基于Fisher判别分析的增量式非负矩阵分解算法

doi:10.16451/j.cnki.issn1003-6059.201806003

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摘要

增量式非负矩阵分解算法是基于子空间降维技术的无监督增量学习方法.文中将Fisher判别分析思想引入增量式非负矩阵分解中,提出基于Fisher判别分析的增量式非负矩阵分解算法.首先,利用初始样本训练的先验信息,通过索引矩阵对新增系数矩阵进行初始化赋值.然后,将增量式非负矩阵分解算法的目标函数改进为批量式的增量学习算法,在此基础上施加类间散度最大和类内散度最小的约束.最后,采用乘性迭代的方法计算分解后的因子矩阵.在ORL、Yale B和PIE等3个不同规模人脸数据库上的实验验证文中算法的有效性.

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	蔡竞
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关键词 ：子空间降维, 有监督学习, Fisher判别分析, 非负矩阵分解, 增量学习

Abstract：

Incremental non-negative matrix factorization is an unsupervised learning algorithm based on subspace dimensionality reduction technology. In this paper, the idea of fisher discriminant analysis is introduced into incremental non-negative matrix factorization, and an incremental learning algorithm of non-negative matrix factorization with discriminative information and constraints is proposed. Firstly, prior information of original training samples is utilized to initialize the incremental coefficient matrix through an index matrix. Secondly, the object function of incremental non-negative matrix factorization is improved to be a batch-incremental learning algorithm with the constraints of maximizing between-class scatter and minimizing within-class scatter. Finally, the factor matrices are calculated by the method of multiplicative iteration. Experimental results on ORL, Yale B and PIE face databases show the effectiveness of the proposed method.

收稿日期: 2018-03-09

ZTFLH:

TP 391.4

基金资助:

国家重点研发计划项目(No.2017YFC0803700)、国家自然科学基金项目(No.61602413)、浙江省教育厅科研项目(N0.Y201431023)、浙江省高校访问学者教师专业发展项目(No.FX2017069)资助

作者简介: 蔡竞(通讯作者),博士研究生,讲师,主要研究方向为图像处理、机器学习.E-mail:caijing@zjjcxy.cn. 王万良,博士,教授,主要研究方向为智能算法、网络控制.E-mail:wwl@zjut.edu.cn. 郑建炜,博士,副教授,主要研究方向为机器学习、特征提取.E-mail:zjw@zjut.edu.cn. 罗志坚,博士研究生,主要研究方向为模式识别、计算机视觉.E-mail:luozhijian@zju.edu.cn. 申思,博士研究生,讲师,主要研究方向为机器学习、智能交通.E-mail:shengsi@zjjcxy.cn.

引用本文:

蔡竞, 王万良, 郑建炜, 罗志坚, 申思. 基于Fisher判别分析的增量式非负矩阵分解算法[J]. 模式识别与人工智能, 2018, 31(6): 505-515. CAI Jing, WANG Wanliang, ZHENG Jianwei, LUO Zhijian, SHEN Si. Incremental Non-negative Matrix Factorization Based on Fisher Discriminant Analysis. , 2018, 31(6): 505-515.

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