Estimating the Posterior Probabilities Using the <i>K</i>-Nearest Neighbor Rule

The proposed posterior probability estimator considers the K-nearest neighbors and attaches a weight to each neighbor that contributes in an additive fashion to the posterior probability estimate.

Abstract

In many pattern classification problems, an estimate of the posterior probabilities (rather than only a classification) is required. This is usually the case when some confidence measure in the classification is needed. In this article, we propose a new posterior probability estimator. The proposed estimator considers the K-nearest neighbors. It attaches a weight to each neighbor that contributes in an additive fashion to the posterior probability estimate. The weights corresponding to the K-nearest-neighbors (which add to 1) are estimated from the data using a maximum likelihood approach. Simulation studies confirm the effectiveness of the proposed estimator.