A Novel Sparse Penalty for Singular Value Decomposition  

作　　者：WANG Caihua LIU Juan MIN Wenwen QU Aiping 

机构地区：[1]The State Key Laboratory of Software Engineering, School of Computer, Wuhan University, Wuhan 430072, China

出　　处：《Chinese Journal of Electronics》2017年第2期306-312,共7页电子学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.61272274,No.60970063);the National Science Foundation of Jiangsu Province(No.BK20161249);the program for New Century Excellent Talents in Universities(No.NCET-10-0644)

摘　　要：Singular value decomposition(SVD) is a tool widely used in data denoising,matrix approximation,recommendation system,text mining and computer vision.A ma jority 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 pro ject a vector onto a given sparse level in O(n) expected time.The efficient pro jection 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.Singular value decomposition（SVD） is a tool widely used in data denoising,matrix approximation,recommendation system,text mining and computer vision.A ma jority 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 pro ject a vector onto a given sparse level in O（n） expected time.The efficient pro jection 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.

关 键 词：Sparse controllable projection（SCP） Sparse singular value decomposition（SSVD） Sparse low rank matrix approximation（SLRMA） 

分 类 号：O241.6[理学—计算数学]