Double-fold localized multiple matrixized learning machine

In this paper, we develop an effective multiple-matrixized learning machine named Double-fold Localized Multiple Matrixized Learning Machine (DLMMLM). The characteristic of the proposed DLMMLM is that it possesses double folds of local information from data. The first fold lies in the whole representation space which consists of different matrix representations. It is known that each pattern can be represented by different matrix representations. The matrices have their respective representation information and can play different discriminant roles in the final classification. Therefore from the viewpoint of the whole representation space, each matrix has its own local information. The second fold is that in each matrix representation learning, different patterns represented with the same matrix representation can carry different information. Therefore in the pattern space with the same matrix size, local information of different patterns should be introduced into the classifier design. On the whole, the advantages of the proposed DLMMLM are: (i) establishing a pattern-depended function in the matrixized learning so as to realize different roles of patterns for the first time; (ii) adopting the double-fold local information in both the representation space and the pattern space; (iii) proposing a new nonlinear classifier that is different from the state-of-the-art kernelization one; and (iv) getting a tighter empirical generalization risk bound in terms of the Rademacher complexity and thus achieving a statistically superior classification performance than those classifiers without the introduction of the double-fold local information.