Relational Fisher Analysis: A general framework for dimensionality reduction

In this paper, we propose a novel and general framework for dimensionality reduction, called Relational Fisher Analysis (RFA). Unlike traditional dimensionality reduction methods, such as linear discriminant analysis (LDA) and marginal Fisher analysis (MFA), RFA seamlessly integrates relational information among data into the representation learning framework, which in general provides strong evidence for related data to belong to the same class. To address nonlinear dimensionality reduction problems, we extend RFA to its kernel version. Furthermore, the convergence of RFA is also proved in this paper. Extensive experiments on documents understanding and recognition, face recognition and other applications from the UCI machine learning repository demonstrate the effectiveness and efficiency of RFA.