基于多核学习的多阶次分数阶傅里叶变换域人脸识别

分数阶傅里叶变换是信号处理与分析的一个重要工具，通过将图像信号投影到不同角度的时频平面可以表征图像的内容信息，其在人脸识别任务中显示出很好的性能。但是分数阶傅里叶变换存在阶次选择的问题，即在没有先验知识的情况下，无法预先知道哪一个阶次的分数阶傅里叶变换域特征具有最好的判别性能。受机器学习中的多核学习理论启发，本文探讨了分数阶傅里叶变换中阶次选择问题和多核学习理论的联系，通过将不同阶次的分数阶傅里叶变化域特征的线性核矩阵作为多核学习网络的输入，结合支持向量机，交替优化更新多核网络中的系数和支持向量机的参数，自动学习多阶次分数阶傅里叶变换域特征的系数，实现多阶次分数阶傅里叶变换域特征的融合。将所提算法应用到人脸识别任务中，在ORL人脸数据集和扩展YaleB人脸数据集上的实验显示所提算法的可行性和有效性。

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

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.