A novel unsupervised neural network for dimensionality reduction which seeks directions emphasizing multimodality is presented, and its connection toexploratory projection pursuit methods is discussed. This leads to a new statistical insight to the synaptic modification equations governing learning in Bienenstock, Cooper, and Munro (BCM) neurons (1982). The importance of a dimensionality reduction principle based solely on distinguishing features, is demonstrated using a linguistically motivated phoneme recognition experiment, and compared with feature extraction using back-propagation network. 1 Introduction Due to the curse of dimensionality (Bellman, 1961) it is desirable to extract features froma high dimensional data space before attempting a classification. How to perform this feature extraction/dimensionality reduction is not that clear. A first simplification is to consider only features defined by linear (or semi-linear) projections ofhigh dimensional data.

A novel unsupervised neural network for dimensionality reduction which seeks directions emphasizing multimodality is presented, and its connection to exploratory projection pursuit methods is discussed. This leads to a new statistical insight to the synaptic modification equations governing learning in Bienenstock, Cooper, and Munro (BCM) neurons (1982). The importance of a dimensionality reduction principle based solely on distinguishing features, is demonstrated using a linguistically motivated phoneme recognition experiment, and compared with feature extraction using back-propagation network. 1 Introduction Due to the curse of dimensionality (Bellman, 1961) it is desirable to extract features from a high dimensional data space before attempting a classification. How to perform this feature extraction/dimensionality reduction is not that clear. A first simplification is to consider only features defined by linear (or semi-linear) projections of high dimensional data. This class of features is used in projection pursuit methods (see review in Huber, 1985). Even after this simplification, it is still difficult to characterize what interesting projections are, although it is easy to point at projections that are uninteresting. A statement that has recently been made precise by Diaconis and Freedman (1984) says that for most high-dimensional clouds, most low-dimensional projections are approximately normal. This finding suggests that the important information in the data is conveyed in those directions whose single dimensional projected distribution is far from Gaussian, especially at the center of the distribution.

The paper suggests a statistical framework for the parameter estimation problem associated with unsupervised learning in a neural network, leading to an exploratory projection pursuit network that performs feature extraction, or dimensionality reduction.

The growth in the amount of available databases far outstrips the growth of corresponding knowledge. This creates both a need and an opportunity for extracting knowledge from databases. Many recent results have been reported on extracting different kinds of knowledge from databases, including diagnostic rules, drug side effects, classes of stars, rules for expert systems, and rules for semantic query optimization.

Analytic solutions to the information-theoretic evolution equation ofthe connection strength of a three-layer feedforward neural net for visual information processing are presented. The results are (1) the receptive fields of the feature-analysing cells correspond tothe eigenvector of the maximum eigenvalue of the Fredholm integral equation of the first kind derived from the evolution equation of the connection strength; (2) a symmetry-breaking mechanism (parity-violation) has been identified to be responsible forthe changes of the morphology of the receptive field; (3) the conditions for the formation of different morphologies are explicitly identified.

The paper suggests a statistical framework for the parameter estimation problemassociated with unsupervised learning in a neural network, leading to an exploratory projection pursuit network that performs feature extraction, or dimensionality reduction.

Analytic solutions to the information-theoretic evolution equation of the connection strength of a three-layer feedforward neural net for visual information processing are presented. The results are (1) the receptive fields of the feature-analysing cells correspond to the eigenvector of the maximum eigenvalue of the Fredholm integral equation of the first kind derived from the evolution equation of the connection strength; (2) a symmetry-breaking mechanism (parity-violation) has been identified to be responsible for the changes of the morphology of the receptive field; (3) the conditions for the formation of different morphologies are explicitly identified.

Academic Press.

Proc. IEEE, 64 (4), 532-56.

This work deals with computer analysis of textured surfaces. Descriptions of textures are form­alized from natural language descriptions. Local texture descriptions are obtained from the directional and non-directional components of the Fourier transform power spectrum. Analytic expressions are de­rived for orientation, contrast, size, spacing, and in periodic cases, the locations of texture elements. The local descriptions are defined over windows of varying sizes.See also: ACM Digital Library.In IJCAI-73: THIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, Stanford University Stanford, California, 20-23 August