Evolutionary Adaptive Neighborhood Learning: A Genetic Algorithm for Instance-Dependent k Optimization in Nearest Neighbor Classification

Isaac Touza, Kaladzavi Guidedi, Kolyang

The number of neighbours k is the central hyperparameter of the k-nearest neighbour (k-NN) classifier and is usually selected globally through cross-validation or evolutionary search. However, the bias-variance trade-off is inherently local: dense and noise-free regions may favour small neighbourhoods, whereas sparse or noisy regions may require larger ones. Since global-k optimization is one-dimensional, replacing exhaustive search with a genetic algorithm offers little computational advantage. We therefore optimize an instance-dependent neighbourhood policy instead. We propose EANK (Evolutionary Adaptive Neighborhood K), which uses a low-dimensional policy to map local neighbourhood descriptors, including density, label entropy, vote margin, and concentration, to an adaptive number of neighbours k(x). A real-coded elitist genetic algorithm optimizes this policy using leave-one-out accuracy with a neighbourhood-smoothness penalty. Precomputed neighbour votes reduce fitness evaluation costs. We investigate theoretical properties of the method, including dominance over global-k solutions on the training criterion, evolutionary convergence, policy regularity, and generalization…