Two dimensional Large Margin Nearest Neighbor for Matrix Classification

Matrices are a common form of data encountered in a wide range of real applications. How to efficiently classify this kind of data is an important research topic. In this paper, we propose a novel distance metric learning method named two dimensional large margin nearest neighbor (2DLMNN), for improving the performance of k-nearest neighbor (KNN) classifier in matrix classification. Different from traditional metric learning algorithms, our method employs a left projection matrix U and a right projection matrix V to define the matrixbased Mahalanobis distance, for constructing the objective aimed at separating points in different classes by a large margin. Since the parameters in those two projection matrices are much less than that in its vector-based counterpart, 2DLMNN can reduce computational complexity and the risks of overfitting. We also introduce a framework for solving the proposed 2DLMNN. The convergence behavior, computational complexity are also analyzed. At last, promising experimental results on several data sets are provided to show the effectiveness of our method.