Interpretable dimension reduction

Abstract

The analysis of high-dimensional data often begins with the identification of lower dimensional subspaces. Principal component analysis (PCA) is a dimension reduction technique that identifies linear combinations of variables along which most variation occurs or which "reconstruct" the original variables the best. For example, many temperature readings may be taken in a production process when in fact there are just a few underlying variables driving the process. A problem with principal components is that the linear combinations can seem quite arbitrary. To make them more interpretable, we introduce constraints on the coefficients of the linear combination. Two classes of constraints are considered - those in which coefficients are equal to one of a small number of values (homogeneous constraints), and those in which many coefficients are set to 0 (sparsity constraints). The resultant interpretable directions may be calculated to be "close" to the original principal components, or...