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.
Share and Cite:
McMullen, P. (2022) A Heuristic Search Approach to Multidimensional Scaling.
American Journal of Operations Research,
12, 179-193. doi:
10.4236/ajor.2022.125010.
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