Using Vector Quantization to Build Nonlinear Factorial Models of the Low-Dimensional Independent Manifolds in Optical Imaging Data

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-Loève 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 embedded in those subspaces, along which the probability density is concentrated. Further, this information can be utilized to improve the probability model by a factorization into: one nonlinear independent parameter along the manifold; and a linear residual. Iteratively, we apply the procedure on the residual until all apparent nonlinearities are eliminated.