Multi-dimensional scaling of sparse block diagonal similarity matrix

Abstract

Similarity matrix represents the relationship of n objects and gives us a useful information about these objects. Several models for analyzing this data assume that each object of n objects is embedded as a point or a vector in t dimensional “common space” of n objects in general. However, these models are not appropriate for analyzing a sparse block diagonal similarity matrix as each block diagonal matrix indicates us that each member of the set of objects in a block is represented as a point or a vector in not “common space,” but, “sub-space.” And a model is proposed to analyze this type of a sparse block diagonal similarity matrix. And application to a real data set will be shown.