Multi-scale Deep Nearest Neighbors

We propose a differentiable loss function for learning an embedding space by minimizing the upper bound of the leave-one-out classification error rate of 1-nearest neighbor classification error in the latent space. To evaluate the resulting space, in addition to the classification performance, we examine the problem of finding subclasses. In many applications, it is desired to detect unknown subclasses that might exist within known classes. For example, discovering subtypes of a known disease may help develop customized treatments. Analogous to the hierarchical clustering, subclasses might exist on different scales. The proposed method provides a mechanism to target subclasses in different scales.