We are very excited to join forces with MLCommons and OctoML.ai! Contact Grigori Fursin for more details!

Improving CUR Matrix Decomposition and the Nyström Approximation via Adaptive Sampling

lib:4668a23645bc87a3 (v1.0.0)

Authors: Shusen Wang,Zhihua Zhang
ArXiv: 1303.4207
Document:  PDF  DOI 
Abstract URL: http://arxiv.org/abs/1303.4207v7

The CUR matrix decomposition and the Nystr\"{o}m approximation are two important low-rank matrix approximation techniques. The Nystr\"{o}m method approximates a symmetric positive semidefinite matrix in terms of a small number of its columns, while CUR approximates an arbitrary data matrix by a small number of its columns and rows. Thus, CUR decomposition can be regarded as an extension of the Nystr\"{o}m approximation. In this paper we establish a more general error bound for the adaptive column/row sampling algorithm, based on which we propose more accurate CUR and Nystr\"{o}m algorithms with expected relative-error bounds. The proposed CUR and Nystr\"{o}m algorithms also have low time complexity and can avoid maintaining the whole data matrix in RAM. In addition, we give theoretical analysis for the lower error bounds of the standard Nystr\"{o}m method and the ensemble Nystr\"{o}m method. The main theoretical results established in this paper are novel, and our analysis makes no special assumption on the data matrices.

Relevant initiatives  

Related knowledge about this paper Reproduced results (crowd-benchmarking and competitions) Artifact and reproducibility checklists Common formats for research projects and shared artifacts Reproducibility initiatives


Please log in to add your comments!
If you notice any inapropriate content that should not be here, please report us as soon as possible and we will try to remove it within 48 hours!