ROBUST NEAREST-NEIGHBOR METHODS FOR CLASSIFYING HIGH-DIMENSIONAL DATA
ROBUST NEAREST-NEIGHBOR METHODS FOR CLASSIFYING HIGH-DIMENSIONAL DATA
复制标题
DOI：
10.1214/08-aos591
复制
发表时间：
2009-12-01
影响因子：
4.5
通讯作者：
Hall, Peter
中科院分区：
文献类型：
--
作者：
Chan, Yao-Ban;Hall, Peter
我们提出了一种鲁棒的最近邻方法来分类高维数据。该方法通过采用阈值和截断为0和1的序列来提高灵敏度，以减少重尾数据的有害影响。提出了阈值选择的经验法则。它们只需要最少的数据，每个种群只需要一个数据向量。研究了性能的理论和数值方面，特别注意数据组件之间的相关性和异质性的影响。在理论方面，我们的截断、阈值、最近邻分类器与更传统的非鲁棒方法具有相同的分类边界，后者需要有限的矩才能获得良好的性能。特别是，我们的方法的更强的健壮性并不是以降低有效性为代价的。此外，当两个训练样本量都等于1时，我们的新方法的性能可以与需要具有已知边缘分布的独立且同分布数据的最优分类器的性能相等；然而，我们的分类器本身并不需要这种类型的条件。
We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of heavy-tailed data. Empirical rules are suggested for choosing the threshold. They require the bare minimum of data only one data vector is needed from each population. Theoretical and numerical aspects of performance are explored, paying particular attention to the impacts of correlation and heterogeneity among data components. On the theoretical side, it is shown that our truncated, thresholded, nearest-neighbor classifier enjoys the same classification boundary as more conventional, nonrobust approaches, which require finite moments in order to achieve good performance. In particular, the greater robustness of our approach does not come at the price of reduced effectiveness. Moreover, when both training sample sizes equal 1, our new method can have performance equal to that of optimal classifiers that require independent and identically distributed data with known marginal distributions; yet, our classifier does not itself need conditions of this type.