基于Fisher判别分析的增量式非负矩阵分解算法  

Incremental Non-negative Matrix Factorization Based on Fisher Discriminant Analysis

作　　者：蔡竞[1,2,3] 王万良[1] 郑建炜 罗志坚[3] 申思[1,2] CAI Jing;WANG Wanliang;ZHENG Jianwei;LUO Zhijian;SHEN Si(College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310014;Department of Forensic Science and Technology, Zhejiang Police College, Hangzhou 310053;College of Computer Science and Technology, Zhejiang University, Hangzhou 310027)

机构地区：[1]浙江工业大学计算机科学与技术学院,杭州310014 [2]浙江警察学院刑事科学技术系,杭州310053 [3]浙江大学计算机科学与技术学院,杭州310027

出　　处：《模式识别与人工智能》2018年第6期505-515,共11页Pattern Recognition and Artificial Intelligence

基　　金：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

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.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.

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 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]