Abstract Multiple kernel clustering (MKC) algorithms have been successfully applied into various applications. However, these successes are largely dependent on the quality of pre-defined base kernels, which cannot be guaranteed in practical applications. This may adversely affect the clustering performance. To address this issue, we propose a simple while effective framework to adaptively improve the quality of base kernels. Under our framework, we instantiate three MKC algorithms based on the widely used multiple kernel k-means clustering (MKKM), MKKM with matrix-induced regularization (MKKM-MR) and co-regularized multiview spectral clustering (CRSC). After that, we design the corresponding algorithms with proved convergence to solve the resultant optimization problems. To the best of our knowledge, our framework fills the gap between kernel adaption and clustering procedure for the first time in the literature and is readily extendable. Extensive experimental research has been conducted on 7 MKC benchmarks. As is shown, our algorithms consistently and significantly improve the performance of the base MKC algorithms, indicating the effectiveness of the proposed framework. Meanwhile, our framework shows better performance than compared ones with imperfect kernels.