Extracting the correlation structure by means of planar embedding

Abstract

The hierarchical structure of correlation matrices in complex systems is studied by extracting a significant sub-set of correlations resulting in a planar graph. Such a graph has been generated by a method introduced in Aste et al.1 and it has the same hierarchical structure of the Minimum Spanning Tree but it contains a larger amount of links, loops and cliques. In Tumminello et al.,2 we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the system clustering revaling the hierarchical organization in the whole system and within each cluster. Here we discuss this filtering correlation procedure and its application to different financial data sets.