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Non-negative factorization (NMF) has been a popular machine learning method for analyzing microarray data. Kernel approaches can capture more non-linear discriminative features than linear ones. In this paper, we propose a novel kernel NMF (KNMF) approach for feature extraction and classification of microarray data. Our approach is also generalized to kernel high-order NMF (HONMF). Extensive experiments on eight microarray datasets show that our approach generally outperforms the traditional NMF and existing KNMFs. Preliminary experiment on a high-order microarray data shows that our KHONMF is a promising approach given a suitable kernel function.