Papers › A Generalized CUR decomposition for matrix pairs
A Generalized CUR decomposition for matrix pairs
Perfect Y. Gidisu, Michiel E. Hochstenbach
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We propose a generalized CUR (GCUR) decomposition for matrix pairs (A, B). Given matrices A and B with the same number of columns, such a decomposition provides low-rank approximations of both matrices simultaneously, in terms of some of their rows and columns. We obtain the indices for selecting the subset of rows and columns of the original matrices using the discrete empirical interpolation method (DEIM) on the generalized singular vectors. When B is square and nonsingular, there are close connections between the GCUR of (A, B) and the DEIM-induced CUR of AB⁻¹. When B is the identity, the GCUR decomposition of A coincides with the DEIM-induced CUR decomposition of A. We also show a similar connection between the GCUR of (A, B) and the CUR of AB^+ for a nonsquare but full-rank matrix B, where B^+ denotes the Moore--Penrose pseudoinverse of B. While a CUR decomposition acts on one data set, a GCUR factorization jointly decomposes two data sets. The algorithm may be suitable for applications where one is interested in extracting the most discriminative features from one data set relative to another data set. In numerical experiments, we demonstrate the advantages of the new method over the standard CUR approximation; for recovering data perturbed with colored noise and subgroup discovery.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections