Abstract
The L1-norm has been used as the distance metric in robust discriminant analysis. However, it is not sufficiently robust and thus we propose the use of cutting L1-norm. Since this norm is helpful for eliminating outliers in learning models, the proposed non-peaked discriminant analysis is better able to perform feature extraction tasks for image classification. We also show that cutting L1-norm can be equivalently computed using the difference of two special convex functions and present an efficient iterative algorithm for the optimization of proposed objective. The theoretical insights and effectiveness of the proposed algorithm are verified by experimental results on images from three datasets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Change history
11 November 2019
The Editors have retracted this chapter [1] because it presents data without authorization for use and contains significant overlap with [2]. Both authors agree to this retraction but not to the wording of the retraction notice.
References
Lai, Z., Xu, Y., Yang, J.: Rotational invariant dimensionality reduction algorithms. IEEE Trans. Cybern. 47(11), 3733–3746 (2017)
Wang, H.X., Lu, X.S., Hu, Z.L., Zheng, W.M.: Fisher discriminant analysis with L1-norm. IEEE Trans. Cybern. 44(6), 828–842 (2014)
Ye, Q.L., Yang, J., Liu, F., et al.: L1-norm distance linear discriminant analysis based on an effective iterative algorithm. IEEE Trans. Circuits Syst. Video Technol. 28(1), 114–129 (2018)
Zheng, W., Lin, Z., Wang, H.: L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction. IEEE Trans. Neural Netw. Learn. Syst. 25(4), 793–805 (2014)
Chen, X., Yang, J., Jin, Z.: An improved linear discriminant analysis with L1-norm for robust feature extraction. In: Proceedings of International Conference on Pattern Recognition, pp. 1585–1590 (2014)
Ye, Q.L., Zhao, H.H., Fu, L.Y., et al.: Underlying connections between algorithms for nongreedy LDA-L1. IEEE Trans. Image Process. 27(5), 2557–2559 (2018)
Zhong, F., Zhang, J.: Linear discriminant analysis based on L1-norm maximization. IEEE Trans. Image Process. 22(8), 3018–3027 (2013)
Liu, Y., Gao, Q., Miao, S.: A non-greedy algorithm for L1-norm LDA. IEEE Trans. Image Process. 26(2), 684–695 (2017)
Zheng, W., Lu, C., Lin, Z.C., et al.: L1-norm heteroscedastic discriminant analysis under mixture of gaussian distributions (2018). https://doi.org/10.1109/tnnls.2018.2863264
Wang, H., Nie, F., Huang, H.: Robust distance metric learning via simultaneous L1-norm minimization and maximization. In: Proceedings of International Conference on Machine Learning, pp. 1836–1844 (2014)
Wang, Q., Gao, Q., Xie, D., et al.: Robust DLPP with nongreedy L1-norm minimization and maximization. IEEE Trans. Neural Netw. Learn. Syst. 29(3), 738–743 (2018)
Zhong, F., Zhang, J., Li, D.: Discriminant locality preserving projections based on L1-norm maximization. IEEE Trans. Neural Netw. Learn. Syst. 25(11), 2065–2074 (2014)
Cevikalp, H.: Best fitting hyperplanes for classification. IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1076–1088 (2017)
Nie, F.P., Huo, Z.Y., Huang, H.: Joint cutting norms minimization for robust matrix recovery. In: The 26th International Joint Conference on Artificial Intelligence (IJCAI) (2017)
Gong, P., Ye, J., Zhang, C.: Multi-stage multi-task feature learning. J. Mach. Learn. Res. 14(1), 2979–3010 (2013)
Geusebroek, J.M., Burghouts, G.J., Smeulders, A.: The Amsterdam library of object images. Int. J. Comput. Vis. 61(1), 103–112 (2005)
Lee, K.C., Ho, J., Kriegman, D.: Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans. Pattern Anal. Mach. Intell. 27(5), 684–698 (2005)
Dua, D., Karra, E.T.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine, CA (2017). Author, F.: Article title. Journal 2(5), 99–110 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Fan, X., Ye, Q. (2019). RETRACTED CHAPTER: Non-peaked Discriminant Analysis for Image Representation. In: Lee, C., Su, Z., Sugimoto, A. (eds) Image and Video Technology. PSIVT 2019. Lecture Notes in Computer Science(), vol 11854. Springer, Cham. https://doi.org/10.1007/978-3-030-34879-3_24
Download citation
DOI: https://doi.org/10.1007/978-3-030-34879-3_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34878-6
Online ISBN: 978-3-030-34879-3
eBook Packages: Computer ScienceComputer Science (R0)