Cardinality-based sparse singular value decomposition for similarity matrices

Sparse decomposition methods have been studied in the context of principal component analysis (PCA). Many of these methods control the number of non-zero elements of the eigenvector through the tuning of a regularization parameter(s). Other approaches allow for the direct choice of cardinality to create sparse eigenvectors. As PCA is not applicable to all settings, such as analyzing the cross-correlation matrix, we extend cardinality-based PCA to cardinality-based singular value decomposition (SVD). Our method allows the user to independently input their desired cardinality of the left and right singular vectors of any continuous data matrix. This will create sparse singular vectors consisting of the most impactful variables. In addition, we extend our method from a rank-1 SVD approximation to an SVD approximation greater than rank 1, and create left and right matrices of sparse singular vectors.