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A tool for filtering information in complex systems M. Tumminello*, T. Aste
 

Summary: A tool for filtering information in complex systems
M. Tumminello*, T. Aste
, T. Di Matteo
, and R. N. Mantegna*
*Istituto Nazionale di Fisica della Materia Unita` di Palermo and Dipartimento di Fisica e Tecnologie Relative, Universita` di Palermo, Viale delle Scienze,
I-90128 Palermo, Italy; Department of Applied Mathematics, Australian National University, Canberra ACT 0200, Australia; and Istituto Nazionale di Fisica
Nucleare, Sezione di Catania, I-95125 Catania, Italy
Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved June 10, 2005 (received for review January 13, 2005)
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 struc-
ture. 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

  

Source: Aste, Tomaso - Department of Applied Mathematics, Australian National University
Di Matteo, Tiziana - Department of Mathematics, King's College London

 

Collections: Materials Science; Mathematics; Physics