Nonparametric Discriminant Analysis Based on the Trace Ratio Criterion
Feature extraction is a hot topic in machine learning and pattern recognition. This paper proposes a new nonparametric linear feature extraction method called nonparametric discriminant analysis based on the trace ratio criterion (TRNDA). The motivation comes principally from the nonparametric maximum margin criterion (NMMC). Based on nonparametric extensions of commonly used scatter matrices, an NMMC is one of the effective nonparametric methods of discriminant analysis for linear feature extraction. However, it is sensitive to outliers. By the proposed TRNDA, new scatter matrices are designed for reducing the influence of outliers, and the trace ratio algorithm is used to learn a set of orthogonal projections in succession. We evaluate the proposed method by several benchmark datasets and the results confirm its effectiveness.
KeywordsFeature extraction Nonparametric discriminant analysis Trace ratio algorithm Orthogonal projections
We would like to thank the associate editor and all anonymous reviewers for their constructive comments and suggestions. This research was partially supported by the National Science Foundation of China (Grant No. 61101246) and the Fundamental Research Funds for the Central Universities (Grant No. JB150209).
- 5.Qiu, X., Wu, L.: Nonparametric Maximum Margin Criterion for Face Recognition. In: IEEE International Conference on Image Processing. ICIP 2005, 2, 918—921, IEEE press, (2005)Google Scholar
- 8.Wang, H., Yan, S., Xu, D., Tang, X., Huang, T.: Trace ratio vs. ratio trace for dimensionality reduction. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2007, pp. 1–8. IEEE press (2007)Google Scholar
- 10.Zhao, M., Zhang, Z., Chow, T.W. S.: ITR-score algorithm: an efficient trace ratio criterion based algorithm for supervised dimensionality reduction. In: The 2011 International Joint Conference on Neural Networks, pp. 145–152. IEEE press (2011)Google Scholar
- 12.Wang, L., Sugiyama, M., Yang, C., Zhou, Z.H., Feng, J.: On the margin explanation of boosting algorithms. In: COLT, pp. 479–490 (2008)Google Scholar
- 13.Schapire, R.E., Freund, Y., Bartlett, P., Lee, W.S.: Boosting the margin: a new explanation for the effectiveness of voting methods. In: Proceedings of the Fourteenth International Conference on Machines Learning, Nashville, Tennessee, USA, pp. 1651–1686 (1998)Google Scholar
- 14.Li, G., Wen, C., Wei, W., Xu, Y., Ding, J., Zhao, G., Shi, L.: Trace ratio criterion for feature extraction in classification. J. Math. Probl. Eng. 2014, 1–9 (2014)Google Scholar
- 16.XM2VTS dataset. http://www.ee.surrey.ac.uk/CVSSP/xm2vtsdb/
- 17.YALE B dataset. http://www.cad.zju.edu.cn/home/dengcai/Data/FaceData.html