Sparse principal components by semi-partition clustering

Abstract

A cluster-based method for constructing sparse principal components is proposed. The method initially forms clusters of variables, using a new clustering approach called the semi-partition, in two steps. First, the variables are ordered sequentially according to a criterion involving the correlations between variables. Then, the ordered variables are split into two parts based on their generalized variance. The first group of variables becomes an output cluster, while the second one—input for another run of the sequential process. After the optimal clusters have been formed, sparse components are constructed from the singular value decomposition of the data matrices of each cluster. The method is applied to simple data sets with smaller number of variables (p) than observations (n), as well as large gene expression data sets with p ≫ n. The resulting cluster-based sparse principal components are very promising as evaluated by objective criteria. The method is also compared with other existing approaches and is found to perform well.