Correntropy induced metric based graph regularized non-negative matrix factorization

Non-negative matrix factorization (NMF) is a popular dimension reduction method which plays an important role in many pattern recognition and computer vision tasks. However, the low-dimensional representations learned by conventional NMF methods neither taking off the effect of outliers nor preserving the geometric structure in datasets. In this paper, we proposed a correntropy induced metric based graph regularized NMF (CGNMF) to overcome the aforementioned deficiencies. CGNMF maximizes the correntropy between data matrix and its reconstruction to filter out the noises of large magnitudes, and preserves the intrinsic geometric structure of data by using graph regularization. To further enhance the reliability of CGNMF, we proposed correntropy induced metric based graph regularized projective NMF (CGPNMF) to learn clean coefficients by minimizing its distance to the projected samples measured by the correntropy induced metric. Experimental results on popular facial image datasets confirm the effectiveness of both CGNMF and CGPNMF comparing with the state-of-the-arts methods.