This paper proposes a simultaneous fault detection and isolation approach based on a novel transfer semi-nonnegative matrix factorization (TSNMF) algorithm. Different from the existing nonnegative matrix factorization (NMF) algorithm, TSNMF takes advantages of a few labeled samples and geometry structures of sample spaces to improve performance. Labeled samples refer to a type of sample whose memberships are already known. On the contrary, unlabeled samples are a type of samples whose memberships are unknown. Theoretically, we will demonstrate how labeled samples and geometry structures of sample spaces can improve fault detection and isolation performance. More importantly, the proposed simultaneous fault detection and isolation approach can achieve the fault detection and isolation purpose without use of monitoring statistics, which means it is easier to be implemented than the existing approaches. In comparison with the existing fault detection and isolation methods, the proposed detection and isolation scheme can have excellent performance. In addition, the proposed approach can be readily used for newly coming samples and demonstrates good generalization, which promotes an online fault detection and isolation scheme. Last, a numerical example and a case study on the penicillin fermentation process will demonstrate the effectiveness of the proposed approaches.