Support Matrix Machine for Large-Scale Data Set

In the computation process of support vector machine (SVM), one of the important step is the formation of the kernel matrix. But the size of kernel matrix scales with the number of data set, it is infeasible to store and compute the kernel matrix when faced with the large-scale data set. To overcome computational and storage problem for large-scale data set, a new framework, Support Matrix Machine (SMM), is proposed. By initially dividing the large scale data set into small subsets, we could treat the autocorrelation matrix of each subset as the special computational unit. A novel polynomial-matrix kernel function is then adopted to compute the similarity between the data matrices in place of vectors. It is also proved that the polynomial kernel is the extreme case of the polynomial-matrix one. The proposed method can greatly reduce the size of kernel matrix, which makes its computation possible. The effectiveness is demonstrated by the experimental results on the artificial and real data set.