Anew sparse dimensionality reduction method named sparse global-local preserving projections (SGLPP) is proposed. The SGLPP has two advantages. First, SGLPP can preserve both global and local structures of the data set. Second, SGLPP extracts sparse transformation vectors from the data set. The extracted sparse transformation vectors are able to reveal meaningful correlations between variables, which significantly improves the interpretability of SGLPP. These two advantages make SGLPP well suitable for fault detection and diagnosis in industrial processes. Therefore, a SGLPP-based process monitoring method is developed to improve the interpretability and the fault detection capability of monitoring models and to enhance the fault diagnosis capability. A full SGLPP model is combined with a set of partial SGLPP models to improve the fault sensitivity and to track the propagation of faults between process variables. In addition, three-level contribution plots, i.e., the variable-wise, group-wise, and group-variable-wise contribution plots, are constructed for fault evaluation and fault diagnosis. The effectiveness and advantages of proposed methods are illustrated with an industrial case study. The results indicate that the SGLPP models reveal real process mechanisms and control loops between process variables, and thus produces interpretable monitoring results. Moreover, the SGLPP-based method has better fault detection capability than conventional monitoring methods. Three-level contribution plots well show the effects of faults on process variables and produce reliable fault diagnosis results. (C) 2016 Elsevier Ltd. All rights reserved.