Clustering and Disjoint Principal Component Analysis

Maurizio Vichi (1) , Gilbert Saporta (2)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
2 CEDRIC - MSDMA - CEDRIC. Méthodes statistiques de data-mining et apprentissage

A constrained principal component analysis, which aims at a simultaneous clustering of objects and a partitioning of variables is proposed. The new methodology allows 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 leastsquares algorithm is proposed to solve the clustering and disjoint PCA. Two applications are given to show the features of the methodology.

Mots clés: PCA; cluster analysis

Mots clés: APC; analyse typologique

Domaines: Statistiques [math.ST]

Maurizio Vichi, Gilbert Saporta. Clustering and Disjoint Principal Component Analysis. Computational Statistics and Data Analysis, 2008, 53 (8), pp.3194-3208. ⟨10.1016/j.csda.2008.05.028⟩. ⟨hal-01125538⟩