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A novel supervised image feature extraction method, called local tensor rank one discriminant analysis (LTRODA) is proposed. LTRODA learns a series of rank one tensor projections with orthogonal constraints to produce compact features for images. To seek the optimal projections with prominent discriminative ability, LTRODA carries out local discriminant analysis. LTRODA is free from the matrix singularity problem owing to its trace difference based learning model, and a novel solving method ensures stability of the solution. Experimental results suggest that LTRODA provides a supervised image feature extraction approach of powerful pattern-revealing capability.