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Center for Nonlinear Studies |
Principal Component Analysis (PCA) is one of the most fundamental tools for general data analysis, but suffers from severe sensitivity to outliers such as impulse noise or (specifically in the context of image/video analysis) small occluding regions. A recent development in matrix completion theory (itself a branch of compressed sensing) is Principal Component Pursuit, a robust form of PCA constructed via a decomposition of a data matrix into low rank and sparse components, the former representing a low-dimensional linear model of the data, and the latter representing sparse deviations from the low-dimensional subspace. This decomposition has been applied, with promising results, to a variety of data analysis problems, including in image and video analysis. A significant limitation, however, is the underlying model of data lying within a single global low-dimensional subspace. We have generalized this model to a union of low-dimensional subspaces, which can describe data lying within a nonlinear manifold. An efficient algorithm has been developed for this new model, and initial validation has been performed on a video background modeling problem.
Host: Humberto C Godinez Vazquez, Mathematical Modeling and Analysis Theoretical Division, 5-9188