Non-Linear Dimensionality Reduction

A method for creating a nonlinear encoder-decoder for multidimensional data with compact representations is presented. The commonly used technique of autoassociation is extended to allow nonlinear representations, and an objective function which penalizes activations of individual hidden units is shown to result in minimum dimensional encodings with respect to allowable error in reconstruction. 1 INTRODUCTION Reducing dimensionality of data with minimal information loss is important for feature extraction, compact coding and computational efficiency. The data can be tranformed into "good" representations for further processing, constraints among feature variables may be identified, and redundancy eliminated. Many algorithms are exponential in the dimensionality of the input, thus even reduction by a single dimension may provide valuable computational savings. Autoassociating feed forward networks with one hidden layer have been shown to extract the principal components of the data (Baldi & Hornik, 1988). Such networks have been used to extract features and develop compact encodings of the data (Cottrell, Munro & Zipser, 1989). Principal Components Analysis projects the data into a linear subspace -email: demers@cs.ucsd.edu