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We briefly introduce classification, a branch of machine learning, and the classification algorithm of Wright, et al., called "Sparse Representation-based Classification,'' or SRC. We'll discuss a weakness of SRC and present our solution to this problem via a modified algorithm called Local PCA SRC (LPCA-SRC). Our modification involves approximating tangent hyperplanes of the class manifolds at selected training samples and using only ``local'' training samples in the SRC framework. We give a brief analysis of the setting of parameters for this approach and show that this method can achieve higher classification accuracy than SRC. Joint work with Naoki Saito.