Dimensionality reduction techniques are widely used in data driven process monitoring methods for extracting key process features from process data. Dimensionality reduction generally leads to information loss, and therefore may reduce the process monitoring performance. However, choosing an appropriate data projection matrix that can minimize the effect of dimensionality reduction on process monitoring performance is often challenging. In this paper, we introduce a method to construct a variable correlation-based sparse projection matrix (VCBSPM) for reducing the dimension of process data and for building the process monitoring model. The VCBSPM is constructed on the basis of variable correlations, with each column of VCBSPM corresponding to a variable group consisting of highly correlated variables. The VCBSPM has two advantages: (1) it implements dimensionality reduction only for highly correlated variables, and therefore the negative effect of dimensionality reduction on process monitoring performance is significantly reduced; (2) the sparsity of VCBSPM not only improves its interpretability, but also enables it to eliminate redundant interferences between variables and to reveal meaningful variable connections. These advantages make the VCBSPM-based monitoring model well suited for fault detection and diagnosis. In addition, to utilize meaningful variable connections revealed by the VCBSPM to improve the fault diagnosis capability, hierarchical contribution plots consisting of group-wise and group variable-wise contribution plots are developed for fault diagnosis. The hierarchical contribution plots can identify both the faulty groups corresponding to actual control loops or physical links in the process and the faulty variables responsible for the fault. The implementation, effectiveness, and key features of the proposed methods are illustrated by an industrial case study.