Patent Application
20160275169
1. Field of the Invention
The present invention relates generally to data mining and more particularly to a system to generate initial cluster centroids.
2. Description of the Related Art
Clustering is an important area of application for a wide range of fields such as data mining, statistical data analysis, compression, and vector quantization. A k-means clustering algorithm is the most popular partition based, iterative algorithm for clustering analysis. These iterative techniques are especially sensitive to initial starting conditions. Therefore, the result of running the k-means clustering algorithm on the same workload varies depending on the chosen initial starting points.
According to one aspect of the disclosure, a method of generating initial cluster centroids using a processor, comprises the steps of: using the processor, generating (Key1, Value1) pairs of input datasets; using the processor, calculating global designated values, among the generated (Key1, Value1) pairs, to be reference values; using the processor, calculating similarity values of the input datasets based on the reference values; and using the processor, generating median similarity values based on the similarity values of the input datasets to generate corresponding initial cluster centroids; wherein the Key1 and the Value1 are a feature variable and a feature value, respectively, of corresponding input dataset; the processor runs the steps of generating (Key1, Value1) pairs, the steps of calculating global designated values, the steps of calculating similarity values and the steps of generating median similarity values by executing a set of instructions storing in a machine readable storage medium.
According to another aspect of the disclosure, a computer program product tangibly is embodied in a machine readable storage medium comprising instructions that when executed by a processor perform a method for generating initial cluster centroids. The method comprises the steps of: calculating global designated values, among a plurality of input datasets, to be reference values; calculating similarity values of the plurality of input datasets based on the reference values; and generating median similarity values based on the similarity values of the plurality of input datasets to generate corresponding initial cluster centroids.
According to another aspect of the disclosure, a computer system comprises: a processor; and a computer-readable storage medium having stored therein instructions that when executed by the processor perform a method for generating initial cluster centroids. The method performed by the processor comprises: generating (Key1, Value1) pairs of input datasets; calculating global designated values, among the generated (Key1, Value1) pairs, to be reference values; calculating similarity values of the input datasets based on the reference values; generating (Key2, Value2) pairs of input datasets; and generating median similarity value, among the generated (Key2, Value2) pairs, to generate corresponding initial cluster centroids, wherein the Key1 and the Value1 are a feature variable and a feature value, respectively, of corresponding input dataset; the Key2 and the Value2 are the similarity value and the feature value, respectively, of corresponding input dataset.
One or more embodiments are illustrated by way of example, and not by limitation, in the figures of the accompanying drawing, wherein elements having the same reference numeral designations represent like elements throughout. It is emphasized that, in accordance with standard practice in the industry various features may not be drawn to scale and are used for illustration purposes only. For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawing, in which:
The making and using of the presently preferred embodiments are discussed in detail below. It should be appreciated, however, that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the invention, and do not limit the scope of the invention.
In operation 210, reference values of input datasets are generated. In some embodiments, global minimum values of the plurality of input datasets are generated to be reference values. In some embodiments, global maximum values of the plurality of input datasets are generated to be reference values. A flowchart 300 in
In operation 220, similarity values of input datasets are calculated. To calculate the similarity values of input datasets, any logical and/or arithmetic operations, or any algorithms, or any distance formulas are within the scope of various embodiments. A flowchart 400 in
In operation 230, initial cluster centroids of input datasets are generated based on the calculated similarity values for each of clusters. A flowchart 500 in
In operation 310, input datasets are divided into a plurality of input splits. The number of input splits is chosen based on cost and performance consideration. For simplicity, three input splits are selected for illustration purpose in
In operation 320, the corresponding (Key1, Value1) pairs are generated for input datasets inputted to each of the plurality of input splits. In some embodiments, (Key1, Value1) pairs are generated for each of the instances of corresponding input split. The “Key1” of the (Key1, Value1) pair is a feature variable of corresponding input dataset. The “Value1” of the (Key1, Value1) pair is a feature value of corresponding input dataset. In some embodiments, (Key1, Value1) pairs are generated in map stage of the MapReduce processes.
For example, the generated (Key1, Value1) pairs in the input split1 regarding the input datasets 100 in
The generated (Key1, Value1) pairs in the input split2 regarding the input datasets 100 in
The generated (Key1, Value1) pairs in the input split3 regarding the input datasets 100 in
In operation 330, local designated values for each of feature variables in each of the plurality of input splits are calculated. In some embodiments, the local designated values are minimum values of feature values of corresponding feature variables in each of the plurality of input splits. In some embodiments, the local designated values are maximum values of feature values of corresponding feature variables in each of the plurality of input splits. In some embodiments, the local designated value is a result of logical and/or arithmetic operations that takes feature values of corresponding feature variables into consideration. The logical operations include AND, NAND, OR, NOR, NOT, SHIFT, exclusive OR, exclusive NOR, etc. The arithmetic operations include addition, subtraction, multiplication, division, remainder, etc. In some embodiments, the local designated values are calculated in combine stage of the MapReduce processes.
For simplicity, minimum values of feature values of corresponding feature variables are selected to be the local designated values in
The local designated values of the input split2 for each of feature variables are (VAR1, XIS2min1), (VAR2, XIS2min2), (VAR3, XIS2min3) and (VAR4, XIS2min4). The XIS2min1 is a minimum value among feature values X4,1, X5,1, and X6,1 in the input split2. The XIS2min2 is a minimum value among feature values X4,2, X5,2, and X6,2 in the input split2. The XIS2min3 is a minimum value among feature values X4,3, X5,3, and X6,3 in the input split2. The XIS2min4 is a minimum value among feature values X4,4, X5,4, and X6,4 in the input split2.
The local designated values of the input split3 for each of feature variables are (VAR1, XIS3min1), (VAR2, XIS3min2), (VAR3, XIS3min3) and (VAR4, XIS3min4). The XIS3min1 is a minimum value among feature values X7,1, X8,1, and X9,1 in the input split3. The XIS3min2 is a minimum value among feature values X7,2, X8,2, and X9,2 in the input split3. The XIS3min3 is a minimum value among feature values X7,3, X8,3, and X9,3 in the input split3. The XIS3min4 is a minimum value among feature values X7,4, X8,4, and X9,4 in the input split3.
In operation 340, global designated values are calculated to be reference values in all of the plurality of input splits. In some embodiments, the global designated values are minimum values of feature values of corresponding feature variables in all of the plurality of input splits. In some embodiments, the global designated values are maximum values of feature values of corresponding feature variables in all of the plurality of input splits. In some embodiments, the global designated value is a result of logical and/or arithmetic operations that takes feature values of corresponding feature variables into consideration. The logical operations include AND, NAND, OR, NOR, NOT, SHIFT, exclusive OR, exclusive NOR, etc. The arithmetic operations include addition, subtraction, multiplication, division, remainder, etc. In some embodiments, the global designated values are calculated in reduce stage of the MapReduce processes.
For example, the global designated values of all of the plurality of input splits are (VAR1, Xmin1), (VAR2, Xmin2), (VAR3, Xmin3) and (VAR4, Xmin4). The Xmin1 is a minimum value among the local designated values XIS1min1, XIS2min1, and XIS3min1. The Xmin2 is a minimum value among the local designated values XIS1min2, XIS2min2 and XIS3min2 The Xmin3 is a minimum value among the local designated values XIS1min3, XIS2min3 and XIS3min3. The Xmin4 is a minimum value among the local designated values XIS1min4, XIS2min4 and XIS3min4.
In operation 410, input datasets are divided into a plurality of input splits. For simplicity, three input splits are selected for illustration purpose in
In operation 420, similarity values for input datasets inputted to each of the plurality of input splits are calculated based on corresponding reference values calculated in the flowchart 300 in
For example, the similarity value IS1S1 for instance1 in input split1 is calculated based on an equation (1).
IS
1
S
1=(X1,1−Xmin1)2+(X1,2−Xmin2)2+(X1,3−Xmin3)2+(X1,4−Xmin4)2 (1)
The similarity value IS1S2 for instance2 in input split1 is calculated based on an equation (2).
IS
1
S
2=(X2,1−Xmin1)2+(X2,2−Xmin2)2+(X2,3−Xmin3)2+(X2,4−Xmin4)2 (2)
The similarity value IS1S3 for instance3 in input split1 is calculated based on an equation (3).
IS
1
S
3=(X3,1−Xmin1)2+(X3,2−Xmin2)2+(X3,3−Xmin3)2+(X3,4−Xmin4)2 (3)
The similarity value IS2S4 for instance4 in input split2 is calculated based on an equation (4).
IS
2
S
4=(X4,1−Xmin1)2+(X4,2−Xmin2)2+(X4,3−Xmin3)2+(X4,4−Xmin4)2 (4)
The similarity value IS2S5 for instance5 in input split2 is calculated based on an equation (5).
IS
2
S
5=(X5,1−Xmin1)2+(X5,2−Xmin2)2+(X5,3−Xmin3)2+(X5,4−Xmin4)2 (5)
The similarity value IS2S6 for instance6 in input split2 is calculated based on an equation (6).
IS
2
S
6=(X6,1−Xmin1)2+(X6,2−Xmin2)2+(X6,3−Xmin3)2+(X6,4−Xmin4)2 (6)
The similarity value IS3S7 for instance7 in input split3 is calculated based on an equation (7).
IS
3
S
7=(X7,1−Xmin1)2+(X7,2−Xmin2)2+(X7,3−Xmin3)2+(X7,4−Xmin4)2 (7)
The similarity value IS3S8 for instance5 in input split3 is calculated based on an equation (8).
IS
3
S
8=(X8,1−Xmin1)2+(X8,2−Xmin2)2+(X8,3−Xmin3)2+(X8,4−Xmin4)2 (8)
The similarity value IS3S9 for instance9 in input split3 is calculated based on an equation (9).
IS
3
S
9=(X9,1−Xmin1)2+(X9,2−Xmin2)2+(X9,3−Xmin3)2+(X9,4−Xmin4)2 (9)
In operation 430, (Key2, Value2) pairs for each of the instances of the plurality of input splits are generated. The Key2 values are respective similarity value of corresponding instance calculated by the equations (1)-(9). The Value2 values are feature values of corresponding instance in
For example, the (Key2, Value2) pairs for instance1 is (IS1S1, {X1,1, X1,2, X1,3, X1,4}). The (Key2, Value2) pairs for instance2 is (IS1S2, {X2,1, X2,2, X2,3, X2,4}). The (Key2, Value2) pairs for instance3 is (IS1S3, {X3,1, X3,2, X3,3, X3,4}). The (Key2, Value2) pairs for instance4 is (IS2S4, {X4,1, X4,2, X4,3, X4,4}). The (Key2, Value2) pairs for instance5 is (IS2S5, {X5,1, X5,2, X5,3, X5,4}). The (Key2, Value2) pairs for instance6 is (IS2S6, {X6,1, X6,2, X6,3, X6,4}). The (Key2, Value2) pairs for instance7 is (IS3S7, {X7,1, X7,2, X7,3, X7,4}). The (Key2, Value2) pairs for instance8 is (IS3S8, {X8,1, X8,2, X8,3, X8,4}). The (Key2, Value2) pairs for instance9 is (IS3S9, {X9,1, X9,2, X9,3, X9,4}).
In operation 440, (Key2, Value2) pairs of all of the instances are sorted based on respective “Key2” value. In some embodiments, the (Key2, Value2) pairs are sorted in shuffle/sort stage of the MapReduce processes.
In some embodiments, the similarity values IS1S1-IS3S9 are sorted in increasing order. In some embodiments, the similarity values IS1S1-IS3S9 are sorted in decreasing order. In some embodiments, the similarity values IS1S1-IS3S9 are sorted in a specific order based on results of arithmetic/logical operations. In
In operation 510, (Key2, Value2) pairs are further divided into N groups for N corresponding clusters. In k-means clustering algorithm, the input datasets are used to divide into N clusters. As a result, there are N initial cluster centroids that are generated for the corresponding N clusters. In such a situation, (Key2, Value2) pairs of all of the instances are arranged to divide into N groups for the corresponding N clusters. It is understood that any operations, such as arithmetic and/or logical operations, may be used to divide the (Key2, Value2) pairs into N groups, and are within the scope of various embodiments. In some embodiments, the (Key2, Value2) pairs are arranged to divide into N groups in map stage of the MapReduce processes.
For example, the (Key2, Value2) pairs of the instances in
In operation 520, (Key3, Value3) pairs for corresponding (Key2, Value2) pairs in each of N groups are generated. The Key3 values are ID symbols to specify characteristics of corresponding (Key2, Value2) pairs. In some embodiments, the ID symbols represent specific operations in future processes. In some embodiments, the ID symbols is arranged to specify specific reducers in map stage of the MapReduce process for the corresponding (Key2, Value2) pairs in each of N groups.
For example, an identical ID symbol “1” is specified for all of corresponding (Key2, Value2) pairs such that the (Key3, Value3) pairs for corresponding (Key2, Value2) pairs in the first group are (1, (IS1S1, {X1,1, X1,2, X1,3, X1,4})), (1, (IS1S2, {X2,1, X2,2, X2,3, X2,4})), (1, (IS1S3, {X3,1, X3,2, X3,3, X3,4})), (1, (IS2S4, {X4,1, X4,2, X4,3, X4,4})) and (1, (IS2S5, {X5,1, X5,2, X5,3, X5,4})). The (Key3, Value3) pairs for corresponding (Key2, Value2) pairs in the second group are (1, (IS2S6, {X6,1, X6,2, X6,3, X6,4})), (1, (IS3S7, {X7,1, X7,2, X7,3, X7,4})), (1, (IS3S8, {X8,1, X8,2, X8,3, X8,4})) and (1, (IS3S9, {X9,1, X9,2, X9,3, X9,4})).
In operation 530, median similarity value in each of N groups based on the corresponding similarity values in Value3 values of the (Key3, Value3) pairs are generated. In some embodiments, the median similarity values are determined in reduce stage of the MapReduce processes.
For example, the sequence of similarity values regarding corresponding (Key3, Value3) pairs in the first group is (IS1S1, IS1S2, IS1S3, IS2S4, IS2S5) such that the median similarity value in the first group is “IS1S3” as it is in the middle of the sequence. Furthermore, the sequence of the similarity values regarding corresponding (Key3, Value3) pairs in the second group is (IS2S6, IS3S7, IS3S8, IS3S9) such that median similarity value in the second group is calculated based on equation (10).
The median similarity value in the second group=(IS3S7+IS3S8)/2 (10)
In some embodiments, the median similarity values in the first and/or second groups are determined to be a specific similarity value near the middle of the sequence of similarity values in each of the first and/or second groups. For example, the median similarity values in the first group may be “IS1S2”, “IS1S3” or “IS2S4”. The median similarity values in the second group may be “IS3S7” or “IS3S8”.
In operation 540, initial cluster centroid in each of N groups are generated based on determined median similarity value. In some embodiments, the median similarity values are determined in reduce stage of the MapReduce processes.
For example, based on the determined median similarity value “IS1S3” in the first group, the initial cluster centroid is ({X3,1, X3,2/X3,3, X3,4}). For another example, based on the calculated median similarity value by equation (10) in the second group, the initial cluster centroid is generated based on equation (11).
The initial cluster centroid in the second group=({(X7,1+X8,1)/2,(X7,2+X8,2)/2,(X7,3+X8,3)/2.(X7,4+X8,4/2}) (11)
Processing system 600 includes a processor 602, which may include a central processing unit, input/output circuitry, signal processing circuitry, and volatile and/or non-volatile memory. Processor 602 receives input, such as user input, from input device 604. Input device may include one or more of a keyboard, a mouse, a tablet, a contact, sensitive surface, a stylus, a microphone, and the like.
Processor 602 may also receive input, such as models, tables, configurations, program codes, databases, and the like, from machine readable storage medium 608. Machine readable storage medium may be located locally to processor 602, or may be remote from processor 602, in which case communications between processor 602 and machine readable storage medium 608 occur over a network, such as a telephone network, the Internet, a local area network, wide area network, or the like.
Machine readable storage medium 608 may include one or more of a hard disk, magnetic storage, optical storage, non-volatile memory storage, and the like. Included in machine readable storage medium 608 may be database software for organizing data and instructions stored on machine readable storage medium 608. Processing system 600 may include output device 606, such as one or more of a display device, speaker, and the like for outputting information to a user.
In some embodiments, a method of generating initial cluster centroids using a processor includes generating (Key1, Value1) pairs of input datasets using the processor. The method also includes calculating global designated values, among the generated (Key1, Value1) pairs, to be reference values using the processor. The method also includes calculating similarity values of the input datasets based on the reference values using the processor. The method further includes generating median similarity values based on the similarity values of the input datasets to generate corresponding initial cluster centroids using the processor. The Key1 and the Value1 are a feature variable and a feature value, respectively, of corresponding input dataset. The processor runs the steps of generating (Key1, Value1) pairs, the steps of calculating global designated values, the steps of calculating similarity values and the steps of generating median similarity values by executing a set of instructions storing in a machine readable storage medium.
In some embodiments, a computer program product tangibly embodied in a machine readable storage medium and comprising instructions that when executed by a processor perform a method for generating initial cluster centroids. The method includes calculating global designated values, among a plurality of input datasets, to be reference values. The method also includes calculating similarity values of the plurality of input datasets based on the reference values. The method further includes generating median similarity values based on the similarity values of the plurality of input datasets to generate corresponding initial cluster centroids.
In some embodiments, a computer system includes a processor and a computer-readable storage medium. The computer-readable storage medium has stored therein instructions that when executed by the processor perform a method for generating initial cluster centroids. The method includes generating (Key1, Value1) pairs of input datasets. The method also includes calculating global designated values, among the generated (Key1, Value1) pairs, to be reference values. The method also includes calculating similarity values of the input datasets based on the reference values. The method further includes generating (Key2, Value2) pairs of input datasets. The method further includes generating median similarity value, among the generated (Key2, Value2) pairs, to generate corresponding initial cluster centroids. The Key1 and the Value1 are a feature variable and a feature value, respectively, of corresponding input dataset. The Key2 and the Value2 are the similarity value and the feature value, respectively, of corresponding input dataset.
The sequences of the operations in the flowcharts 200-500 are used for illustration purpose. Moreover, the sequences of the operations in the flowcharts 200-500 can be changed. Some operations in the flowcharts 200-500 can be skipped, and/or other operations can be added without limiting the scope of claims appended herewith.
While the disclosure has been described by way of examples and in terms of disclosed embodiments, the invention is not limited to the examples and disclosed embodiments. To the contrary, various modifications and similar arrangements are covered as would be apparent to those of ordinary skill in the art. Therefore, the scope of the appended claims should be accorded the broadest interpretation so as to encompass such modifications and arrangements.
