Beyond trace ratio: weighted harmonic mean of trace ratios for multiclass discriminant analysis

Linear discriminant analysis (LDA) is one of the most important supervised linear dimensional reduction techniques which seeks to learn low-dimensional representation from the original high-dimensional feature space through a transformation matrix, while preserving the discriminative information via maximizing the between-class scatter matrix and minimizing the within class scatter matrix. However, the conventional LDA is formulated to maximize the arithmetic mean of trace ratios which suffers from the domination of the largest objectives and might deteriorate the recognition accuracy in practical applications with a large number of classes. In this paper, we propose a new criterion to maximize the weighted harmonic mean of trace ratios, which effectively avoid the domination problem while did not raise any difficulties in the formulation. An efficient algorithm is exploited to solve the proposed challenging problems with fast convergence, which might always find the globally optimal solution just using eigenvalue decomposition in each iteration. Finally, we conduct extensive experiments to illustrate the effectiveness and superiority of our method over both of synthetic datasets and real-life datasets for various tasks, including face recognition, human motion recognition and head pose recognition. The experimental results indicate that our algorithm consistently outperforms other compared methods on all of the datasets.