arXiv Machine Learning By Vincent Szolnoky

D-SLR: The Disjoint Row-Sparse plus Low-Rank Decomposition

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The paper introduces D‑SLR, a closed‑form decomposition that combines a low‑rank approximation with a disjoint row‑sparse component, offering a drop‑in replacement for truncated SVD. Unlike previous joint methods, D‑SLR restricts each row to either be stored verbatim or approximated by the low‑rank fit, achieving the joint optimum without extra parameters and without iterative solvers or regularization tuning. The authors provide an assumption‑free, a‑posteriori error bound for every shape, and demonstrate performance gains on synthetic data, LLM embedding tables, network traffic, and hyperspectral images.

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arXiv Machine Learning
Sep 25

Stacked SVD or SVD stacked? A Random Matrix Theory perspective on data integration

The paper compares two popular data‑integration techniques—Stack‑SVD, which concatenates datasets before performing singular value decomposition, and SVD‑Stack, which first decomposes each dataset separately and then aggregates the leading singular vectors. By deriving exact asymptotic performance expressions and phase transitions in a proportional regime, the authors show that neither method uniformly dominates the other when unweighted, but optimally weighted Stack‑SVD outperforms optimally weighted SVD‑Stack when the low‑rank signal is fully shared. They also demonstrate that SVD‑Stack can excel with partially shared components and provide practical algorithms for estimating optimal weights, supported by simulations and genomic experiments.

By Tavor Z. Baharav, Phillip B. Nicol, Rafael A. Irizarry, Rong Ma