Abstract

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 orderof the classes, two criteria are proposed: 1) minimizationof the classification error with the assumption that eachclass is homogenous Guassian distributed; 2) maximiza-tion of the sum (average) of the k minimum distances ofall neighboring-class (centroid) pairs. Both criteria canbe efficiently solved by the convex optimization for one-dimensional subspace. Greedy algorithm is applied to extend the results to the multi-dimensional subspace. Experimental results show that 1) LRA with both criteria achieve state-of-the-art performance on the tasks of ranking learning and zero-shot learning; and 2) the maximum margin criterion provides a discriminative subspace selection method, which can significantly remedy the class separation problem in comparing with several representative extensions ofLDA.