崔振, 山世光, 陈熙霖. 结构化稀疏线性判别分析[J]. 计算机研究与发展, 2014, 51(10): 2295-2301.
 引用本文: 崔振, 山世光, 陈熙霖. 结构化稀疏线性判别分析[J]. 计算机研究与发展, 2014, 51(10): 2295-2301.
Cui Zhen, Shan Shiguang, Chen Xilin. Structured Sparse Linear Discriminant Analysis[J]. Journal of Computer Research and Development, 2014, 51(10): 2295-2301.
 Citation: Cui Zhen, Shan Shiguang, Chen Xilin. Structured Sparse Linear Discriminant Analysis[J]. Journal of Computer Research and Development, 2014, 51(10): 2295-2301.

## Structured Sparse Linear Discriminant Analysis

• 摘要: 在监督场景下线性判别分析(linear discriminant analysis, LDA)是一种非常有效的特征提取方法.然而，LDA在小样本情况下通常会出现过拟合现象，并且学习的投影变换难以给出人类认知上的解释.针对这些问题，特别是可解释性结构的发现，借助于LDA的线性回归模型和结构化稀疏L\-2,1范数，提出了结构化稀疏线性判别分析(structured sparse LDA, SSLDA)方法.进一步，为了去除线性变换间的相关性，提出了正交化的SSLDA(orthogonalized SSLDA, OSSLDA)，它能更加有效地学习到细致的结构信息.为了求解这2个模型，引入了一个半二次的优化算法,它在投影变换和新引入的辅助变量之间采用交替优化的思想.为了验证所提出的方法，在AR、扩展的YaleB和MultiPIE 3个人脸数据库上对比了LDA及其变种方法，实验表明了所提出方法的有效性以及可解释性.

Abstract: Linear discriminant analysis (LDA) is a very efficient image feature extraction technique in the supervised scenario. However, LDA often leads to over-fitting when using small scale training samples, and simultaneously might not show an intuitive explanation for the learnt projections from the view of human cognition. To handle these problems, especially for the discovery of those interpretability structures, a called structured sparse LDA (SSLDA) method is proposed by employing the linear regression model of LDA and the structured sparse L\-2,1 mixed norm. Furthermore, to remove the correlations of the learnt linear transforms, the orthogonalized SSLDA (OSSLDA) is also proposed to learn more subtle textural structure information from face images. To solve both two proposed models: SSLDA and OSSLDA, we further introduce a simply and efficient half-quadratic optimization algorithm, which incorporates an auxiliary variable into the objective function and then alternately optimizes between the projecting variable and the auxiliary variable. To evaluate our proposed method, SSLDA and OSSLDA, we conduct extensive experiments on three public face datasets, AR, Extended Yale B and MultiPIE, for the face recognition task by comparing LDA and its several classical variants. The experimental results show the benefits of the proposed methods on both classification accuracy and interpretability.

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