  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 a restricted singular value decomposition
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 restricted singular value decomposition 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 multi-view 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.
