Estimating the posterior probabilities using the K-nearest neighbor rule

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.