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Physica A 370 (2006) 156161 Dynamical networks from correlations

Summary: Physica A 370 (2006) 156­161
Dynamical networks from correlations
T. Aste, T. Di MatteoĆ
Department of Applied Mathematics, Research School of Physical Sciences and Engineering, The Australian National University,
0200 Canberra, Australia
Available online 15 May 2006
The extraction of relevant and meaningful information from large streams of data has become one of the major
challenges for scientists working in the field of complex systems. In particular, one of the main goals is to get information
about the underlying system of interactions that leads to complex collective dynamics. In this paper, we discuss how a set
of relevant interactions can be extracted from the analysis of the cross-correlation matrix. We show that an active and
adaptive correlation filtering procedure can be associated to the dynamics of a network which is a sort of `hyper-molecule'
warped on a D-dimensional unitary sphere.
r 2006 Elsevier B.V. All rights reserved.
Keywords: Complex systems; Time series analysis; Networks; Financial data correlations; Econophysics
1. Introduction
The analysis of the correlations is one of the main instruments in the study of the collective behavior of a
system comprised by many elements. In general, the goal is to extract a structure of relevant interactions which
give information about the collective properties of the system under investigation. However, the extraction of
information from the observed correlations is not straightforward. Schematically, one can point out two


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