Kernel naive Bayes discrimination for high-dimensional pattern recognition.
Kernel naive Bayes discrimination for high-dimensional pattern recognition.
复制标题
用于高维模式识别的内核朴素贝叶斯判别。
DOI：
10.1111/anzs.12279
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发表时间：
2019
影响因子：
1.1
通讯作者：
Kanta Naito and Hiroaki Tanaka,
中科院分区：
文献类型：
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作者：
Inge Koch;Kanta Naito and Hiroaki Tanaka,
核判别分析将原始分类问题转化为特征空间，解决了维度和样本量互换的问题。在高维低样本大小(HDLSS)设置中，这会将“维”降低到样本大小。对于HDLSS两类问题，我们修改了Mika的核Fisher判别函数，它通常即使在核设置下也是不适定的；参见Mikaet等人。(1999年)。利用一次和二次多项式核函数，提出了一种核朴素贝叶斯判别函数及其光滑化形式。在固定样本量和增加维度的情况下，我们给出了核判别函数、判别方向和核判别函数的误差概率的渐近表达式。理论计算得到了模拟的补充，模拟结果表明，随着维度的增长，估计器收敛到总体数量。在实际的HDLSS数据上，我们展示了新的易于实现的判别规则的性能。对于这样的数据，我们的结果清楚地表明了新的判别规则，特别是它们的平滑版本，相对于Mika的核Fisher版本，并且通常也超过了常用的朴素贝叶斯判别规则的性能。
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 Mikaet al. (1999). We propose a kernel naive Bayes discriminant function and itssmoothedversion, 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.