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Supervised feature extraction (SFE) algorithms can be divided into two categories: those optimised by global criteria and those optimised by local ones. Proposed is a new approach designed by integrating global and local criteria, namely, combinatorial discriminant analysis (CDA), to perform SFE. It is shown that CDA inherits both the robustness of global criteria and the flexibility of local ones. Experimental comparisons with typical global and local SFE algorithms on real-world datasets empirically justify the superiority of CDA.