and SP(P) is the maximum of all other SP(P′) for all other partitions P′ of S. SP(P) is defined as function to determine the “strength of a partition.” Thus, for all partitions P1, P2, . . . , Pp of S, and where SP(P) is defined as “strength of partition P” the optimal partition Pi is the one where SP(Pi) yields the largest value. This invention teaches a method where SP(Pi) yields a value 0.0 to 1.0 (where 1.0 is the strongest). SP(P) is defined using a summation of all weighted SGS(GS) for each set of groups in the partition. SGS(GS) is defined as the “strength of a set of groups” and GS is that set of groups. SGS(GS) is defined using a summation of all weighted SM(M) for all members in the set of groups. SM(M) is defined as the “strength of a member” and M is that member. Said another way, SP(P) is the strongest when it defines a partition P that has the strongest set of groups where each group claims membership of the strongest set of members.
The weighting factors affect the strength of a value by considering the context of that value. As such, we define all of our computational elements as:
Using semi formal mathematical notation, the strength T=SP(P) of a partition P is given as:
SP(Partition)=Σ SGS(GSi)*WGS(GSi), for all groups GSi in the partition and where SGS(GS)=Σ SM(Mj)*WM(Mj), for all members Mj in the groups and where SM(Member)=(Number of total groups having that member)/(total numbers of groups); and where WGS(GS) is the relative strength of this set of groups compared with the total number of original groups and WM(M) is the relative strength of this member compared with the total number of members in all the groups of this set of groups. Specifically WGS(GS)=this number of groups/number of all original groups and WM(M)=(1.0)/(total number of members in this set of groups).
The following is a pseudo-code representation of the method
Applying the foregoing, we revisit our example Set S, where S={A, B, C, D} and where
and the desired outcome is the best (strongest) partitioning of S. First we consider what are all possible partitions of set S. To do this we apply well know algorithms in the area of permutations and combinations yielding all possible partitions of S. In this example, the possible partitions of S are:
. . . , and so on.
Of the foregoing, skilled artisans should observe that many of these partitions are identical (e.g., 7=12=17=22 and 16=24). In turn, only one partition out of an equivalent set of identical partitions need be processed since the strength of identical partitions will be identical.
In applying the weighting, we will consider just two partitions and compare strength for each and then compare the two strengths to determine which of the two partitions is the strongest. Let the first partition be P1 which only has one set of groups:
A: {1, 2, 3}
B: {2, 3}
C: {1, 2}
D: {1, 4}
This partition can be represented using our shorter notation above as Partition 1: {A, B, C, D}.
Let the second partition be P2 which has two sets of groups:
A: {1, 2, 3}
B: {2, 3}
C: {1, 2,}
D: {1, 4}
which, in our shorter notation above, is Partition 18: {A, B, C}, {D}.
In examining the strength of the first partition, P1, there are four (4) total groups. There are three (3) instances of file 1 in the four total groups, three (3) instances of file 2 in the four total groups, two (2) instances of file 3 in the four total groups, and one (1) single instance of file 4 in the four total groups. Also, there are four (4) total members in the four total groups. Namely, files 1, 2, 3, and 4 are the members spread over the many groups.
Applying these facts to the foregoing equations, WM(1)=WM(2)=WM(3)=WM(4)=1.0/4. Since member or file 1 appears in three (3) groups, the strength of file 1, SM(1) becomes three out of four, or SM(1)=3/4. Similarly, SM(2)=3/4, SM(3)=2/4, and SM(4)=1/4. Summing these together, as weighted by WM, we get: (3/4*1/4)+(3/4*1/4)+(2/4*1/4)+(1/4*1/4)=0.56=SGS(Groups 1). WGS(Groups 1)=4.0/4 since there are 4 groups in Groups 1 and there are 4 original groups. The ultimate strength of the partition for P1 is SP(P1)=0.56*4/4=0.56.
Conversely, consider the strength of the second partition P2. For the first major subgroup (Groups 1) there are three total members, so WM(1)=WM(2)=WM(3)=1.0/3. For the second major subgroup (Groups 2) there are two total members, so WM(1)=SM(4)=1.0/2. The strength of the individual files in Groups 1 is SM(1)=2/3, SM(2)=3/3, and SM(3)=2/3, while the strength of the individual files in Groups 2 is SM(1)=1/1 and SM(4)=1/1. Summing these together per their individual subgroups, we get (2/3*1/3)+(3/3*1/3)+(2/3*1/3)=0.78 and (1/1*1/2)+(1/1*1/2)=1.00. Bringing the two major groups together, and weighting them for the entire partition (e.g., WGS(Groups 1) is three groups out of four total groups in the entire partition (or ¾), and WGS(Groups 2) is one group out of four total groups in the entire partition (or ¼)), we get the strength of the partition P2 as: SP(P2)=(0.78*3/4)+(1.0*1/4)=0.83. Since 0.83 for partition P2 is closer to 1.0 than 0.56 is for partition P1, partition P2 is the strongest partition for set S. The same approach for all possible partitions would occur to reveal the strongest possible partition for the set.
The following is a more concise summary of the computations involved in this example of S and two partitions of P1 and P2 and determining which partition is the strongest:
P1:
P2:
Among certain advantages, skilled artisans should now appreciate that the foregoing provides: 1) an optimal partitioning of “fuzzy” overlapping relevance groups into clearly distinguishable, minimally overlapping relevance groups; 2) identifiable bridging information that causes the overlap which is helpful in determining the semantic information that can be associated with the new clearly distinguishable groups; 3) fuzzy logic weighting factors that beget crisp and distinct membership information; and 4) new partitions that generate new insights, observations, and cognitions that were not perceivable in the original overlapping groups due to the obfuscation inherent in the fuzziness.
The inventors ran many samples using the JAVA code appended in the code Exhibit. Examples t1-t8 below are a few of the results. In all, the inputs (.in) are groups of files that resulted in the partitioning of two optimal subgroups (.out). However, the algorithm works for breaking the possible output partitions into any number N groups where there are enough members to support N groups.
- - -
t1.in
- - -
1, 2, 3
1, 2
2, 3
1, 4
- - -
t1.out
- - -
1, 4
1, 2, 3
- - -
- - -
t2.in
- - -
20, 29, 30, 35
20, 21, 24, 25, 33, 34
20, 31, 32, 33, 35
20, 25, 29, 30, 31, 33, 34
21, 24, 25, 34
29, 30, 31, 35
20, 25, 21, 33, 34
31, 32
19, 21, 24, 25
19, 27, 28, 34
19, 21, 27, 28
- - -
t2.out
- - -
20, 25, 29, 30, 31, 32, 33, 34, 35
19, 20, 21, 24, 25, 27, 28, 33, 34
- - -
- - -
t3.in
- - -
1, 2, 3
2, 3
1, 2
4, 5, 6
4, 5
5, 6
- - -
t3.out
- - -
1, 2, 3
4, 5, 6
- - -
- - -
t5.in
- - -
1, 2
3, 4
- - -
t5.out
- - -
1, 2
3, 4
- - -
- - -
t6.in
- - -
13, 16, 17, 18, 19
13, 15, 17, 18, 19
15, 16, 17, 18, 19
13, 15, 16, 18, 19
13, 14, 16, 18, 19
- - -
t6.out
- - -
13, 14, 16, 18, 19
13, 15, 16, 17, 18, 19
- - -
- - -
t7.in
- - -
48, 54, 59, 66, 89
22, 37, 63, 66, 88
37, 63, 66, 79, 88
54, 59, 70, 87, 89
43, 45, 53, 68, 89
44, 56, 59, 86, 89
54, 59, 68, 70, 89
48, 54, 59, 70, 89
20, 54, 59, 70, 89
54, 61, 68, 70, 89
- - -
t7.out
- - -
22, 37, 43, 44, 45, 53, 56, 59, 63, 66, 68, 79, 86, 88, 89
20, 48, 54, 59, 61, 66, 68, 70, 87, 89
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- - -
t8.in
- - -
1, 4, 5, 6, 35
1, 4, 5, 35, 36
1, 2, 4, 5, 80
1, 5, 25, 34, 36
25, 34, 35, 36, 60
- - -
t8.out
- - -
1, 2, 4, 5, 6, 35, 80
1, 4, 5, 25, 34, 35, 36, 60
- - -
Upon inspection, skilled artisans should see that examples t7 and t8 show a separation into the two largest groups with non-overlapping nodes with the smallest bridge group. This allows users to see at what point the fuzzy overlapping groups overlap the most and at what point the overlap the least.
For instance, example t8 reveals:
Largest Non Overlapping Group 1: 2, 6, 80 (e.g., the group 1, 2, 4, 5, 6, 35, 80 absent the bridge group);
Largest Non Overlapping Group 2: 25, 34, 36, 60 (e.g., the group 1, 4, 5, 25, 34, 35, 36, 60 absent the bridge group); and
From venn diagramming, the smallest bridge group in both Group 1 (1, 2, 4, 5, 6, 35, 80) and Group 2 (1, 4, 5, 25, 34, 35, 36, 60) is the “Smallest Bridge Group: 1, 4, 5, 35.” However, if the bridge group is made a group separate from either groups 1 and 2, the “bridge” can be more readily identified. Said in more mathematical language:
Let G1′ be all members in G1 and not in G2;
Let G2′ be all members in G2 and not in G1; and
Let B be all members in G1 and in G2.
In turn, G1′ and G2′ are no longer overlapping at all and B shows why G1 and G2 were overlapping in the first place. Again, this can be expanded to 3, 4, . . . , N groups. The inventors have also proved this with jpeg photographs and other files as seen in their provisional application U.S. Ser. No. 61/271,079, filed Jul. 16, 2009, incorporated herein by reference in its entirety.
Still further advantages of the partitioning techniques include: defining the strongest possible membership assignments possible given the input, overlapping groups; defining the smallest number of groups while still allowing members to be in more than one group (not forcing mutually exclusive groups)—the natural and social worlds we live in have naturally occurring fuzzy overlapping groups and even though many of those are optimized they stay a bit fuzzy (consider the problem of where to classify and place items in a hardware or grocery store, the ever changing 6 Kingdom or 3 Domain Scientific Classification taxonomies, social and cultural groups that we humans belong to, etc); making observable, new, clear, and distinct groups from less distinct and less clear fuzzy overlapping groups; and a specific algorithm for determining the weight of each member in the fuzzy overlapping groups and the number of fuzzy overlapping groups to determine a strength for every possible new partition of groups created from the members of the fuzzy overlapping groups in order to mathematically (objectively) determine the optimal set of groups (partitioning of the original groups).
The foregoing has been described in terms of specific embodiments, but one of ordinary skill in the art will recognize that additional embodiments are possible without departing from its teachings. This detailed description, therefore, and particularly the specific details of the exemplary embodiments disclosed, is given primarily for clarity of understanding, and no unnecessary limitations are to be implied, for modifications will become evident to those skilled in the art upon reading this disclosure and may be made without departing from the spirit or scope of the invention. Relatively apparent modifications, of course, include combining the various features of one or more figures with the features of one or more of the other figures.
This utility application claims priority to U.S. Provisional Application Ser. Nos. 61/236,571 and 61/271,079, filed Aug. 25, 2009, and Jul. 16, 2009, respectively. Their contents are expressly incorporated herein as if set forth herein.
| Number | Date | Country | |
|---|---|---|---|
| 61236571 | Aug 2009 | US | |
| 61271079 | Jul 2009 | US |
