Clustering and Disjoint Principal Component Analysis

A constrained principal component analysis, which aims at a simultaneous clustering ofobjects and a partitioning of variables is proposed. The new methodology allows to identifycomponents with maximum variance, each one a linear combination of a subset of variables. All thesubsets form a partition of variables. Simultaneously, a partition of objects is also computedmaximizing the between cluster variance. The methodology is formulated in a semi-parametricleast-squares framework as a quadratic mixed continuous and integer problem. An alternating leastsquaresalgorithm is proposed to solve the clustering and disjoint PCA. Two applications are givento show the features of the methodology