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Entropy 2015, 17(4), 1775-1794;

Multidimensional Scaling Visualization Using Parametric Similarity Indices

Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, Porto 4200-072, Portugal
Institute of Mechanical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Porto 4200-465, Portugal
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 19 February 2015 / Revised: 21 March 2015 / Accepted: 25 March 2015 / Published: 30 March 2015
(This article belongs to the Section Complexity)
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In this paper, we apply multidimensional scaling (MDS) and parametric similarity indices (PSI) in the analysis of complex systems (CS). Each CS is viewed as a dynamical system, exhibiting an output time-series to be interpreted as a manifestation of its behavior. We start by adopting a sliding window to sample the original data into several consecutive time periods. Second, we define a given PSI for tracking pieces of data. We then compare the windows for different values of the parameter, and we generate the corresponding MDS maps of ‘points’. Third, we use Procrustes analysis to linearly transform the MDS charts for maximum superposition and to build a globalMDS map of “shapes”. This final plot captures the time evolution of the phenomena and is sensitive to the PSI adopted. The generalized correlation, theMinkowski distance and four entropy-based indices are tested. The proposed approach is applied to the Dow Jones Industrial Average stock market index and the Europe Brent Spot Price FOB time-series. View Full-Text
Keywords: clustering; complex systems; multidimensional scaling; parametric similarity indices; visualization clustering; complex systems; multidimensional scaling; parametric similarity indices; visualization
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Tenreiro Machado, J.A.; Lopes, A.M.; Galhano, A.M. Multidimensional Scaling Visualization Using Parametric Similarity Indices. Entropy 2015, 17, 1775-1794.

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