Rival penalization controlled competitive learning for data clustering with unknown cluster number

Conventional clustering algorithms such as k-means (Forgy 1965, MacQueen 1967) need to know the exact cluster number k* before performing data clustering. Otherwise, they will lead to a poor clustering performance. Unfortunately, it is often hard to determine k* in advance in many practical problems. Under the circumstances, Xu et al. in 1993 proposed an approach named Rival Penalized Competitive Learning (RPCL) algorithm that can perform appropriate clustering without knowing the cluster number by automatically driving extra seed points far away from the input data set. Although RPCL has made great success in many applications, its performance is however very sensitive to the selection of the de-learning rate. To our best knowledge, there is still an open problem to guide this rate selection. We further investigate RPCL by presenting a mechanism to dynamically control the rival-penalizing forces. Consequently, we give out a rival penalized controlled competitive learning (RPCCL) approach, which circumvents the selecting problem of the de-learning rate by always fixing it at the same value as the learning rate. In contrast, the RPCL cannot do that in the same way. The experiments have shown the outstanding performance of this algorithm in comparison with the RPCL.