Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation from the others, i.e., edge class, which occurs frequently in multi-class classification. First, the existence of edge classes often makes the total mean biased in the calculation of between-class scatter matrix. Second, the exploitation of ℓ 2 -norm based between-class distance criterion magnifies the extremely large distance corresponding to edge class. In this regard, a novel self-weighted robust LDA with ℓ 2,1 -norm based pairwise between-class distance criterion, called SWRLDA, is proposed for multi-class classification especially with edge classes. SWRLDA can automatically avoid the optimal mean calculation and simultaneously learn adaptive weights for each class pair without setting any additional parameter. An efficient re-weighted algorithm is exploited to derive the global optimum of the challenging ℓ 2,1 -norm maximization problem. The proposed SWRLDA is easy to implement and converges fast in practice. Extensive experiments demonstrate that SWRLDA performs favorably against other compared methods on both synthetic and real-world datasets while presenting superior computational efficiency in comparison with other techniques.

中文翻译：

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具有边缘类的多类分类的自加权鲁棒 LDA

线性判别分析 (LDA) 是一种流行的技术，用于学习多类分类中最具判别性的特征。现有的绝大多数LDA算法都容易被与其他类偏差很大的类所支配，即边缘类，这种情况在多类分类中经常出现。首先，边类的存在往往使总均值在类间散布矩阵的计算中产生偏差。二、利用ℓ2-基于类间距离标准的范数放大了对应于边缘类的极大距离。在这方面，一种新颖的具有 ℓ 的自加权稳健 LDA2,1基于 -norm 的成对类间距离准则，称为 SWRLDA，被提出用于多类分类，尤其是边缘类。SWRLDA 可以自动避免最优均值计算，同时学习每个类对的自适应权重，而无需设置任何额外的参数。利用有效的重新加权算法来推导具有挑战性的 ℓ 的全局最优值2,1-范数最大化问题。所提出的 SWRLDA 易于实现并且在实践中快速收敛。大量实验表明，SWRLDA 在合成数据集和真实世界数据集上优于其他比较方法，同时与其他技术相比具有更高的计算效率。