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Linear Ranking Analysis

We extend the classical linear discriminant analysis (LDA) technique to linear ranking analysis (LRA), by considering the ranking order of classes centroids on the projected 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) maximization 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 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 of LDA.

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