Multiclass Classification via Class-Weighted Nearest Neighbors
This work addresses classification challenges in imbalanced settings, but it is incremental as it builds on existing k-nearest neighbors methods with theoretical extensions.
The paper tackles multiclass classification with imbalanced classes by analyzing a class-weighted k-nearest neighbors variant, deriving theoretical bounds on accuracy and error metrics, and enabling optimization of practical classification metrics like F1 score.
We study statistical properties of the k-nearest neighbors algorithm for multiclass classification, with a focus on settings where the number of classes may be large and/or classes may be highly imbalanced. In particular, we consider a variant of the k-nearest neighbor classifier with non-uniform class-weightings, for which we derive upper and minimax lower bounds on accuracy, class-weighted risk, and uniform error. Additionally, we show that uniform error bounds lead to bounds on the difference between empirical confusion matrix quantities and their population counterparts across a set of weights. As a result, we may adjust the class weights to optimize classification metrics such as F1 score or Matthew's Correlation Coefficient that are commonly used in practice, particularly in settings with imbalanced classes. We additionally provide a simple example to instantiate our bounds and numerical experiments.