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Nonpeaked Discriminant Analysis for Data Representation

机译：数据表示的非言语判别分析

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摘要

Of late, there are many studies on the robust discriminant analysis, which adopt L-1-norm as the distance metric, but their results are not robust enough to gain universal acceptance. To overcome this problem, the authors of this article present a nonpeaked discriminant analysis (NPDA) technique, in which cutting L-1-norm is adopted as the distance metric. As this kind of norm can better eliminate heavy outliers in learning models, the proposed algorithm is expected to be stronger in performing feature extraction tasks for data representation than the existing robust discriminant analysis techniques, which are based on the L-1-norm distance metric. The authors also present a comprehensive analysis to show that cutting L-1-norm distance can be computed equally well, using the difference between two special convex functions. Against this background, an efficient iterative algorithm is designed for the optimization of the proposed objective. Theoretical proofs on the convergence of the algorithm are also presented. Theoretical insights and effectiveness of the proposed method are validated by experimental tests on several real data sets.
机译：最近，有很多关于鲁棒判别分析的研究，它们采用L-1-范数作为距离度量，但是其结果不足以使鲁棒判别分析获得普遍认可。为了克服这个问题，本文的作者提出了一种非峰值判别分析（NPDA）技术，其中采用了切割L-1-范数作为距离度量。由于这种范式可以更好地消除学习模型中的异常值，因此与基于L-1-范数距离度量的现有鲁棒判别分析技术相比，预期该算法在执行数据表示的特征提取任务方面更强。作者还提出了一项综合分析，以表明利用两个特殊凸函数之间的差，可以同样好地计算出切削L-1-范数距离。在这种背景下，设计了一种有效的迭代算法来优化所提出的目标。给出了算法收敛性的理论证明。通过对几个真实数据集的实验测试，验证了该方法的理论见解和有效性。

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    Nanjing Forestry Univ Coll Informat Sci & Technol Nanjing 210037 Jiangsu Peoples R China|Chinese Acad Forestry Inst Forest Resource Informat Tech Beijing 100091 Peoples R China;

    Nanjing Univ Sci & Technol Coll Comp Sci & Technol Nanjing 210094 Jiangsu Peoples R China;

    Chinese Acad Forestry Inst Forest Resource Informat Tech Beijing 100091 Peoples R China|Natl Forestry & Grassland Adm Key Lab Forest Management & Growth Modeling Beijing 100091 Peoples R China;

    Soochow Univ Sch Comp Sci & Technol Suzhou 215000 Peoples R China|Hefei Univ Technol Sch Comp & Informat Hefei 230000 Anhui Peoples R China;

    Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China;

    Nanjing Audit Univ Jiangsu Key Lab Auditing Informat Engn Nanjing 211815 Jiangsu Peoples R China|Nanjing Audit Univ Sch Informat Engn Nanjing 211815 Jiangsu Peoples R China;

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  • 正文语种 eng
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  • 关键词

    Cutting L-norm distance; data classification; discriminant analysis; robustness;

    机译：切割L范数距离;数据分类;判别分析;健壮性;

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