A new fuzzy k-nearest neighbor classifier based on the Bonferroni mean

Abstract

We present a new generalized version of the fuzzy k-nearest neighbor (FKNN) classifier that uses local mean vectors and utilizes the Bonferroni mean. We call the proposed new method Bonferroni-mean based fuzzy k-nearest neighbor (BM-FKNN) classifier. The BM-FKNN classifier can be easily fitted for various contexts and applications, because the parametric Bonferroni mean allows for problem-based parameter value fitting. The BM-FKNN classifier can perform well also in situations where clear imbalances in class distributions of data are found. The performance of the proposed classifier is tested with six real-world data sets and with one artificial data set. The results are benchmarked with classification results obtained with the classical k-nearest neighbor-, the local mean-based k-nearest neighbor-, the fuzzy k-nearest neighbor- and other three selected classifiers. In addition to this, an enhancement of the local mean-based k-nearest neighbor classifier by using the Bonferroni means is also proposed and tested. The results show that the proposed new BM-FKNN classifier has the potential to outperform the benchmarks in classification accuracy and confirm the usefulness of using the Bonferroni mean in the learning part of classifiers.