A closed-form solution for conditional multidimensional scaling

Abstract

Conditional multidimensional scaling seeks for a low-dimensional configuration from pairwise dissimilarities, in the presence of other known features. This method enables a simpler knowledge discovery process. Thus, it has broad application across different science and engineering domains because prior information of such known features is often available. The current solution of conditional multidimensional scaling is obtained via minimizing its conditional stress objective function with conditional SMACOF, an iterative optimization algorithm. However, iterative optimization is sensitive to starting values and can be time consuming for large problems. This paper proposes an alternative closed-form solution for conditional multidimensional scaling to address these deficits. The proposed method is based on multiple linear regression and eigendecomposition. The proposed algorithm does not necessarily replace conditional SMACOF. The former can be used to initialize the latter to improve its speed and accuracy. • A closed-form solution for conditional multidimensional scaling is proposed • This solution addresses limitations of the existing iterative optimization method • This solution can be used to initialize the iterative method to enhance performance