A Local-Mean Based Pseudo Nearest Neighbor Method

The k-nearest neighbor method is a fundamental machine learning algorithm for classification. However, when the sample size is small and outliers exist, the classification performance of this algorithm may be degraded. To solve the issue, a local-mean based pseudo nearest neighbor method (LAPNN) is introduced to reduce the influence of outliers for classification. In the LAPNN method, the local mean categorical points are obtained by computing the mean of the random two points in the first <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2k$</tex> nearest neighbors of every class. Then, the first <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> pseudo neighbors are selected from the local mean points of each category to decide the pattern of the test sample. The local mean points can improve classification performance to some extent. Some experiments are performed on 19 numerical real data sets, comparing LAPNN with the other ten classification rules. The experimental results show the efficacy of LAPNN in the presence of small-scale points with outliers.