Spare L1-norm-based maximum margin criterion

Lu Gui-Fu; Tang Ganyi; Zou Jian

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Spare L1-norm-based maximum margin criterion

机译：基于备用L1范数的最大余量准则

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摘要

Maximum margin criterion (MMC) is a popular method for dimensionality reduction or feature extraction. MMC can alleviate the small size sample (SSS) problem encountered by linear discriminant analysis (LDA) and extract more discriminant vectors than LDA. However, the objective function of MMC is derived from L2-norm, which makes MMC be sensitive to noise and outliers. Besides, the basis vectors of MMC are dense, which makes it hard to explain the obtained features. To address the drawbacks of MMC, in this paper, we propose a novel sparse L1-norm-based maximum margin criterion (SMMC-L1). L1-norm rather than L2-norm is used in the objective function of SMMC-L1. Besides, L1-norm is also used as a lasso penalty to regularize the basis vectors. An iterative algorithm for solving SMMC-L1 is proposed. Experiment results on some databases show the effectiveness of the proposed SMMC-L1. (C) 2016 Elsevier Inc. All rights reserved.

机译：最大余量标准（MMC）是降维或特征提取的常用方法。 MMC可以缓解线性判别分析（LDA）遇到的小尺寸样本（SSS）问题，并提取比LDA更多的判别向量。但是，MMC的目标函数来自L2-范数，这使得MMC对噪声和离群值敏感。此外，MMC的基本向量很密集，这使得难以解释所获得的特征。为了解决MMC的缺点，在本文中，我们提出了一种基于稀疏L1范数的最大余量准则（SMMC-L1）。在SMMC-L1的目标函数中使用L1-norm而不是L2-norm。此外，L1-范数还用作套索罚分以对基向量进行正则化。提出了一种求解SMMC-L1的迭代算法。在一些数据库上的实验结果表明了所提出的SMMC-L1的有效性。（C）2016 Elsevier Inc.保留所有权利。

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来源
《Journal of visual communication & image representation》 |2016年第7期|11-17|共7页
作者
Lu Gui-Fu; Tang Ganyi; Zou Jian;
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作者单位

AnHui Polytech Univ, Sch Comp & Informat, Wuhu 241000, AnHui, Peoples R China|Nanjing Univ Sci & Technol, Key Lab Intelligent Percept & Syst High Dimens In, Minist Educ, Nanjing 210094, Jiangsu, Peoples R China;

AnHui Polytech Univ, Sch Comp & Informat, Wuhu 241000, AnHui, Peoples R China;

AnHui Polytech Univ, Sch Comp & Informat, Wuhu 241000, AnHui, Peoples R China;

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正文语种 eng
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Feature extraction; Linear discriminant analysis; L1-norm; L2-norm; Maximum margin criterion; Elastic net; Sparse subspace; Face recognition;

机译：特征提取线性判别分析L1范数L2范数最大边际准则弹性网稀疏子空间人脸识别;

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Spare L1-norm-based maximum margin criterion

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