KNN Loss and Deep KNN

The k Nearest Neighbor (KNN) algorithm has been widely applied in various supervised learning tasks due to its simplicity and effectiveness. However, the quality of KNN decision making is directly affected by the quality of the neighborhoods in the modeling space. Efforts have been made to map data to a better feature space either implicitly with kernel functions, or explicitly through learning linear or nonlinear transformations. However, all these methods use pre-determined distance or similarity functions, which may limit their learning capacity. In this paper, we present two loss functions, namely KNN Loss and Fuzzy KNN Loss, to quantify the quality of neighborhoods formed by KNN with respect to supervised learning, such that minimizing the loss function on the training data leads to maximizing KNN decision accuracy on the training data. We further present a deep learning strategy that is able to learn, by minimizing KNN loss, pairwise similarities of data that implicitly maps data to a feature space where the quality of KNN neighborhoods is optimized. Experimental results show that this deep learning strategy (denoted as Deep KNN) outperforms state-of-the-art supervised learning methods on multiple benchmark data sets.