This paper proposes a novel correlation metrics‐based convolutional neural network (CNN) classification model for chemical process fault diagnoses, creating a heuristic representation concerning process variable locations in grey correlation space (GCS) in terms of the copula entropy to guide the learning of classifiers. The proposed method based on correlation metrics can help solve the problem of insufficient information caused by a lack of labelled data. Specifically, variable correlations are fused into a heuristic matrix to provide prior knowledge for network learning in compensating data information before the CNN is employed to build the classifier for mining features in GCS. Driven by this mechanism, fault classifications in the case of small numbers of fault samples are successfully implemented. With successful simulation experiments carried out on the Tennessee Eastman (TE) process platform, we found that in GCS, different fault samples can represent hugely different features, while data resulting from the same fault rarely contribute to different ones. This observation lays a solid foundation for constructing superior fault classifiers. In addition, compared with conventional approaches, the proposed method has demonstrated better fault classification performances in the case of limited labelled fault samples.