One-step Multiple Kernel k−means Clustering Based on Block Diagonal Property

Multiple kernel k-means clustering (MKKC) can effiffifficiently incorporate multiple base kernels to generate an optimal kernel. However, many existing MKKC methods all need two-step operation: learning clustering indicator matrix and performing clustering on it. These results are not necessarily optimal because the optimal values of two steps are not equivalent to those of original problem. To address this issue, in this paper we propose a novel algorithm named one-step multiple kernel k-means clustering based on block diagonal property(OSMKKC-BD). By imposing a block diagonal constraint on the product of indicator matrix and its transpose and enhancing its block diagonalization, this algorithm can promote the indicator matrix to get explicit clustering indicator, so as to implement one-step clustering. Furthermore, a simple kernel weighting strategy is used to obtain an optimal kernel, and boosts the quality of optimal kernel. In addition, a three-step iterative algorithm is designed to solve the corresponding optimization problem, in which the Riemann conjugate gradient iterative method is used to solve the optimization problem about the indicator matrix. Finally, by extensive experiments on ten real data sets and comparison of clustering results with the state-of-the-art MKKC methods, it is concluded that OSMKKC-BD is effffective.