k*-Nearest Neighbors: From Global to Local

TL;DR

This paper introduces an adaptive, locally weighted regression/classification method that optimally determines the number of neighbors and weights for each data point, improving performance over standard methods.

Contribution

It presents a simple, efficient approach to locally weighted regression/classification that explicitly models the bias-variance tradeoff and adaptively finds optimal weights and neighbor counts.

Findings

Demonstrates superior performance on multiple datasets.

Efficiently finds optimal weights and neighbors for each data point.

Provides a formulation that makes the bias-variance tradeoff explicit.

Abstract

The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have remained unsettled. In this paper we offer a simple approach to locally weighted regression/classification, where we make the bias-variance tradeoff explicit. Our formulation enables us to phrase a notion of optimal weights, and to efficiently find these weights as well as the optimal number of neighbors efficiently and adaptively, for each data point whose value we wish to estimate. The applicability of our approach is demonstrated on several datasets, showing superior performance over standard locally weighted methods.