Fast Convergent Factorial Learning of the Low-Dimensional Independent Manifolds in Optical Imaging D

In many functional-imaging scenarios, it is a challenge to s eparate the response to stimulation from the other, presumabl y independent, sources that contribute to the image formation. When the brain is optically imaged, the typical variabilities of some of these sources force the data to lie close to a low-dimensiona l, nonlinear manifold. When an initial probability model is deriv ed by the Karhunen-Loève Transform (KLT) of the data, and some fa ctors of this manifold happen to be accessibly embedded in sui tably chosen KLT subspaces, vector quantization has been used to c haracterize this embedding as the locus of maximum likelihood o f the data, and to derive an improved probability model, in which t he factors—the dynamics on this locus and away from it—are esti mated independently. Here we show that such a description ca n serve as the starting point for a convergent procedure that a ltern tively refines the estimates of the embedding of, and the dyna mics on, the manifold. Further, we show that even a very crude init ial estimate, from a heavily mixed subspace, is sufficient for co nvergence in a small number of steps. This opens the possibility o f hierarchical semi-blind separation of the independent sou rces in optical imaging data, even when their contributions are non li ear.