Robust nearest-neighbor methods for classifying high-dimensional data

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.Comment: Published in at http://dx.doi.org/10.1214/08-AOS591 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Clustering and classifying images with local and global variability

A procedure for clustering and classifying images determined by three classification variables is presented. A measure of global variability based on the singular value decomposition of the image matrices, and two average measures of local variability based on spatial correlation and spatial changes. The performance of the procedure is compared using three different databases