Representing Data by Sparse Combination of Contextual Data Points for Classification

In this paper, we study the problem of using contextual data points of a data point for its classification problem. We propose to represent a data point as the sparse linear reconstruction of its context, and learn the sparse context to gather with a linear classifier in a supervised way to increase its discriminative ability. We proposed a novel formulation for context learning, by modeling the learning of context reconstruction coefficients and classifier in a unified objective. In this objective, the reconstruction error is minimized and the coefficient sparsity is encouraged. Moreover, the hinge loss of the classifier is minimized and the complexity of the classifier is reduced. This objective is optimized by an alternative strategy in an iterative algorithm. Experiments on three benchmark data set show its advantage over state-of-the-art context-based data representation and classification methods.