NSF Award
9704094
This project will develop local linear and network models for application to detection problems, and to transform coding. The focus is on the development and adaptation of nonlinear extensions of principal component analysis (PCA) to these domains. Our previous work on nonlinear PCA (1,2,3) showed that local linear models are faster to compute, and provide more accurate encodings that neural network-based nonlinear PCA. A major thrust of this work is adapting and applying our models to detection problems, and to fast optimal transform coding. The work is fault detection builds in part on the recent use of three-layer autoassociative neural networks in this realm (4,5). In work, networks are used to provide a model of data corresponding to normal system behavior. Abnormal behavior (faults) are the indicated by the failure to accurately model the new data. However three-layer autoassociateve networks provide a very crude model of data, essentially a PCA subspace model. Real data can be more accurately represented by generally curved manifolds, as provided by nonlinear PCA will apply models based on nonlinear PCA to detection problems form benchmark datasets. This project will also apply nonlinear PCA to transform coding. This a natural extension of the work on nonlinear, and local linear transforms. As in the detection paradigms discussed above, the use of PCA for transform coding is suboptimal because real data is not adequately modeled by second order statistics, or by subspace geometric models. Nonlinear PCA is able to detect and reduce higher-order redundancies between data components, thus providing more compact representations. Adaptation of nonlinear PCA algorithms for transform coding (e.g. of images) will provide rate distortion curves superior to those obtained form DCT or PCA transform codes.
