Abstract
Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression matrix or introducing factorization technique. In this paper, we propose a multi-distance support matrix machine (MDSMM), which formulates the optimization problem by introducing the concept of multi-distance. Unlike traditional matrix-based classifiers, the proposed approach uses a vector-based distance to quantify the cost function and penalty function. We further study the generalization bounds for i.i.d. processes and non i.i.d. processes based on different classifiers. For typical hypothesis classes where matrix norms are constrained, MDSMM achieves a faster learning rate than conventional methods. We demonstrate the merits of the proposed approach by conducting comparative experiments on both simulation study and a number of real-world datasets.
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