Visualization and self organization of multidimensional data through equalized orthogonal mapping

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.

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 {x.sub.p } is a set of data pattern vectors;
• p=1,2, . . . ,P;
• P is defined as a positive integer;
• <x.sub.i >
• denotes the mean value of of x.sub.ip evaluated over the set of data pattern vectors;
• S is the number of dimensions;
• x.sub.ip is the ith component of x.sub.p, the pth member of a set of data pattern vectors.

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 {x.sub.p } 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 {x.sub.p } is a set of data pattern vectors;
• p=1,2, . . . ,P;
• P is defined as a positive integer;
• <x.sub.i >
• denotes the mean value of of x.sub.ip evaluated over the set of data pattern vectors;
• S is the number of dimensions;
• x.sub.ip is the ith component of x.sub.p, 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.