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Concept Factorization (CF) improves Nonnegative matrix factorization (NMF), which can be only performed in the original data space, by conducting factorization within proper kernel space where the structure of data become much clear than the original data space. CF-based methods have been widely applied and yielded impressive results in optimal data representation and clustering tasks. However, CF methods still face with the problem of proper kernel function design or selection in practice. Most existing Multiple Kernel Clustering (MKC) algorithms do not sufficiently consider the intrinsic neighborhood structure of base kernels. In this paper, we propose a novel Discriminative Multiple Kernel Concept Factorization method for data representation and clustering. We first extend the original kernel concept factorization with the integration of multiple kernel clustering framework to alleviate the problem of kernel selection. For each base kernel, we extract the local discriminant structure of data via the local discriminant models with global integration. Moreover, we further linearly combine all these kernel-level local discriminant models to obtain an integrated consensus characterization of the intrinsic structure across base kernels. In this way, it is expected that our method can achieve better results by more compact data reconstruction and more faithful local structure preserving. An iterative algorithm with convergence guarantee is also developed to find the optimal solution. Extensive experiments on benchmark datasets further show that the proposed method outperforms many state-of-the-art algorithms.

Discriminative Multiple Kernel Concept Factorization for Data Representation