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[1]唐肝翌*,卢桂馥. 基于L1-范数的鲁棒稀疏的张量PCA人脸图像分析[J].南京大学学报(自然科学),2018,54(1):31.[doi:10.13232/j.cnki.jnju.2018.01.004]
 Tang Ganyi*,Lu Guifu. Robust and sparse tensor PCA with L1-norm for faces analysis[J].Journal of Nanjing University(Natural Sciences),2018,54(1):31.[doi:10.13232/j.cnki.jnju.2018.01.004]
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 基于L1-范数的鲁棒稀疏的张量PCA人脸图像分析()
     

《南京大学学报(自然科学)》[ISSN:0469-5097/CN:32-1169/N]

卷:
54
期数:
2018年第1期
页码:
31
栏目:
出版日期:
2018-02-01

文章信息/Info

Title:
 Robust and sparse tensor PCA with L1-norm for faces analysis
作者:
 唐肝翌*卢桂馥
 安徽工程大学计算机与信息学院,芜湖,241000
Author(s):
 Tang Ganyi*Lu Guifu
 School of Computer and Information,Anhui Polytechnic University,Wuhu,241000,China
关键词:
 主成分分析(PCA)张 量稀疏模型L1-范数鲁 棒
Keywords:
 principal component analysis(PCA)tensorsparse modelL1-normrobust
分类号:
TP391
DOI:
10.13232/j.cnki.jnju.2018.01.004
文献标志码:
A
摘要:
 张量主成分分析(Tensor Principal Component Analysis,TPCA)是主成分分析(Principal Component Analysis,PCA)在多维空间上的推广,能充分利用图像/视频的空间关联,在图像分析和视频处理中扮演了重要的角色.传统的张量PCA方法提取的特征向量是非稀疏的,这使得其很难进行解释.近年来出现了众多稀疏PCA方法,能提取只包含少量非零元的特征.把稀疏特征提取引入到张量分析,提出一种鲁棒稀疏的张量PCA方法(TPCA-L1S).首先,设计了能实现稀疏特征提取的目标函数.一方面,用L1范数代替Frobenius-范数,使得算法对异常数据更加鲁棒;另一方面,在目标函数中引入弹性网,联合使用Lasso与Ridge惩罚因子来实现稀疏化,增强了算法的语义解释性.然后,设计了一种基于二阶张量的投影矩阵交替求解算法,二阶张量便于数学描述,也易于推广到更高阶张量.此求解算法分为两个步骤(V,U分别表示左投影矩阵和右投影矩阵),先固定U优化V,再固定V的值优化U,两个步骤反复交替执行,直到收敛.每个步骤都采用贪心算法以迭代的方式逐个特征提取以求得U或V.最后,对迭代过程的单调性做了理论证明.基于ORL,Yale和Feret库,将TPCA-L1S应用于人脸图像分析并与其他常见方法作比较,实验结果验证了该模型的有效性.
Abstract:
 Tensor Principal Component Analysis(TPCA),which is a generalization of classical PCA(Principal Component Analysis)in multiple dimension space and can make full use of the spatial relationship of images/videos,plays an important role in image analysis and vision processing.The basis vectors of tensor PCA,however,are still dense,which makes it difficult to explain.Various sparse PCA methods,which extract principal components of the given data with sparse non-zero loadings,have been proposed in recent years.In this paper,we extend sparse feature extraction of PCA to tensor analysis and propose a robust and sparse tensor PCA with L1-norm(TPCA-L1S).Firstly,an objective function for TPCA-L1S is designed.On the one hand,we replace Frobenius-norm with L1-norm in the objective function,which makes it more robust to outlier.On the other hand,the elastic net,which generalizes the sparsity-inducing lasso penalty by combining the ridge penalty,is integrated into the objective function to enhance the interpretability of the tensor PCA.Then,an alternative tensor projection optimization procedure is developed in the second-order tensor PCA which is easy to be formulated and can be extended to much higher order.It is convenient to use U and V to denote the projection matrices and refer V and U as to the left and right projection matrices respectively.The procedure is divided into two steps.At the first step, V is computed while U is fixed,and then at the second step, U is computed while V is fixed.The two steps repeat until convergence.A greedy procedure,which is for computing projection matrices U and V,is designed to extract basic features one by one.Finally,the monotonicity of the iterative greedy procedure is theoretically guaranteed.The proposed TPCA-L1S is applied to several face image analysis problems upon ORL,Yale and Feret databases and compared with some other conventional methods.Experimental results confirm its effectiveness.

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备注/Memo

备注/Memo:
基金项目:国家自然科学基金(61572033),安徽省高校自然科学研究重大项目(KJ2015ZD08),安徽省高等教育提升计划(TSKJ2015B14)
收稿日期:2017-12-12
*通讯联系人,E-mail:tangganhyi.tony@qq.com
更新日期/Last Update: 2018-01-31