Nonlinear projection to submanifolds using neural networks with circuit realization and its application to data reduction

The Principal Component Analysis (PCA) approach and its variations compute eigenvalues and eigenvectors and hence planar surfaces. An extension of the PCA approach, which computes nonplanar (folded) surfaces, is a computational tool that computes submanifolds in higher dimensional spaces. The focus of this work is an application of this nonlinear projection approach to nonlinear data reduction/compression of color images and 3-band radar signals. Results of various image processing from both computer simulations of the circuit model and chip experiments are reported. Furthermore, we describe how certain neural networks can be constructed as computational tools for general submanifold charts and parameterization maps of nonlinear dynamical systems. Moreover, the architectural framework is compatible with basic circuit realization using micropower microelectronic components.