Claims
- 1. A system for organizing multi-dimensional pattern data into a reduced-dimension representation comprising:
a neural network comprised of a plurality of layers of nodes, the plurality of layers including:
an input layer comprised of a plurality of input nodes, a hidden layer, and an output layer comprised of a plurality of non-linear output nodes, wherein the number of non-linear output nodes is less than the number of input nodes; receiving means for receiving multi-dimensional pattern data into the input layer of the neural network; output means for generating an output signal for each of the output nodes of the output layer of the neural network corresponding to received multi-dimensional pattern data; and training means for completing a training of the neural network, wherein the training means includes means for equalizing and orthogonalizing the output signals of the output nodes by reducing a covariance matrix of the output signals to the form of a diagonal matrix.
- 2. A system according to claim 1, wherein said training means uses backpropagation to iteratively update weights for the links between nodes of adjacent layers.
- 3. A system according to claim 2, wherein said weights are generated randomly in the interval (W, −W).
- 4. A system according to claim 3, wherein averaged variance of all dimensions of the multi-dimensional pattern data is:
- 5. A system according to claim 4, wherein weights Δwkj between the hidden layer and the output layer are iteratively updated according to the expression:
- 6. A system according to claim 5, wherein:
- 7. A system according to claim 6, wherein:
- 8. A system according to claim 5, wherein backpropogation of error to the weights Δwji between the jth node in a layer of nodes and the ith node in its' preceeding layer:
- 9. A method for effecting the organization of multi-dimensional pattern data into a reduced dimensional representation using a neural network having an input layer comprised of a plurality of input nodes, a hidden layer, and an output layer comprised of a plurality of non-linear output nodes, wherein the number of non-linear output nodes is less than the number of input nodes, said method comprising:
receiving multi-dimensional pattern data into the input layer of the neural network; generating an output signal for each of the ouput nodes of the neural network corresponding to received multi-dimensional pattern data; and training the neural network by equalizing and orthogonalizing the output signals of the output nodes by reducing a covariance matrix of the output signals to the form of a diagonal matrix.
- 10. A method according to claim 9, wherein said step of training includes backpropagation to iteratively update weights for links between nodes of adjacent layers.
- 11. A method according to claim 10, wherein said weights are generated randomly in the interval (W, −W).
- 12. A method according to claim 11, wherein averaged variance of all dimensions of the multi-dimensional pattern data is:
- 13. A method according to claim 12, wherein weights Δwkj between the hidden layer and the output layer are iteratively updated according to the expression:
- 14. A method according to claim 13, wherein:
- 15. A method according to claim 14, wherein δkp,1, δkp,2 and δkp,3 are given by:
- 16. A method according to claim 13, wherein backpropogation of error to the weights Δwji between the jth node in a layer of nodes and the ith node in its' preceeding layer are:
- 17. A system for organizing multi-dimensional pattern data into a reduced dimensional representation comprising:
a neural network comprised of a plurality of layers of nodes, the plurality of layers including:
an input layer comprised of a plurality of input nodes, and an output layer comprised of a plurality of non-linear output nodes, wherein the number of non-linear output nodes is less than the number of input nodes; receiving means for receiving multi-dimensional pattern data into the input layer of the neural network; output means for generating an output signal at the output layer of the neural network corresponding to received multi-dimensional pattern data; and training means for completing a training of the neural network, wherein the training means conserves a measure of the total variance of the output nodes, wherein the total variance of the output nodes is defined as: 35V=(1/P)∑p=1p=P∑i=1i=S(xip-⟨xi⟩)2,where {xp} is a set of data pattern vectors; p=1, 2, . . . , P; P is defined as a positive integer; <xi> denotes the mean value of of xip evaluated over the set of data pattern vectors; S is the number of dimensions; xip is the ith component of xp, the pth member of a set of data pattern vectors.
- 18. A system according to claim 17, wherein said training means completes the training of the neural network via backpropagation for progressively changing weights for the output nodes.
- 19. A system according to claim 18, wherein said training means further includes,
means for training the neural network by backpropagation by progressively changing weights wkj at the output layer of the neural network in accordance with, 36Δ wkj=(1/P)∑p=1p=PΔ wp,kj=(1/P)∑p=1p=PηδpkOpj,where Opj is the output signal from the jth node in the layer preceeding the output layer due to the pth data pattern, η is a constant of suitable value chosen to provide efficient convergence but to avoid oscillation, and δpk is a value proportional to the contribution to the error E by the outputs of the kth node of the output layer for the pth input data pattern.
- 20. A system according to claim 19, wherein:
- 21. A system according to claim 19, wherein said neural network further comprises at least one hidden layer comprised of hidden nodes, wherein adaptive weights wji for each hidden node is progressively improved in accordance with,
- 22. A system according to claim 21, wherein:
- 23. A method for effecting the organization of multi-dimensional pattern data into a reduced dimensional representation using a neural network having an input layer comprised of a plurality of input nodes, and an output layer comprised of a plurality of non-linear output nodes, wherein the number of non-linear output nodes are less than the number of input nodes, said method comprising:
receiving a set {xp} of data pattern vectors into the input layer of the neural network, wherein p=1, 2, . . . , P and wherein P is defined as a positive integer, and wherein the set of data pattern vectors has a total variance defined as, 40V=(1/P)∑p=1p=P∑i=1i=S(xip-⟨xi⟩)2,where {xp} is a set of data pattern vectors; p=1, 2, . . . , P; P is defined as a positive integer; <xi> denotes the mean value of of xip evaluated over the set of data pattern vectors; S is the number of dimensions; xip is the ith component of xp, the pth member of a set of data pattern vectors; training the neural network by backpropagation; and displaying a multi-dimensional output signal from the output layer of the neural network.
- 24. A method according to claim 23, wherein said step of training the neural network by backpropogation includes progressively changing weights wkj at the output layer of the neural network in accordance with,
- 25. A system according to claim 24, wherein:
- 26. A method according to claim 23, wherein said neural network further comprises at least one hidden layer comprised of hidden nodes, wherein adaptive weights w for each hidden node of the neural network is progressively improved in accordance with,
- 27. A method according to claim 26, wherein
- 28. A method according to claim 23, wherein said multi-dimensional output signal is a two-dimensional output signal.
- 29. A method according to claim 23, wherein said two-dimensional output signal includes data points plotting in relation to 2-dimensional axes.
RELATED APPLICATIONS
[0001] The present application is a Continuation-In-Part (CIP) of co-pending U.S. application Ser. No. 08/536,059 filed Sep. 29, 1995.
Continuations (2)
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Number |
Date |
Country |
Parent |
09562777 |
May 2000 |
US |
Child |
09816909 |
Mar 2001 |
US |
Parent |
08991031 |
Dec 1997 |
US |
Child |
09562777 |
May 2000 |
US |
Continuation in Parts (1)
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Number |
Date |
Country |
Parent |
08536059 |
Sep 1995 |
US |
Child |
08991031 |
Dec 1997 |
US |