Multiple order fractional Fourier transformation for face recognition based on multiple kernel learning

Abstract

Fractional Fourier transformation (FRFT) is a very useful tool for signal processing and analysis, which can well represent the content of the image by projecting it to the time-frequency plane. The features extracted by 2D-FRFT have shown very promising results for face recognition. However, there is one problem when dealing with 2D-FRFT: it is hard to know that which order of 2D-FRFT (the angle of projection of time-frequency plane) is best for the specific task without prior knowledge. In spirit of multiple kernel learning in machine learning, we discuss the relations between the order selection in 2D-FRFT and kernel selection in multiple kernel learning. By treating the linear kernels over different features from 2D-FRFT with different orders as the input to multiple kernel learning framework, and also by applying support vector machines (SVM) on top of the learned kernels, we can update the weights in the multiple kernel learning framework and SVM parameters through alternative optimization. Therefore, the problem of order selection of 2D-FRFT is solved by the off-the-shelf algorithm of multiple kernel learning. The experiments of face recognition on ORL dataset and extended YaleB dataset show the effectiveness of the proposed algorithm.