Linear ranking analysis

We extend the classical linear discriminant analysis (L-DA) technique to linear ranking analysis (LRA), by con-sidering the ranking order of classes centroids on the pro-jected subspace. Under the constrain on the ranking order of the classes, two criteria are proposed: 1) minimization of the classification error with the assumption that each class is homogenous Guassian distributed; 2) maximiza-tion of the sum (average) of the k minimum distances of all neighboring-class (centroid) pairs. Both criteria can be efficiently solved by the convex optimization for one-dimensional subspace. Greedy algorithm is applied to ex-tend the results to the multi-dimensional subspace. Experi-mental results show that 1) LRA with both criteria achieve state-of-the-art performance on the tasks of ranking learn-ing and zero-shot learning; and 2) the maximummargin cri-terion provides a discriminative subspace selection method, which can significantly remedy the class separation prob-lem in comparing with several representative extensions of LDA. 1