This paper presents a monitoring approach for nonlinear processes based on a new semi-supervised kernel nonnegative matrix factorization (SKNMF). Different from the existing nonnegative matrix factorization (NMF) and kernel nonnegative matrix factorization (KNMF), SKNMF is a semi-supervised matrix factorization algorithm, which takes advantages of both labelled and unlabelled samples to improve algorithm performance. Labelled samples refer to the samples whose memberships are already known, while unlabelled samples are a set of samples whose memberships are unknown. In fact, both NMF and KNMF are unsupervised algorithms, and they cannot make full use of labelled samples to improve algorithm performance. More importantly, we explain the reasons why labelled samples can improve algorithm performance even if the amount of labelled samples is small. Last but not least, SKNMF induces a simultaneous fault detection and isolation scheme for online processes monitoring. Case studies of a numerical example and a penicillin fermentation process (PFP) demonstrate that the proposed process monitoring approaches outperform the existing process monitoring approaches.