¹School of Computer Science, University of Waterloo, Ontario N2L3G1, Canada
²Department of Computer Science, University of North Georgia, Oakwood, GA 30566, USA
³PRIS Lab, Beijing University of Posts and Telecommunications, Beijing 100876, P.R.China
⁴SEEE, Huazhong University of Science and Technology, Hubei 430074, P.R.China

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Abstract—Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are l₂ distance or Kullback- Leibler (KL) divergence. However, nonlinear cases are not properly handled when we use these error measures. As a consequence, alternative measures based on nonlinear kernels, such as correntropy, are proposed. However, the current correntropy-based NMF only targets on the lowlevel features without considering the intrinsic geometrical distribution of data. In this paper, we propose a new NMF algorithm that preserves local invariance by adding graph regularization into the process of max-correntropybased matrix factorization. Meanwhile, each feature can learn corresponding kernel from the data. The experiment results of Caltech101 and Caltech256 show the benefits of such combination against other NMF algorithms for the unsupervised image clustering.

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Cite: Le Li, Jianjun Yang, Kaili Zhao, Yang Xu, Honggang Zhang, and Zhuoyi Fan, "Graph Regularized Non-negative Matrix Factorization By Maximizing Correntropy," Journal of Computers vol. 9, no. 11, pp. 2570-2579, 2014.