Vector Set Classification by Signal Subspace Matching

We present a powerful solution to the problem of vector set classification, based on a novel goodness-of-fit metric, referred to as signal subspace matching (SSM). Unlike the existing solutions based on principal component analysis (PCA), this solution is eigendecomposition-free and dimension-selection-free, i.e., it does not require PCA nor the election of the subspace dimension, which is done implicitly. More importantly, it copes effectively with the challenging cases wherein the subspaces characterizing the classes are partially or fully overlapping. The SSM metric matches the subspaces characterizing the vector sets of the test and the classes by minimizing the distance between respective soft-projection matrices constructed from the vector sets. We prove the consistency of the solution for the high signal-to-noise-ratio limit, and also for the large-sample limit, conditioned on the noise being white. Experimental results, demonstrating the superiority of the SSM solution over the existing PCA-based solutions, especially in the challenging cases of overlapping subspaces, are included.