Using vector quantization to build nonlinear factorial models of the low-dimensional independent manifolds in optical imaging data

Abstract

In many functional-imaging scenarios, four sources contribute to the image formation: the intrinsic variability of the object under study, the variability due to the experimentally controlled stimulus, the state of the equipment, and white noise. These sources are presumably independent, and under a multidimensional Gaussian assumption, linear discriminant analysis is typically used to separate them. Here we show that when an initial entropy model of optical imaging data is derived by the Karhunen-Loeve transform (KLT), vector quantization can be used to find KLT subspaces in which the Gaussian assumption does not hold; this results in the characterization of low-dimensional nonlinear manifolds that are embedded in those subspaces, and along which the probability density clusters. Further, this information is utilized to improve the probability model by a factorization into: one nonlinear independent parameter along the manifold and a linear residual.