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首页> 外文期刊>Australian & New Zealand journal of statistics >Kernel naive Bayes discrimination for high-dimensional pattern recognition
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Kernel naive Bayes discrimination for high-dimensional pattern recognition

机译：内核天真贝叶斯歧视高维模式识别

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摘要

Kernel discriminant analysis translates the original classification problem into feature space and solves the problem with dimension and sample size interchanged. In high-dimension low sample size (HDLSS) settings, this reduces the 'dimension' to that of the sample size. For HDLSS two-class problems we modify Mika's kernel Fisher discriminant function which - in general - remains ill-posed even in a kernel setting; see Mika et al. (1999). We propose a kernel naive Bayes discriminant function and its smoothed version, using first- and second-degree polynomial kernels. For fixed sample size and increasing dimension, we present asymptotic expressions for the kernel discriminant functions, discriminant directions and for the error probability of our kernel discriminant functions. The theoretical calculations are complemented by simulations which show the convergence of the estimators to the population quantities as the dimension grows. We illustrate the performance of the new discriminant rules, which are easy to implement, on real HDLSS data. For such data, our results clearly demonstrate the superior performance of the new discriminant rules, and especially their smoothed versions, over Mika's kernel Fisher version, and typically also over the commonly used naive Bayes discriminant rule.
机译：内核判别分析将原始分类问题转化为特征空间，并解决了尺寸和样本大小的问题互换。在高尺寸低样体大小（HDLSS）设置中，这将其降低到样本大小的“维度”。对于HDLSS两类问题，我们修改Mika的内核Fisher判别函数 - 通常 - 即使在内核设置中也仍然没有姿势;见mika等。 （1999）。我们使用第一和二级多项式内核提出了一个内核天真贝叶斯判别功能及其平滑的版本。对于固定样本大小和增加的维度，我们向内核判别函数，判别方向和核心判别函数的误差概率提出渐近表达。理论计算通过模拟补充，显示估算器在尺寸的增加时估计到群体数量的收敛性。我们说明了新的判别规则的性能，即在真正的HDLS数据上易于实现。对于此类数据，我们的结果清楚地展示了新判别规则的卓越性能，特别是他们的平滑版本，尤卡尔的内核Fisher版本，通常也在常用的天真贝叶斯判别规则上。

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