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The problem of appearance-based recognition of faces and facial expressions is addressed. Previous work on sliced inverse regression (SIR) resulted in the formulation of an appearance-based face recognition technique termed as Sirface that is insensitive to large variation in lighting direction and facial expression. Sirface was shown to be superior to the well known Fisherface technique, that is based on Fisher's linear discriminant analysis (LDA), in terms of both, dimensionality reduction and classification accuracy. However, Sirface, which relies only on first-order statistics, is shown to be poor at discriminating between facial expressions. A novel statistical data dimensionality reduction technique based on sliced average variance estimation (SAVE) is shown to be effective in distinguishing between different facial expressions of the same face. SAVE, which exploits the difference in second-order statistics between the pattern classes, is shown to result in an optimal reduced dimensional subspace for quadratic discriminant analysis (QDA). The resulting appearance-based technique for recognition effaces and facial expressions, termed as Saveface, is experimentally compared to Sirface in terms of classification accuracy and data dimensionality reduction.