Abstract
Multidimensional Scaling (MDS) requires the multimodal Stress function optimization to estimate the model parameters, i.e. the coordinates of points in a lower-dimensional space. Therefore, finding the global optimum of the Stress function is very important for applications of MDS. The main idea of this paper is replacing the difficult multimodal problem by a simpler unimodal constrained optimization problem. A coplanarity measure of points is used as a constraint while the Stress function is minimized in the original high-dimensional space. Two coplanarity measures are proposed. A simple example presented illustrates and visualizes the optimization procedure. Experimental evaluation results with various data point sets demonstrate the potential ability to simplify MDS algorithms avoiding multidimodality.
Keywords
- Local Optimization
- Multidimensional Scaling
- Conjugate Gradient Method
- Stress Function
- Optimal Stress
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© 2006 Springer-Verlag Berlin Heidelberg
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Saltenis, V. (2006). Constrained Optimization of the Stress Function for Multidimensional Scaling. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758501_94
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DOI: https://doi.org/10.1007/11758501_94
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34379-0
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