Multidimensional Scaling Visualization Using Parametric Similarity Indices

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Tenreiro Machado, JAT (Author) Other; António Mendes Lopes (Author) FEUP; Galhano, AM (Author) Other

Journal

Title: Entropy

Vol. 17

Pages: 1775-1794

ISSN: 1099-4300

Publisher: MDPI

Indexing

ISI Web of Knowledge - 39 Citations

Scopus - 43 Citations

Other information

Authenticus ID: P-00G-49A

DOI: 10.3390/e17041775

Abstract (EN): 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 global MDS map of "shapes". This final plot captures the time evolution of the phenomena and is sensitive to the PSI adopted. The generalized correlation, the Minkowski 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20