Data dimensionality reduction is an important part of chemical process fault identification. It includes two main methods: feature extraction and feature selection. The fault identification methods based on data dimensionality reduction and deep learning are proposed to explore the effects of different data dimensionality reduction methods on chemical process fault identification. First, the low-dimensional spatial representation of the original process data is obtained by generative topographic mapping (GTM), the correlation between variables is calculated by Spearman’s rank correlation coefficient (SRCC) and the key variables are thus obtained. Then, the deep-level features of the key variable set are learned by the Long Short-Term Memory Network (LSTM) to identify faults in the chemical process. The application of the Tennessee-Eastman (TE) process indicates that the GTM-LSTM is more suitable for the identification of step type faults, while the SRCC-LSTM has a good effect on all types of fault identification, therefore the latter is more suitable for data dimensionality reduction of chemical processes.