A Restricted SVD Type CUR Decomposition for Matrix Triplets

.We present a new restricted SVD-based CUR (RSVD-CUR) factorization for matrix triplets \((A, B, G)\) that aims to extract meaningful information by providing a low-rank approximation of the three matrices using a subset of their rows and columns. The proposed method utilizes the discrete empirical interpolation method (DEIM) to select the subset of rows and columns from the orthogonal and nonsingular matrices obtained through an RSVD of the matrix triplet. We explore the relationships between a DEIM type RSVD-CUR factorization, a DEIM type CUR factorization, and a DEIM type generalized CUR decomposition and provide an error analysis that establishes the accuracy of the RSVD-CUR decomposition within a factor of the approximation error of the RSVD of the given matrices. The RSVD-CUR factorization can be used in applications that require approximating one data matrix relative to two other given matrices. We discuss two such applications, namely multiview dimension reduction and data perturbation problems where a correlated noise matrix is added to the input data matrix. Our numerical experiments demonstrate the advantages of the proposed method over the standard CUR approximation in these scenarios.Keywordsrestricted SVDlow-rank approximationCUR decompositioninterpolative decompositionDEIMsubset selectioncanonical correlation analysismultiview learningnonwhite noisecolored noisestructured perturbationMSC codes65F5515A2315A1815A2165F1568W25