Generalized Non-linear Sparse Classifier

In a recent study a novel classification algorithm called the Sparse Classifier (SC) assumes that if a test sample belongs to class k then it can be approximately represented by a linear combination of the training samples belonging to k. Good face recognition results were obtained by the SC method. This paper proposes two generalizations of the aforesaid assumption. The first generalization assumes that the test sample raised to a power can be approximated by a linear combination of the training samples of that class raised to the same powers. The second generalization assumes that the test samples raised to a power can be approximately represented by a non-linear combination of the training samples raised to the same power. The first generalization requires solving a group-sparse optimization problem with linear constraints while the second assumption requires solving a group-sparse optimization problem with non-linear constraints. We propose two greedy sub-optimal algorithms to solve the said problems. The classifiers developed in this work are used for single-image-per-person face recognition. We find that our first generalization leads to an improvement of 2-3% in recognition accuracy over SC, while the second generalization improves the recognition accuracy even further; about 6-7% better than the first generalization.