An Improved LMDS Algorithm

摘要

Classical multidimensional scaling (CMDS) is a widely used method for dimensionality reduction and data visualization, but it's very slow. Landmark MDS (LMDS) is a fast algorithm of CMDS. In LMDS, some data points are designated as landmark points. When the intrinsic dimension of the landmark points is less than the intrinsic dimension of the data set, the embedding recovered by LMDS is not consistent with that of classical multidimensional scaling. A selection algorithm of landmark points is put forward in this paper to ensure the intrinsic dimension of the landmarks to be equal to that of the data set, so as to ensure that the embedding recovered by LMDS is the same as that of CMDS. By introducing the selection algorithm into the original LMDS, an improved LMDS algorithm called iLMDS is presented in this paper. The experimental results verify the consistency of iLMDS and CMDS.