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Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing “related” objects/phenomena. The first one of these models straddles the two extremes of the subspace model and the union-of-subspaces...
This paper addresses the problem of learning a collection of nonlinear manifolds. Inspired by kernel methods, it puts forth a generalization of the kernel subspace model, termed the Metric-Constrained Kernel Union-of-Subspaces (MC-KUoS) model. It then develops an iterative method for learning of an MC-KUoS whose solution is based on the data representation capability of the manifolds and distances...
This paper studies the problem of matched subspace detection in high-dimensional feature space where the signal in the input space is partially observed. We present a test statistic for our detection problem using kernel functions and provide kernel function value estimators with missing data for different kernels. The test statistic can be calculated approximately with estimated kernel function values...
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