A Novel Sparse Penalty for Singular Value Decomposition. Issue 2 (1st March 2017)

• Record Type: Journal Article
• Authors: Wang, Caihua; Liu, Juan; Min, Wenwen; Qu, Aiping
• Is Part Of: Chinese journal of electronics. Volume 26:Issue 2(2017)
• Page Start: 306
• Page End: 312
• Publication Date: 2017-03-01
• Subjects: Sparse controllable projection (SCP) -- Sparse singular value decomposition (SSVD) -- Sparse low rank matrix approximation (SLRMA); approximation theory -- computational complexity -- data analysis -- singular value decomposition; sparse penalty -- sparse singular value decomposition -- SSVD -- data analysis -- O(n) time -- sparse low rank matrix approximation -- SLRMA; Electronics -- Periodicals; Electronics -- China -- Periodicals; Electronics; China; Periodicals; 621.38105
• DOI: 10.1049/cje.2017.01.025
• Languages: English
• ISSNs: 1022-4653

Abstract

Abstract : Singular value decomposition (SVD) is a tool widely used in data denoising, matrix approximation, recommendation system, text mining and computer vision. A majority of applications prefer sparse singular vectors to capture inherent structures and patterns of the input data so that the results are interpretable. We present a novel penalty for SVD to achieve sparsity. Comparing with the traditional penalties, the proposed penalty is scale, dimensional insensitive and bounded between 0 and 1, which are in favor of controlling sparsity. Regulated by the penalty, we provide an efficient algorithm to project a vector onto a given sparse level in O ( n ) expected time. The efficient projection algorithm serve as a drudge for sparse SVD (SSVD). In experiments, SSVD is efficient and could capture the latent structures and patterns of the input data.