Pareto-optimal discriminant analysis

In this work, we have proposed the Pareto-optimal discriminant analysis (PDA), an optimally designed linear subspace learning method that harnesses advantages across many well-known methods such as PCA, LDA, UDP and LPP. By optimizing over the joint objective function and carrying out an alternative coefficients updating scheme, we are able to obtain a linear subspace which is optimized to truly maximize the objective function in discriminant analysis. The proposed method also provides flexibility for formulating the linear transformation matrix in an overcomplete fashion, allowing for a sparse representation. We have shown, in the context of large scale unconstrained face recognition and illumination invariant face recognition, that our proposed PDA significantly outperforms other linear subspace methods.