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Multiple kernel k‐means clustering (MKKC) can efficiently incorporate multiple base kernels to generate an optimal kernel. Many existing MKKC methods all need two‐step operation: learning clustering indicator matrix and performing clustering on it. However, the optimal clustering results of two steps are not equivalent to those of original problem. To address this issue, in this paper we propose a novel method named one‐step multiple kernel k‐means clustering based on block diagonal representation (OS‐MKKC‐BD). By imposing a block diagonal constraint on the product of indicator matrix and its transpose, this method can encourage the indicator matrix to be block diagonal. Then the indicator matrix can produce explicit clustering indicator, so as to implement one‐step clustering, which avoids the disadvantage of two‐step operation. Furthermore, a simple kernel weighting strategy is used to obtain an optimal kernel, which boosts the quality of optimal kernel. In addition, a three‐step iterative algorithm is designed to solve the corresponding optimization problem, where the Riemann conjugate gradient iterative method is used to solve the optimization problem of the indicator matrix. Finally, by extensive experiments on eleven real data sets and comparison of clustering results with 10 MKC methods, it is concluded that OS‐MKKC‐BD is effective. [ABSTRACT FROM AUTHOR]

Among the methods of multiple kernel clustering (MKC), some adopt a neighborhood kernel as the optimal kernel, and some use local base kernels to generate an optimal kernel. However, these two methods are not synthetically combined together to leverage their advantages, which affects the quality of the optimal kernel. Furthermore, most existing MKC methods require a two-step strategy to cluster, i.e., first learn an indicator matrix, then executive clustering. This does not guarantee the optimality of the final results. To overcome the above drawbacks, a one-step clustering with adaptively local kernels and a neighborhood kernel (OSC-ALK-ONK) is proposed in this paper, where the two methods are combined together to produce an optimal kernel. In particular, the neighborhood kernel improves the expression capability of the optimal kernel and enlarges its search range, and local base kernels avoid the redundancy of base kernels and promote their variety. Accordingly, the quality of the optimal kernel is enhanced. Further, a soft block diagonal (BD) regularizer is utilized to encourage the indicator matrix to be BD. It is helpful to obtain explicit clustering results directly and achieve one-step clustering, then overcome the disadvantage of the two-step strategy. In addition, extensive experiments on eight data sets and comparisons with six clustering methods show that OSC-ALK-ONK is effective. [ABSTRACT FROM AUTHOR]