A flexible and efficient algorithm for regularized Marginal Fisher analysis

Marginal Fisher analysis (MFA) is a well-known linear dimensionality reduction method. However, MFA does not utilize the local diversity information of the training data, which will degrade its performance. In order to enhance the discriminant power of MFA, this paper considers introducing local variation quantity to enlarge the distances between local neighborhood embeddings and proposes a flexible and efficient implementation of MFA (F-MFA) within the regularization framework. Therefore, the discriminant structure and diversity of data are preserved in low-dimensional subspace. Computationally, F-MFA is formulated as a trace differential optimization problem which can completely avoids the singularity problem as it exists in MFA. Further, an efficient algorithm is developed for implementing F-MFA via QR-decomposition. Experimental results on four face data sets demonstrate the effectiveness of our approach.