Face recognition using maximum local Fisher Discriminant Analysis

Compared to globality based supervised dimensionality reduction methods such as Fisher Discriminant Analysis (FDA), locality based ones including Local Fisher Discriminant Analysis (LFDA) have attracted increasing interests since they aim to preserve the intrinsic data structures and are able to handle multimodally distributed data. However, both FDA and LFDA are usually solved via a ratio trace form to approximate the trace ratio, which is the Fisher's original objective criterion. In this paper, a novel trace optimization framework is presented to solve the original trace ratio problem. It offers an exact solution via mathematical programming and recovers Fisher's maximal separability faithfully. The resulting maximum Local Fisher Discriminant Analysis (maxLFDA) not only inherits the merits of LFDA, but also boosts the classification accuracy in each target subspace with expected maximum trace ratio value. Experiments on a toy example and real-world face databases validate the effectiveness of the proposed method.