Towards multi-scale fuzzy sparse discriminant analysis using local third-order tensor model of face images

Traditional discriminant analysis (DA) methods are usually not amenable to being studied only with a few or even single facial image per subject. The fundamental reason lies in the fact that the traditional DA approaches cannot fully reflect the variations of a query sample with illumination, occlusion and pose variations, especially in the case of small sample size. In this paper, we develop a multi-scale fuzzy sparse discriminant analysis using a local third-order tensor model to perform robust face classification. More specifically, we firstly introduced a local third-order tensor model of face images to exploit a set of multi-scale characteristics of the Ridgelet transform. Secondly, a set of Ridgelet transformed coefficients with respect to each block from a face image are respectively generated. We then merge all these coefficients to form a new representative vector for the image. Lastly, we evaluate the sparse similarity grade between each training sample and class by constructing a sparse similarity metric, and redesign the traditional discriminant criterion that contains considerable fuzzy sparse similarity grades to perform robust classification. Experimental results conducted on a set of well-known face databases demonstrate the merits of the proposed method, especially in the case of insufficient training samples.