Face recognition by Fisher and scatter linear discriminant analysis

Fisher linear discriminant analysis (FLDA) based on variance ratio is compared with scatter linear discriminant (SLDA) analysis based on determinant ratio. It is shown that each optimal FLDA data model is optimal SLDA data model but not opposite. The novel algorithm 2SS4LDA (two singular subspaces for LDA) is presented using two singular value decompositions applied directly to normalized multiclass input data matrix and normalized class means data matrix. It is controlled by two singular subspace dimension parameters q and r, respectively. It appears in face recognition experiments on the union of MPEG-7, Altkom, and Feret facial databases that 2SS4LDA reaches about 94% person identification rate and about 0.21 average normalized mean retrieval rank. The best face recognition performance measures axe achieved for those combinations of q, r values for which the variance ratio is close to its maximum, too. None such correlation is observed for SLDA separation measure.