A new formulation of sparse multiple kernel k$$ k $$ ‐means clustering and its applications

Multiple kernel k$$ k $$ ‐means (MKKM) clustering has been an important research topic in statistical machine learning and data mining over the last few decades. MKKM combines a group of prespecified base kernels to improve the clustering performance. Although many efforts have been made to improve the performance of MKKM further, the present works do not sufficiently consider the potential structure of the partition matrix. In this paper, we propose a novel sparse multiple kernel k$$ k $$ ‐means (SMKKM) clustering by introducing a ℓ1$$ {\ell}_1 $$ ‐norm to induce the sparsity of the partition matrix. We then design an efficient alternating algorithm with curve search technology. More importantly, the convergence and complexity analysis of the designed algorithm are established based on the optimality conditions of the SMKKM. Finally, extensive numerical experiments on synthetic and benchmark datasets demonstrate that the proposed method outperforms the state‐of‐the‐art methods in terms of clustering performance and robustness.