A fast multidimensional scaling algorithm

Classical multidimensional scaling (CMDS) is a common method for dimensionality reduction and data visualization. Aimed at the problem of slow speed of CMDS, a divide-and-conquer based MDS (dcMDS) algorithm is put forward in this paper. In this algorithm, the distance matrix between samples is divided along its main diagonal into several submatrices, which are solved respectively. By isometric transformation, the solutions of the submatrices can be integrated to form the solution of the whole matrix. The solution of dcMDS is the same as that of CMDS. Moreover, when the intrinsic dimension of the samples is much smaller than the number of samples, the speed of dcMDS is significantly improved than CMDS. In this paper, a detailed theoretical analysis of dcMDS is presented, and its efficiency is verified by experiments.