张量补全算法及其在人脸识别中的应用

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摘要数据丢失问题通常可以归结为矩阵补全问题，而矩阵补全是继压缩感知理论之后的又一种重要的信号获取方法。在实际应用中，数据样例往往具有多线性性，即数据集可以表示成高阶张量。本文研究了张量补全问题及其在人脸识别中的应用。基于张量的低维Tucker分解，提出张量补全的迭代算法，并且证明在算法的迭代过程中，估计张量与其Tucker逼近张量的距离是单调递减的。实验结果表明张量补全算法在补全张量和人脸识别上的可行性与有效性。

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	史加荣
	焦李成
	尚凡华

关键词 ：张量补全, 人脸识别, 数据丢失问题, 矩阵补全, Tucker分解

Abstract：Missing data problems are commonly attributed to the matrix completion problem, and matrix completion is an important method of signal acquisitions following compressing sensing. The data examples have the property of multi-linearity in applications, that is, the data set can be represented by higher order tensors. The tensor completion problem and its applications in face recognition are studied. Based on lower-dimensional Tucker decomposition of tensors, an iterative algorithm is proposed to complete tensors. And the distance between the estimating tensor and its Tucker approximation tensor monotonically decreases during the iterative procedure. Experimental results demonstrate the effectiveness and feasibility of the proposed method in completing tensor and face recognition.

Key words： Tensor Completion Face Recognition Missing Data Problem Matrix Completion Tucker Decomposition

收稿日期: 2009-09-10

ZTFLH:

TP391.4

基金资助:国家973重点基础研究发展计划(No.2006CB705707),国家863高技术研究发展计划(No.2007AA12Z223,2007AA12Z136),国家自然科学基金(No.60603019,60602064,60702062)资助

作者简介: 史加荣，男，1979年生，博士研究生，主要研究方向为机器学习与模式识别.E-mail:jiarongs3@yahoo.cn.焦李成，男，1959年生，教授，博士生导师，主要研究方向为自然计算，数据挖掘，图像处理，智能信息处理.尚凡华，男，1979年生，博士研究生，主要研究方向为机器学习.

引用本文:

史加荣，焦李成，尚凡华. 张量补全算法及其在人脸识别中的应用[J]. 模式识别与人工智能, 2011, 24(2): 255-261. SHI Jia-Rong, JIAO Li-Cheng, SHANG Fan-Hua. Tensor Completion Algorithm and Its Applications in Face Recognition. , 2011, 24(2): 255-261.

链接本文:

http://manu46.magtech.com.cn/Jweb_prai/CN/ 或 http://manu46.magtech.com.cn/Jweb_prai/CN/Y2011/V24/I2/255

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