A fast fuzzy K -nearest neighbour algorithm for pattern classification

Abstract

A fast procedure for classifying a given test pattern to one of its possible classes using both the K-NN decision rule and concepts of the fuzzy set theory is described in this paper. The method is divided into two steps; in the first step the K nearest neighbours are found using a fast procedure, whereas in the second step the test pattern is classified using a fuzzy distance measure. The fast K-NN algorithm proceeds in finding a region containing at least K neighbours around the test sample by utilising an ordered search procedure of the test point from three reference points. In the sequence the found region is modified in such a way that the real K nearest neighbours of the given point will be always inside it. Then a small number of distance calculations are required to identify the true K-nearest neighbours and the fuzzy measure is applied to classify the test pattern. The pre-processing load is quite moderate and computer simulation results show that the misclassification rate is lower than, or similar to, the crisp version, while presenting results richer in information content than its crisp counterpart. This rate is also kept low even in the case we do not perform modifications that ensure the true K-NN finding.