SMART: A subspace clustering algorithm that automatically identifies the appropriate number of clusters

This paper presents a subspace κ-means clustering algorithm for high-dimensional data with automatic selection of κ. A new penalty term is introduced to the objective function of the fuzzy κ-means clustering process to enable several clusters to compete for objects, which leads to merging some cluster centres and the identification of the 'true' number of clusters. The algorithm determines the number of clusters in a dataset by adjusting the penalty term factor. A subspace cluster validation index is proposed and employed to verify the subspace clustering results generated by the algorithm. The experimental results from both the synthetic and real data have demonstrated that the algorithm is effective in producing consistent clustering results and the correct number of clusters. Some real datasets are used to demonstrate how the proposed algorithm can determine interesting sub-clusters in the datasets.