Visualization and self organization of multidimensional data through equalized orthogonal mapping
First Claim
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, andan 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.
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Abstract
The subject system provides reduced-dimension mapping of pattern data. Mapping is applied through conventional single-hidden-layer feed-forward neural network with non-linear neurons. According to one aspect of the present invention, the system functions to equalize and orthogonalize lower dimensional output signals by reducing the covariance matrix of the output signals to the form of a diagonal matrix or constant times the identity matrix. The present invention allows for visualization of large bodies of complex multidimensional data in a relatively "topologically correct" low-dimension approximation, to reduce randomness associated with other methods of similar purposes, and to keep the mapping computationally efficient at the same time.
65 Citations
29 Claims
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1. A system for organizing multi-dimensional pattern data into a reduced-dimension representation comprising:
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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. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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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. - View Dependent Claims (10, 11, 12, 13, 14, 15, 16)
- receiving multi-dimensional pattern data into the input layer of the neural network;
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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;
##EQU35## 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. - View Dependent Claims (18, 19, 20, 21, 22)
- a neural network comprised of a plurality of layers of nodes, the plurality of layers including;
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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, ##EQU39## 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. - View Dependent Claims (24, 25, 26, 27, 28, 29)
- 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, ##EQU39## where {xp } is a set of data pattern vectors;
Specification