Bayes optimal kernel discriminant analysis
Bayes optimal kernel discriminant analysis
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DOI：
10.1109/cvpr.2010.5539952
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
Di You;Aleix M. Martinez
中科院分区：
文献类型：
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作者：
Di You;Aleix M. Martinez
核方法提供了一种有效的机制来获得非线性算法。在分类问题以及特征提取中，基于核的方法将原始非线性可分离的数据映射到本质上更高维的空间中，其中数据是线性可分离的，并且可以很容易地用现有的有效线性方法进行分类。对于一个给定的核函数，主要的挑战是确定核的参数，将原来的非线性问题映射到一个线性的。本文导出了判别分析中核参数选择的贝叶斯最优准则。我们的标准选择的内核参数，最大限度地提高（贝叶斯）的分类精度在内核空间。我们还展示了如何使用相同的标准在多峰类分布问题的核空间中进行子类选择。广泛的实验评估表明，所提出的标准的优越性超过国家的最先进的。
Kernel methods provide an efficient mechanism to derive nonlinear algorithms. In classification problems as well as in feature extraction, kernel-based approaches map the originally nonlinearly separable data into a space of intrinsically much higher dimensionality where the data is linearly separable and can be readily classified with existing and efficient linear methods. For a given kernel function, the main challenge is to determine the parameters of the kernel which maps the original nonlinear problem to a linear one. This paper derives a Bayes optimal criterion for the selection of the kernel parameters in discriminant analysis. Our criterion selects the kernel parameters that maximize the (Bayes) classification accuracy in the kernel space. We also show how we can use the same criterion to do subclass selection in the kernel space for problems with multimodal class distributions. Extensive experimental evaluation demonstrates the superiority of the proposed criterion over the state of the art.