论文标题
封顶规范线性判别分析及其应用
Capped norm linear discriminant analysis and its applications
论文作者
论文摘要
经典的线性判别分析（LDA）基于平方的曲折标准，因此对异常值和噪声敏感。为了提高LDA的鲁棒性，在本文中，我们介绍了矩阵的限制L_ {2,1} - 使用非方格的L_2-Norm和“限制”操作，并进一步提出了一种新颖的限制L_ {2,1} -Snorm线性线性判别分析，称为Clda。由于使用了限制的L_ {2,1} -Norm，CLDA可以有效地删除极端异常值并抑制噪声数据的效果。实际上，CLDA也可以被视为加权LDA。 CLDA通过一系列具有理论收敛性的广义特征值问题解决。人工数据集，一些UCI数据集和两个图像数据集的实验结果证明了CLDA的有效性。
Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, in this paper, we introduce capped l_{2,1}-norm of a matrix, which employs non-squared l_2-norm and "capped" operation, and further propose a novel capped l_{2,1}-norm linear discriminant analysis, called CLDA. Due to the use of capped l_{2,1}-norm, CLDA can effectively remove extreme outliers and suppress the effect of noise data. In fact, CLDA can be also viewed as a weighted LDA. CLDA is solved through a series of generalized eigenvalue problems with theoretical convergency. The experimental results on an artificial data set, some UCI data sets and two image data sets demonstrate the effectiveness of CLDA.
