arXiv:2609.09211v1 Announce Type: new
Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...
By Huan Qing
arXiv:2608. 12503v1 Announce Type: cross Abstract: We describe a simple rejection-sampling-based algorithm to perform length-squared sampling on an $n \times n$ positive-semidefinite (psd) matrix: that is, to sample a column with probability proportional to its squared $\ell_2$-norm.
By Rajarshi Bhattacharjee, Ethan N. Epperly, Cameron Musco, Aaron Tian
The paper introduces two randomized approaches to accelerate spectral co‑clustering of word‑document matrices: one based on randomized SVD via random projection, and another combining partial SVD with element‑wise random sampling. Experiments on real and synthetic data show both methods cut runtime compared to full SVD, with the projection technique offering more consistent performance across varied sparsity levels, while the sampling method excels on denser matrices. The study highlights that the choice of approximation should align with the data’s structural properties.
By Fateme Mazdarani, Carlos Toxtli
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
By Hoang-Son Tran, Pranav Gupta, Subhroshekhar Ghosh
arXiv:2602. 05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion.
By Hengrui Luo, Anna Ma, Ludovic Stephan, Yizhe Zhu
arXiv:2507.02248v2 Announce Type: replace-cross
Abstract: In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank t...
By Dali Liu, Yuying Xie, Haolei Weng