Hierarchically nested factor model from multivariate data

Details Hierarchically nested factor model from multivariate data Hierarchically nested factor model from multivariate data

2005-11-30

arxiv.org/abs/cond-mat/0511726v2

Europhys. Lett. 78, 30006 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 5 figures; accepted for publication in Europhys. Lett. ; the Appendix corresponds to the additional material of the a

Scientific paper

10.1209/0295-5075/78/30006

We show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a factor model, the hierarchically nested factor model. In this model, factors are mutually independent and hierarchically organized. Finally, we use a bootstrap based procedure to reduce the number of factors in the model with the aim of retaining only those factors significantly robust with respect to the statistical uncertainty due to the finite length of data records.

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