Sparsified Multidimensional Scaling and Sparsified Multidimensional Distance Analysis

In this article we introduce new multidimensional scaling variants: sparsified multidimensional scaling (SMDS), sparsified power multidimensional scaling (SPMDS), sparsified multidimensional distance analysis (SMDDA), sparsified power multidimensional distance analysis (SPMDDA). These methods are inspired by the idea of curvilinear component analysis and weight the approximation error with a heaviside function to ignore larger fitted distances in the configuration, thus effectively providing a localized version of multidimensional scaling. Sparsified refers to the weight matrix being sparse. We estimate the models with a quasi-majorization algorithm.