Probabilistic learning of similarity measures for tensor PCA

In order to extract low-dimensional features from image data, matrix-based subspace methods such as 2DPCA and tensor PCA have been recently proposed. Since these methods extract features based on 2D image matrices rather than 1D vectors, they can preserve useful information in image matrices and we can expect better classification performance by using the matrix features. In order to maximize the advantages of the matrix features, it is also important to use an appropriate similarity measure between two feature matrices. This paper proposes a method for learning similarity measures for feature matrices, which utilizes distribution properties of given data set and class membership. Through computational experiments with facial image data, we confirm that the obtained similarity measure by the proposed method can give better classification performance than conventional similarity measures for matrix data.