Clustering and disjoint principal component analysis

Authors:
Maurizio Vichi;Gilbert Saporta
Affiliations:
Department of Statistics, Probability, and Applied Statistics, University "La Sapienza", P.le A. Moro 5, 00185 Rome, Italy;CEDRIC, CNAM, 292 rue Saint Martin, 75003 Paris, France
Venue:
Computational Statistics & Data Analysis
Year:
2009

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Abstract

A constrained principal component analysis, which aims at a simultaneous clustering of objects and a partitioning of variables, is proposed. The new methodology allows us to identify components with maximum variance, each one a linear combination of a subset of variables. All the subsets form a partition of variables. Simultaneously, a partition of objects is also computed maximizing the between cluster variance. The methodology is formulated in a semi-parametric least-squares framework as a quadratic mixed continuous and integer problem. An alternating least-squares algorithm is proposed to solve the clustering and disjoint PCA. Two applications are given to show the features of the methodology.