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★ Robust Classification using Structured Sparse Representation

by Ehsan Elhamifar Ren
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2011 ()

Abstract

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 clas- sification in the multi-subspace setting using sparse repre- sentation techniques. We exploit the fact that the dictio- nary of all the training data has a block structure where the training data in each class form few blocks of the dic- tionary. 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 pro- grams 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 im- prove the results of the state-of-the-art face recognition al- gorithms, 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 face recognition results by 10% with only 25% of the training data. In addition, we show that the algorithms are robust

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