Fuzzy clustering based on k -nearest-neighbours rule

In cluster analysis, several algorithms have been made for partitioning a~set of objects into c natural clusters. In general, this problem is formulated as being an objective function optimization approach. However, it is known that the function being minimized is nonconvex and hence it may lead to convergence to many local minima, i.e., to different partitions. Thus, the clustering is repeated with different initializations hoping that some runs will lead to the global minimum. Therefore, the performance of these algorithms depends largely on good choice of these initializations. The most widely used algorithm using this function is called fuzzy c-means algorithm (FCMA). In this paper a~new algorithm is proposed to carry out fuzzy clustering without a~priori assumptions on initial guesses. This algorithm is based on two-layer clustering strategy. During the first layer, the K-nearest-neighbours decision rule is used. Then, to achieve an optimal partition, the second layer involves one iteration of FCMA. The performance of the proposed algorithm and that of FCMA have been tested on six data sets. The results obtained show that the new algorithm possesses a~number of advantages over the FCMA.