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We present Stochastic Neighborhood Compression (SNC), an algorithm to compress a dataset for the purpose of k-nearest neighbor (kNN) classification. Given training data, SNC learns a much smaller synthetic data set, that minimizes the stochastic 1-nearest neighbor classification error on the training data. This approach has several appealing properties: due to its small size, the compressed set speeds up kNN testing drastically (up to several orders of magnitude, in our experiments); it makes the kNN classifier substantially more robust to label noise; on 4 of 7 data sets it yields lower test error than kNN on the entire training set, even at compression ratios as low as 2%; finally, the SNC compression leads to impressive speed ups over kNN even when kNN and SNC are both used with ball-tree data structures, hashing, and LMNN dimensionality reduction, demonstrating that it is complementary to existing state-of-the-art algorithms to speed up kNN classification and leads to substantial further improvements.