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

Jiu Mingyuan; Chen Enqing; Qi Lin; Tie Yun

doi:10.12086/oee.2018.170744

Article navigation > Opto-Electronic Engineering > 2018 Vol. 45 > No. 6 > 170744

Next Article Previous Article

Jiu Mingyuan, Chen Enqing, Qi Lin, et al. Multiple order fractional Fourier transformation for face recognition based on multiple kernel learning[J]. Opto-Electronic Engineering, 2018, 45(6): 170744. doi: 10.12086/oee.2018.170744

Citation:

Jiu Mingyuan, Chen Enqing, Qi Lin, et al. Multiple order fractional Fourier transformation for face recognition based on multiple kernel learning[J]. Opto-Electronic Engineering, 2018, 45(6): 170744. doi: 10.12086/oee.2018.170744

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

School of Information Engineering, Zhengzhou University, Zhengzhou, Henan 450001, China

Fund Project: Supported by National Natural Science Foundation of China (Key Program)(61331021)

More Information

Corresponding author: Qi Lin, E-mail:ielqi@zzu.edu.cn

Received Date 31 December 2017

Revised Date 02 May 2018

Published Date 01 June 2018

Abstract

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.
- fractional Fourier transformation /
- multiple kernel learning /
- face recognition /
- feature fusion

FullText(HTML)

References

[1]	Zafeiriou S, Zhang C, Zhang Z Y. A survey on face detection in the wild: past, present and future[J]. Computer Vision and Image Understanding, 2015, 138: 1-24. doi: 10.1016/j.cviu.2015.03.015 CrossRef Google Scholar
[2]	任福继, 李艳秋, 胡敏, 等.多特征描述及局部决策融合的人脸识别[J].光电工程, 2016, 43(9): 1-8. Google Scholar Ren F J, Li Y Q, Hu M, et al. Face recognition method based on multi features description and local fusion classification decision[J]. Opto-Electronic Engineering, 2016, 43(9): 1-8. Google Scholar
[3]	龚飞, 金炜, 符冉迪, 等.融合小波包细节子图及稀疏表示的人脸识别[J].光电工程, 2016, 43(6): 32-38. Google Scholar Gong F, Jin W, Fu R D, et al. Face recognition based on the fusion of wavelet packet sub-images and sparse representation[J]. Opto-Electronic Engineering, 2016, 43(6): 32-38. Google Scholar
[4]	冯海亮, 王应健, 罗甫林.基于稀疏相似保持算法的人脸识别[J].光电工程, 2016, 43(6): 19-24. Google Scholar Feng H L, Wang Y J, Luo F L. Face recognition based on sparse similarity preserving algorithm[J]. Opto-Electronic Engineering, 2016, 43(6): 19-24. Google Scholar
[5]	余祥, 刘凯.基于相位测量轮廓术的人脸识别[J].光电工程, 2016, 43(6): 39-43. Google Scholar Yu X, Liu K. Face recognition based on phase measuring profilometry[J]. Opto-Electronic Engineering, 2016, 43(6): 39-43. Google Scholar
[6]	Cootes T F, Taylor C J, Cooper D H, et al. Active shape models-their training and application[J]. Computer Vision and Image Understanding, 1995, 61(1): 38-59. doi: 10.1006/cviu.1995.1004 CrossRef Google Scholar
[7]	Cootes T F, Edwards G J, Taylor C J. Active appearance models[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(6): 681-685. doi: 10.1109/34.927467 CrossRef Google Scholar
[8]	Turk M A, Pentland A P. Face recognition using eigenfaces[C]// Proceedings of 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991. Google Scholar
[9]	Ahonen T, Hadid A, Pietikäinen M. Face description with local binary patterns: application to face recognition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(12): 2037-2041. doi: 10.1109/TPAMI.2006.244 CrossRef Google Scholar
[10]	Dalal N, Triggs B. Histograms of oriented gradients for human detection[C]//Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 1: 886-893. Google Scholar
[11]	Tirilly P, Claveau V, Gros P. Language modeling for bag-of-visual words image categorization[C]//Proceedings of the 2008 International Conference on Content-Based Image and Video Retrieval, 2008: 249-258. Google Scholar
[12]	Belongie S, Malik J, Puzicha J. Shape matching and object recognition using shape contexts[J]. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2002, 24(4): 509-522. Google Scholar
[13]	Hinton G E, Osindero S, Teh Y W. A fast learning algorithm for deep belief nets[J]. Neural Computation, 2006, 18(7): 1527-1554. doi: 10.1162/neco.2006.18.7.1527 CrossRef Google Scholar
[14]	Bengio Y. Learning deep architectures for AI[J]. Foundations and Trends in Machine Learning, 2009, 2(1): 1-127. Google Scholar
[15]	Krizhevsky A, Sutskever I, Hinton G E. ImageNet classification with deep convolutional neural networks[C]//Neural Information Processing Systems Conference, 2012. Google Scholar
[16]	Bruna J, Mallat S. Invariant scattering convolution networks[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(8): 1872-1886. doi: 10.1109/TPAMI.2012.230 CrossRef Google Scholar
[17]	陶然, 邓兵, 王越.分数阶傅里叶变换及其应用[M].北京:清华大学出版社, 2009. Google Scholar Tao R, Deng B, Wang Y. Fractional Fourier Transform and Its Applications[M]. Beijing: Tsinghua University Press, 2009. Google Scholar
[18]	Burges C J C. A tutorial on support vector machines for pattern recognition[J]. Data Mining and Knowledge Discovery, 1998, 2(1): 121-167. Google Scholar
[19]	王亚星, 齐林, 郭新, 等.基于稀疏PCA的多阶次分数阶傅里叶变换域特征人脸识别[J].计算机应用研究, 2016, 33(4): 1253-1257. Google Scholar Wang Y X, Qi L, Guo X, et al. Fusion of complementary discrete fractional fourier features extracted through sparse PCA in generalized frequency domains for face recognition[J]. Application Research of Computers, 2016, 33(4): 1253-1257. Google Scholar
[20]	Sun H J, Chen E Q, Qi L. Face recognition based on the feature fusion in fractional fourier domain[C]//Proceedings of the 12th International Conference on Signal Processing, 2014: 1210-1214. Google Scholar
[21]	Liu B W, Wang F. Face recognition approach based on 2D discrete fractional fourier transform[C]//Proceedings of the 3rd International Conference on Communication Software and Networks, 2011: 656-660. Google Scholar
[22]	Lanckriet G, Cristianini N, Bartlett P, et al. Learning the kernel matrix with Semi-Definite programming[J]. Journal of Machine Learning Research, 2004, 5: 27-72. Google Scholar
[23]	Bach F R, Lanckriet G R G, Jordan M I. Multiple kernel learning, conic duality, and the SMO algorithm[C]//Proceedings of the 21st International Conference on Machine Learning, 2004. Google Scholar
[24]	Rakotomamonjy A, Bach F R, Canu S, et al. SimpleMKL[J]. Journal of Machine Learning Research, 2008, 9: 2491-2521. Google Scholar
[25]	Sonnenburg S, Rätsch G, Schäfer C, et al. Large scale multiple kernel learning[J]. Journal of Machine Learning Research, 2006, 7: 1531-1565. Google Scholar
[26]	Varma M, Babu B R. More generality in efficient multiple kernel learning[C]//Proceedings of the 26th Annual International Conference on Machine Learning, 2009: 1065-1072. Google Scholar
[27]	Chang C C, Lin C J. LIBSVM: a library for support vector machines[J]. ACM Transactions on Intelligent Systems and Technology, 2011, 2(3): 27. Google Scholar

Overview

Overview

Overview: 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 planes. The features extracted by 2D-FRFT have shown very promising results for face recognition. However, one problem is encountered when we apply 2D-FRFT tools for recognition problem: it is hard to know that which order of 2D-FRFT (the angle of projection of time-frequency plane) is suitable for the specific task without prior knowledge. The common method is that different orders are experimented and we empirically select the best one. 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. Both problems can be considered as an equivalent problem when the features from 2D-FRFT in different orders with the subsequent SVM classifier can be transformed to linear kernels with SVM according to Representer Theorem. 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, the weights in the multiple kernel learning framework correspond to the order weights in the fusion of 2D-FRFT features of different orders, we can then update the weights in the multiple kernel learning framework and SVM parameters through alternative optimization. It is proceeding by first learning the parameters of SVM when fixing the parameters of multiple kernel learning, and then updating the parameters of multiple kernel learning by gradient descent algorithm when fixing the parameters of SVM. Learning iterations are stopped until convergence. Therefore, the problem of order selection of 2D-FRFT can be solved by the off-the-shelf algorithms of multiple kernel learning. We apply the proposed algorithm to face recognition task, and the experiments are conducted on the ORL dataset and the extended YaleB dataset. From the results it can be observed that: 1) The performance are improved by combining different 2D-FRFT features in different orders in compared to single order 2D-FRFT features; 2) The performance of different 2D-FRFT order fusion are comparable and even better than other classical features for face recognition, such as Eigenface, LBP and HOG; 3) The learned weights in the multiple kernel learning frameworks can give us clues about the contribution of each order of 2D-FRFT. In a nutshell, the experimental results show the effectiveness of the proposed algorithm.