Worst-Case Linear Discriminant Analysis
Worst-Case Linear Discriminant Analysis
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发表时间：
2010-12
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通讯作者：
Yu Zhang;D. Yeung
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作者：
Yu Zhang;D. Yeung
由于所涉及数据的高维度，在许多应用中常常需要进行降维。在本文中，我们首先分析了传统线性判别分析（LDA）模型中使用的离散度度量，并注意到其公式是基于平均情况的观点。基于此分析，我们接着通过定义新的类间和类内离散度度量，提出了一种新的降维方法，称为最坏情况线性判别分析（WLDA）。这个新模型采用了最坏情况的观点，这种观点可以说更适合于诸如分类之类的应用。当训练数据点的数量或特征的数量不是很大时，我们放宽所涉及的优化问题，并将其表述为一个度量学习问题。否则，我们采用一种贪心方法，每次找到变换的一个方向。此外，我们还分析了WLDA的一种特殊情况，以展示它与传统LDA的关系。在几个基准数据集上进行的实验表明，与一些相关的降维方法相比，WLDA是有效的。
Dimensionality reduction is often needed in many applications due to the high dimensionality of the data involved. In this paper, we first analyze the scatter measures used in the conventional linear discriminant analysis (LDA) model and note that the formulation is based on the average-case view. Based on this analysis, we then propose a new dimensionality reduction method called worst-case linear discriminant analysis (WLDA) by defining new between-class and within-class scatter measures. This new model adopts the worst-case view which arguably is more suitable for applications such as classification. When the number of training data points or the number of features is not very large, we relax the optimization problem involved and formulate it as a metric learning problem. Otherwise, we take a greedy approach by finding one direction of the transformation at a time. Moreover, we also analyze a special case of WLDA to show its relationship with conventional LDA. Experiments conducted on several benchmark datasets demonstrate the effectiveness of WLDA when compared with some related dimensionality reduction methods.