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. © 2008 Elsevier B.V. All rights reserved.

Clustering and disjoint principal component analysis / Vichi, Maurizio; Gilbert, Saporta. - In: COMPUTATIONAL STATISTICS & DATA ANALYSIS. - ISSN 0167-9473. - 53:8(2009), pp. 3194-3208. [10.1016/j.csda.2008.05.028]

Clustering and disjoint principal component analysis

VICHI, Maurizio;
2009

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. © 2008 Elsevier B.V. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/12999
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