A Tool for Filtering Information in Complex Systems

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving fi...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2005-07, Vol.102 (30), p.10421-10426
Main Authors: Tumminello, M., Aste, T., Di Matteo, T., Mantegna, R. N., Stanley, H. Eugene
Format: Article
Language:English
Subjects:
Complex systems
Correlations
Data analysis
Economic sectors
Graphs
Hyperlinks
Information
Mathematical surfaces
Physical Sciences
Planar graphs
Time series
Topology
Trees
Vertices
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Summary:We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.0500298102