Ehsan Elhamifar presents the "Structured-Sparse Subspace Classification is an algorithm based on block-sparse representation techniques for classifying multi-subspace data, where the training data in each class lie in a union of subspaces." The attendant paper is: Robust Classification using Structured Sparse Representation by Ehsan Elhamifar, Rene Vidal. The abstract reads:
In many problems in computer vision, data in multiple classes lie in multiple low-dimensional subspaces of a high-dimensional ambient space. However, most of the existing classiﬁcation methods do not explicitly take this structure into account. In this paper, we consider the problem of classiﬁcation in the multi-subspace setting using sparse representation techniques. We exploit the fact that the dictionary of all the training data has a block structure where the training data in each class form few blocks of the dictionary. We cast the classiﬁcation as a structured sparse recovery problem where our goal is to ﬁnd a representation of a test example that uses the minimum number of blocks from the dictionary. We formulate this problem using two different classes of non-convex optimization programs. We propose convex relaxations for these two non-convex programs and study conditions under which the relaxations are equivalent to the original problems. In addition, we show that the proposed optimization programs can be modiﬁed properly to also deal with corrupted data. To evaluate the proposed algorithms, we consider the problem of automatic face recognition. We show that casting the face recognition problem as a structured sparse recovery problem can improve the results of the state-of-the-art face recognition agorithms, especially when we have relatively small number of training data for each class. In particular, we show that the new class of convex programs can improve the state of the art recognition results by 10% with only 25% of the training data. In addition, we show that the algorithms are robust to occlusion, corruption, and disguise.
see also Block-Sparse Recovery via Convex Optimization by Ehsan Elhamifar, Rene Vidal
The code is here.
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