Clustering and Disjoint Principal Component Analysis
Résumé
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.