Industrial process data have the characteristics of high dimensions and nonlinearity, so it is very important to extract the data features for fault diagnosis. Two kinds of improved exponential discriminant analysis methods, local linear exponential discriminant analysis (LLEDA) and neighbourhood preserving embedding discriminant analysis (NPEDA), are proposed and the fault diagnosis schemes based on the two methods are given. The two methods both combine the global discriminant analysis with the local structure preserving. LLEDA is a parallel strategy to find a trade-off projection vector between the local geometric structure preserving and the global data classification. NPEDA is a cascaded strategy whose dimensionality reduction process is implemented in two serial steps. The two methods emphasize the intrinsic structure of the data while utilizing the global discriminant information, so they have better discrimination power than the traditional EDA method. Finally, a typical penicillin fermentation simulation platform and Tennessee Eastman process are used to verify the performance of the proposed methods.