Granular Vectors and K Nearest Neighbor Granular Classifiers

K nearest neighbor (KNN) classifier is a classical, simple and effective classifier. It has been widely employed in the fields of artificial intelligence and machine learning. Aiming at the problem that traditional classifiers are difficult to deal with uncertain data, we study a technique of neighborhood granulation of samples on each atom feature, construct some granular vectors, and propose a K nearest neighbor classification method based on these granular vectors in this paper. The method introduces a neighborhood rough set model to granulate samples in a classification system, and the raw data can be converted into some feature neighborhood granules. Then, a granular vector is induced by a set of neighborhood granules, and several operators of granular vectors are defined. We present two metrics of granular vectors which are relative granular distance and absolute granular distance, respectively. The monotonicity of distance of granular vectors is proved. Furthermore, the concept of K nearest neighbor granular vector is defined based on the distance of granular vectors, and K nearest neighbor granular classifier is designed. Finally, the K nearest neighbor granular classifier is compared with the classical K nearest neighbor classifier using several UCI datasets. Theoretical analysis and experimental results show that the K nearest neighbor granular classifier has better classification performance under suitable granulation parameters and k values.