aknn

Adaptive k-nearest neighbors (AKNN) refers to a family of non-parametric methods that extend the standard k-nearest neighbors algorithm by allowing the neighborhood size or the influence of neighbors to vary across data points or queries. In AKNN, the number of neighbors k is not fixed globally; instead it can be determined locally based on data density, distance to the decision boundary, or other criteria, and neighbor contributions can be weighted accordingly.

The core idea is to make the model more responsive to local structure. In some implementations, each query point selects its own k based on a density estimate or a threshold on neighborhood distances. In others, all points use a fixed pool of neighbors but assign weights to neighbors that reflect distance or local density, so closer or denser regions have greater influence. Some methods combine both strategies, adapting both the neighborhood size and the weighting scheme. This adaptivity can help address issues such as imbalanced classes or varying data density, where a single global k may be suboptimal.

AKNN shares the simplicity and interpretability of standard k-NN while offering improved flexibility. However, it can introduce additional computational overhead, especially if local density estimates are required for each query. Efficient implementations often rely on indexing structures or approximate nearest-neighbor techniques, and may combine AKNN with distance-weighted schemes or local density estimators.

Applications of AKNN include pattern recognition, image and text classification, regression tasks, and anomaly detection. Related concepts include the classical k-NN algorithm, distance weighting, and density-aware methods.