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arXiv · 2604.14418

Subset selection for matrices by column exchange

Alexander Osinsky·Ivan Kozyrev
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Abstract

The paper considers the problem of finding a submatrix $X_{\mathcal{S}} \in \mathbb{R}^{m \times k}$ in a matrix $X \in \mathbb{R}^{m \times n}$, such that the spectral or Frobenius norm of $X_{\mathcal{S}}^{\dag} X$ is limited, which guarantees it provides a good representation of the whole matrix. Such bounds can be reached by applying greedy algorithms, maximizing the submatrix volume. We suggest a modification of a greedy volume maximization, which performs column exchanges asymptotically faster for $n \gg m$ than the known alternatives, while guaranteeing the same bounds on $X_{\mathcal{S}}^{\dag} X$. In addition, we prove a new upper bound on the number of required exchanges, which is applicable to the new algorithm as well as to other greedy volume maximization algorithms.

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Alexander Osinsky, Ivan Kozyrev. 2026-04-15. Subset selection for matrices by column exchange. https://arxiv.org/abs/2604.14418

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