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RESEARCH PRODUCT

Spectral properties of correlation matrices for some hierarchically nested factor models

Michele TumminelloFabrizio LilloRosario N. MantegnaSumiyoshi AbeHans HerrmannPiero QuaratiAndrea RapisardaConstantino Tsallis

subject

Set (abstract data type)Discrete mathematicsTree (data structure)Multiple correspondence analysisPrincipal component analysisBijectionCluster analysisRandom matrixFactor analysisMathematics

description

We show that spectral methods, such as Principal Component Analysis and Random Matrix Theory, are unable to reveal the hierarchical (or nested) structure of a set of mutivariate data. We consider the method introduced in M. Tumminello et al., EPL 78, 30006 (2007) to associate a hierarchical factor model with a set of data by making use of clustering algorithms. This is done by proving the existence of a bijective correspondence between a hierarchical tree and a factor model.

yearjournalcountryeditionlanguage
2007-01-01
10.1063/1.2828748http://hdl.handle.net/10447/7794