An analysis of the coupling between training set and neighborhood sizes for the kNN classifier

We consider the relationship between training set size and the parameter k for the k-Nearest Neighbors (kNN) classifier. When few examples are available, we observe that accuracy is sensitive to k and that best k tends to increase with training size. We explore the subsequent risk that k tuned on partitions will be suboptimal after aggregation and re-training. This risk is found to be most severe when little data is available. For larger training sizes, accuracy becomes increasingly stable with respect to k and the risk decreases.