融合协作表达和重构判别分析的数据降维算法  

Dimensionality reduction via collaborative constrained reconstructive discriminant analysis

作　　者：楼宋江 马杨珲[1] 向坚[1] 赵小明[2] LOU Song-jiang;MA Yang-hui;XIANG Jian;ZHAO Xiao-ming(School of Information and Electronic Engineering, Zhejiang University of Science and Technology, Hangzhou 310023,China;Institute of Image Processing ＆ Pattern Recognition, Tai Zhou University, Taizhou Zhejiang, 318000, China)

机构地区：[1]浙江科技学院,信息与电子工程学院,浙江杭州310023 [2]台州学院图像处理与模式识别研究所,浙江台州318000

出　　处：《光电子．激光》2018年第5期553-559,共7页Journal of Optoelectronics·Laser

基　　金：浙江省自然科学基金项目(LQ15F020001)资助项目

摘　　要：数据降维是处理高维数据的有效手段。子空间学习算法由于其计算量小,性能较为出色而广泛应用于模式识别等领域,传统的子空间学习算法均可归纳为图嵌入算法框架中。稀疏表达是近年来的一个研究热点,并广泛应用于信号处理和模式识别等领域,但计算复杂度较高。在稀疏表达的基础上,研究者提出了协作表达。相比稀疏表达,协作表达算法由于其有一个闭式解,因而计算量较小且判别性能较好,可以看成是数据表达的一种有效方法。本文从协作表达的角度来解释图嵌入算法,将图嵌入算法看作是一类回归模型。通过最小化类内重构误差散度的同时最大化类间重构误差散度,提出了一种新的图嵌入算法,即重构判别分析,并将它应用于该回归模型中,然后将问题归结为一广义的特征值问题,算法在某种程度上能有效避免子空间学习过程中矩阵的奇异性问题。在人脸识别上的实验验证了算法的正确性和有效性。Dimensionality reduction is an effective method for treating high dimensional data.Subspace learning is widely used in pattern recognition due to its low complexity and desirable performance,and most of the subspace learning algorithms can be plugged into the graph embedding framework.Sparse representation gains much attention in recent years,and has wide applications in signal processing and pattern recognition,but it is time consuming.Based on sparse representation,collaborative representation is proposed.Compared with sparse representation,collaborative representation has a tractable closedform solution and better discriminative power,so it is widely used in data representation and visual classification.In this paper,the graph embedding is formulated as a manner of collaborative representation.By minimizing the intra-class reconstructive error scatter and maximizing the inter-class reconstructive error scatter,a new graph embedding algorithm called reconstructive discriminant analysis is proposed,and is applied in this regression model,then the solution is reduced to a generalized eigen-value problem,which to some extent can avoid the singularity problem in subspace learning algorithms.Various experiments on face recognition demonstrate the correctiveness and effectiveness of the proposed algorithm.

关 键 词：数据降维 协作表达 图嵌入算法 重构判别分析 人脸识别 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]