Invariant extreme physical information and fuzzy clustering
Ravi C. Venkatesan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2004
A principled formulation for knowledge acquisition from discrete data based on a continuum-free invariance preserving extension of the Extreme Physical Information (EPI) theory of Frieden is presented. A systematic invariance preserving methodology to formulate and minimize lattice EPI fuzzy clustering objective functions, and, determine the concomitant constraints is suggested. Equivalence between invariant EPI (IEPI) fuzzy clustering, described within a discrete time-independent Schrodinger-like framework, and robust Possibilistic c-Means (PcM) clustering is exemplified. The constraints are shown to be consistent with Heisenberg's uncertainty principle. Numerical examples for exemplary cases are provided for multiple potential wells, without a-priori knowledge of the number of clusters.