基于多核学习的投影非负矩阵分解算法

计算机科学 ›› 2014, Vol. 41 ›› Issue (2): 64-67.

基于多核学习的投影非负矩阵分解算法

李谦,景丽萍,于剑

北京交通大学计算机与信息技术学院数字出版技术国家重点实验室筹北京100044;北京交通大学计算机与信息技术学院北京100044;北京交通大学计算机与信息技术学院北京100044

出版日期:2018-11-14 发布日期:2018-11-14
基金资助:
本文受中央高校基金科研业务费专项基金(2011JBM030,2013JBZ005),教育部博士点基金(20120009110006),北大方正集团有限公司数字出版技术国家重点实验室开放课题资助

Multi-kernel Projective Nonnegative Matrix Factorization Algorithm

LI Qian,JING Li-ping and YU Jian

Online:2018-11-14 Published:2018-11-14

摘要/Abstract

摘要： 非负矩阵分解(NMF)把给定的数据矩阵分解成低维的非负基矩阵和对应的系数矩阵,两者之间存在必然联系。为此,研究者将基矩阵转换为系数矩阵的投影,进一步提高分解效率。但是该方法无法处理非线性数据,核函数的引入部分解决了此问题,却同时导致核函数参数选择的问题。基于多核学习理论,提出了一种多核学习的投影非负矩阵分解(MKPNMF)算法,该算法有效地避免了核函数参数选择的问题,同时提高了学习性能。在实际人脸数据上的实验结果表明,MKPNMF较已有的NMF类方法具备明显的性能优势。

关键词: 投影非负矩阵分解,核函数,多核学习中图法分类号TP391文献标识码A

Abstract: Nonnegative Matrix Factorization (NMF) decomposes the data into non-negative base matrix and coefficient matrix,and both of them have relationship with each other．Thus,some researchers rebuild the base matrix based on the projection of coefficient matrix．However,these two NMF-type methods can not satisfy the requirement of non-linear data analysis．With the development kernel learning,kernel function is introduced into the traditional NMF model for non-linear data analysis,which results in another problem,i.e.,kernel parameter selection.We presented a Multi-Kernel Projective Nonnegative Matrix Factorization(MKPNMF) method,which has ability to avoid the problem of kernel parameter selection and improves the final learning performance．A series of experiments on real-world face data were conducted.The results show that MKPNMF outperforms the existing NMF-type methods.

Key words: Projective nonnegative matrix factorization,Kernel function,Multi-kernel learning

李谦,景丽萍,于剑. 基于多核学习的投影非负矩阵分解算法[J]. 计算机科学, 2014, 41(2): 64-67. https://doi.org/

LI Qian,JING Li-ping and YU Jian. Multi-kernel Projective Nonnegative Matrix Factorization Algorithm[J]. Computer Science, 2014, 41(2): 64-67. https://doi.org/

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