Correntropy induced metric based graph regularized non-negative matrix factorization

Non-negative matrix factorization (NMF) is an efficient dimension reduction method and plays an important role in many pattern recognition and computer vision tasks. However, conventional NMF methods are not robust since the objective functions are sensitive to outliers and do not consider the geometric structure in datasets. In this paper, we proposed a correntropy graph regularized NMF (CGNMF) to overcome the aforementioned problems. CGNMF maximizes the correntropy between data matrix and its reconstruction to filter out the noises of large magnitudes, and expects the coefficients to preserve the intrinsic geometric structure of data. We also proposed a modified version of our CGNMF which construct the adjacent graph by using sparse representation to enhance its reliability. Experimental results on popular image datasets confirm the effectiveness of CGNMF.