Multiple Marginal Fisher Analysis

Dimension reduction is a fundamental task of machine learning and computer vision, which is widely used in a variety of industrial applications. Over past decades, a lot of unsupervised and supervised algorithms have been proposed. However, few of them can automatically determine the feature dimension that could be adaptive to different data distributions. To obtain a good performance, it is popular to seek the optimal dimension by exhaustively enumerating some possible values. Clearly, such a scheme is ad hoc and computationally extensive. Therefore, a method which can automatically estimate the feature dimension in an efficient and principled manner is of significant practical and theoretical value. In this paper, we propose a novel supervised subspace learning method called multiple marginal Fisher analysis (MMFA), which can automatically estimate the feature dimension. By maxing the interclass separability among marginal points while minimizing within-class scatter, MMFA obtains low-dimensional representations with outstanding discriminative properties. Extensive experiments show that MMFA not only outperforms other algorithms on clean data, but also show robustness on corrupted and disguised data.