摘要
对于遮挡、光照等影响因素,低秩线性回归模型具有很好的鲁棒性。LRRR(Low Rank Ridge Regression)以及DENLR(Discriminative Elastic-net Regularized Linear Regression)通过正则化系数矩阵在一定程度上减少了LRLR(Low Rank Linear Regression)产生的过拟合现象。但其没有考虑子空间数据的错误逼近,投影矩阵不能准确地将数据映射到目标空间。鉴于此,提出了一种运算更快、更具判别性的低秩线性回归分类新方法。首先,将0-1构成的矩阵作为线性回归的目标值;其次,利用核范数作为低秩约束的凸近似;然后,通过正则化各类别之间的距离矩阵和模型输出矩阵来降低过拟合,同时可以增强投影子空间的判别性;再次,利用增广拉格朗日乘子(Augmented Lagrangian Multiplier,ALM)优化目标函数;最后,在子空间中利用最近邻分类器进行分类。在AR、FERET人脸数据库、Stanford 40Actions、Caltech-UCSD Bird以及Oxford 102Flowers数据库上进行相关算法的对比实验,结果表明所提算法是有效的。
The low rank linear regression model has good robustness for the influence of occlusion and illumination and so on.To a certain extent,the overfitting phenomenon of LRLR(Low Rank Linear Regression)is reduced in LRRR(Low Rank Ridge Regression)and DENLR(Discriminative Elastic-Net Regularized Linear Regression)by regularization coefficient matrix.Because the error approximation of data in subspace is ill-considered,the data are hardly mapped to the target space accurately via projection matrix.This paper proposed has low rank linear regression classification method which has a faster computing speed and is more discriminative.Firstly,the 0-1 constitutive matrix is regarded as the target value of the linear regression.Secondly,the kernel norm is used as the convex approximation of low rank constraints.Thirdly,all kinds of the distance matrix and the model output matrix are regularized to reduce overfitting phenomenon,at the same time it can enhance the spatial discriminant of projection subspace.Then,the augmented Lagrange multiplier(ALM)is used to optimize the objective function.Finally,the nearest neighbor classifier is used for classification in subspace.We compared the related algorithms on AR,FERET face database,Stanford 40 Actions database,Caltech-UCSD Birds database and Oxford 102 Flowers database.The experimental results show that the proposed algorithm is effective.
作者
于传波
聂仁灿
周冬明
黄帆
丁婷婷
YU Chuan- bo ,NIE Ren- can ,ZHOU Dong-ming ,HUANG Fan ,DING Ting- ring(School of Information Science and Engineering, Yunnan University, Kunming 650500, Chin)
出处
《计算机科学》
CSCD
北大核心
2018年第B06期151-156,共6页
Computer Science
基金
国家自然科学基金(61365001
61463052)资助
关键词
低秩
线性回归
正则化
分类
Low rank
Linear regression
Regularization
Classification