Robust semi-supervised nonnegative matrix factorization for image clustering

Abstract Nonnegative matrix factorization (NMF) is a powerful dimension reduction method, and has received increasing attention in various practical applications. However, most traditional NMF based algorithms are sensitive to noisy data, or fail to fully utilize the limited supervised information. In this paper, a novel robust semi-supervised NMF method, namely correntropy based semi-supervised NMF (CSNMF), is proposed to solve these issues. Specifically, CSNMF adopts a correntropy based loss function instead of the squared Euclidean distance (SED) in constrained NMF to suppress the influence of non-Gaussian noise or outliers contaminated in real world data, and simultaneously uses two types of supervised information, i.e., the pointwise and pairwise constraints, to obtain the discriminative data representation. The proposed method is analyzed in terms of convergence, robustness and computational complexity. The relationships between CSNMF and several previous NMF based methods are also discussed. Extensive experimental results show the effectiveness and robustness of CSNMF in image clustering tasks, compared with several state-of-the-art methods.