A generalized mean distance-based k-nearest neighbor classifier

Abstract K-nearest neighbor (KNN) rule is a well-known non-parametric classifier that is widely used in pattern recognition. However, the sensitivity of the neighborhood size k always seriously degrades the KNN-based classification performance, especially in the case of the small sample size with the existing outliers. To overcome this issue, in this article we propose a generalized mean distance-based k-nearest neighbor classifier (GMDKNN) by introducing multi-generalized mean distances and the nested generalized mean distance that are based on the characteristic of the generalized mean. In the proposed method, multi-local mean vectors of the given query sample in each class are calculated by adopting its class-specific k nearest neighbors. Using the achieved k local mean vectors per class, the corresponding k generalized mean distances are calculated and then used to design the categorical nested generalized mean distance. In the classification phase, the categorical nested generalized mean distance is used as the classification decision rule and the query sample is classified into the class with the minimum nested generalized mean distance among all the classes. Extensive experiments on the UCI and KEEL data sets, synthetic data sets, the KEEL noise data sets and the UCR time series data sets are conducted by comparing the proposed method to the state-of-art KNN-based methods. The experimental results demonstrate that the proposed GMDKNN performs better and has the less sensitiveness to k. Thus, our proposed GMDKNN with the robust and effective classification performance could be a promising method for pattern recognition in some expert and intelligence systems.