Portland State University
Fariborz Maseeh Department of Mathematics & Statistics
The Maseeh Mathematics and Statistics Colloquium Series*
"Department of Mathematics and Science Programs,
Washington State University at Vancouver "
Soft Clustering Decoding of Neural Codes
Methods based on Rate Distortion theory have been successfully used to cluster stimuli and neural responses in order to study neural codes at a level of detail supported by the amount of available data. They approximate the joint stimulus-response distribution by soft-clustering paired stimulus-response observations into smaller reproductions of the stimulus and response spaces. An optimal soft clustering is found by maximizing an information-theoretic cost function subject to both equality and inequality constraints, in hundreds to thousands of dimensions.
The method of annealing has been used to solve the corresponding high dimensional non-linear optimization problems. The annealing solutions undergo a series of bifurcations in order to reach the optimum, which we study using bifurcation theory in the presence of symmetries. The optimal models found by the Information Distortion methods have symmetries: any classification of the data can lead to another equivalent model simply by permuting the labels of the classes. These symmetries are described by S_N, the algebraic group of all permutations on N symbols. The symmetry of the bifurcating solutions is dictated by the subgroup structure of S_N. In this contribution we describe these symmetry breaking bifurcations in detail, and indicate some of the consequences of the form bifurcations.
Friday, November 5th, 2010, 3:15pm
Neuberger Hall room 350
(Refreshments served at 3:00 in NH 344)
* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.