It was empirically shown that the matrixized classifier design is superior to the vectorized one in terms of classification performance. However, it has not been demonstrated for the superiority of the matrixized classifier in terms of theory. To this end, this manuscript analyzes the general risk bounds for both the matrixized and vectorized classifiers. Here, we adopt the risk bound composed of the Rademacher complexity. Therefore, we investigate the Rademacher complexity of both matrixized and vectorized classifiers. Since the solution space of the matrixized classifier function is contained in that of the vectorized one, it can be proven that the Rademacher complexity of the matrixized classifier is less than that of the vectorized one. As a result, the general risk bound of the matrixized classifier is tighter than that of the vectorized one. Further, we compute the empirical Rademacher complexity for both the matrixized and vectorized classifiers and give a discussion.
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