Linear discriminant analysis (LDA) is a well-known supervised method for dimensionality reduction in which the global structure of data can be preserved. The classical LDA is sensitive to the noises, and the projection direction of LDA cannot preserve the main energy. This article proposes a novel feature extraction model with l 2,1 norm constraint based on LDA, termed as RALDA. This model preserves within-class local structure in the latent subspace according to the label information. To reduce information loss, it learns a projection matrix and an inverse projection matrix simultaneously. By introducing an implicit variable and matrix norm transformation, the alternating direction multiple method with updating variables is designed to solve the RALDA model. Moreover, both computational complexity and weak convergence property of the proposed algorithm are investigated. The experimental results on several public databases have demonstrated the effectiveness of our proposed method.

中文翻译：

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具有双向重构约束的鲁棒自适应线性判别分析

线性判别分析 (LDA) 是一种众所周知的降维监督方法，其中可以保留数据的全局结构。经典LDA对噪声敏感，LDA的投影方向不能保留主能量。本文提出了一种新颖的特征提取模型l 2,1基于LDA的范数约束，称为RALDA。该模型根据标签信息在潜在子空间中保留类内局部结构。为了减少信息损失，它同时学习了一个投影矩阵和一个逆投影矩阵。通过引入隐变量和矩阵范数变换，设计了具有更新变量的交替方向多重方法来求解RALDA模型。此外，还研究了该算法的计算复杂度和弱收敛性。在几个公共数据库上的实验结果证明了我们提出的方法的有效性。