Adaptive Nearest Neighbor: A General Framework for Distance Metric Learning
This work addresses the challenge of distance metric learning for K-NN classification, offering a more flexible framework that could benefit machine learning practitioners, though it is incremental as it builds upon and generalizes prior methods.
The authors tackled the problem of improving K-NN classifier performance by learning an appropriate distance metric, proposing a novel adaptive nearest neighbor (ANN) algorithm that generalizes existing methods and demonstrates effectiveness across various datasets.
$K$-NN classifier is one of the most famous classification algorithms, whose performance is crucially dependent on the distance metric. When we consider the distance metric as a parameter of $K$-NN, learning an appropriate distance metric for $K$-NN can be seen as minimizing the empirical risk of $K$-NN. In this paper, we design a new type of continuous decision function of the $K$-NN classification rule which can be used to construct the continuous empirical risk function of $K$-NN. By minimizing this continuous empirical risk function, we obtain a novel distance metric learning algorithm named as adaptive nearest neighbor (ANN). We have proved that the current algorithms such as the large margin nearest neighbor (LMNN), neighbourhood components analysis (NCA) and the pairwise constraint methods are special cases of the proposed ANN by setting the parameter different values. Compared with the LMNN, NCA, and pairwise constraint methods, our method has a broader searching space which may contain better solutions. At last, extensive experiments on various data sets are conducted to demonstrate the effectiveness and efficiency of the proposed method.