Abstract: No Free Lunch Theorem says that only taking full advantage of learning machine of priori knowledge related to the problem under consideration can have a good learning performance．However,the vectorization of the images used in conventional linear discriminant analysis (LDA) damages the spatial structure of initial images,and restricts the improvement of the learning performance of LDA．Spatially smoothing linear discriminant analysis (SLDA) tries to overcome this problem by introducing the spatial regularization to the objective of LDA,whereas IMage Euclidean Distance Discriminant Analysis (IMEDA) substitutes IMage Euclidean Distance (IMED) for the original Euclidean metric in the objective of LDA to utilize the spatially structure information.This paper attempted to explore the intrinsic link between SLDA and IMEDA:theoretically proved that SLDA is the special case of IMEDA when the sample mean of the data set is zero,analyzed the time complexity and the space complexity of the algorithms．The experiments were conducted to compare SLDA with IMEDA on Yale,AR and FERET face datasets,and the influences of the parameters on perfor-mance of the algorithms were analyzed.

Key words: Linear discriminant analysis,Dimensionality reduction,Spatial structure information,Spatially smooth