Local Polynomial Metrics for K Nearest Neighbor Classifiers

Abstract

In many pattern recognition systems, metrics are frequently employed to quantify the dissimilarity that exists between two given patterns. Common applications occur in clustering algorithms, radial basis function classifiers, and nearest neighbor classifiers (Duda et al., 2001). A bounty of results exist that demonstrate the importance of selecting a metric (or dissimilarity measure) with care (e.g., Simard et al., 1993). In the following, we present an adaptive algorithm that uses local polynomial regression to construct a metric useful for a pattern classification problem described by a set of correctly classified patterns. Although we introduce this algorithm in the context of the k nearest neighbor classifier, it is applicable to other pattern classifiers that use proximity in feature space as a measure of pattern similarity.