A Heuristic Search Approach to Multidimensional Scaling

Abstract

This research effort presents an approach to accomplish Multidimensional Scaling (MDS) via the heuristic approach of Simulated Annealing. Multidimensional scaling is an approach used to convert matrix-based similarity (or dissimilarity data) into spatial form, usually via two or three dimensions. Performing MDS has several important applications — Geographic Information Systems, DNA Sequencing, and Marketing Research are just a few. Traditionally, classical MDS decomposes the similarity or dissimilarity matrix into its eigensystem and uses the eigensystem to calculate spatial coordinates. Here, a heuristic search-based approach is used to find coordinates from a dissimilarity matrix that minimizes a cost function. The proposed methodology is used over a variety of problems. Experimentation shows that the presented methodology consistently outperforms solutions obtained via the classical MDS approach, and this approach can be used for other important applications.