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Structure regularized self-paced learning for robust semi-supervised pattern classification

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Semi-supervised classification is a hot topic in pattern recognition and machine learning. However, in presence of heavy noise and outliers, the unlabeled training data could be very challenging or even misleading for the semi-supervised classifier. In this paper, we propose a novel structure regularized self-paced learning method for semi-supervised classification problems, which can efficiently learn partially labeled training data sequentially from the simple to the complex ones. The proposed formulation consists of three components: a cost function defined by a mixture of losses, a functional complexity regularizer, and a self-paced regularizer; and the corresponding optimization algorithm involves three iterative steps: classifier updating, sample importance calculating, and pseudo-labeling. In the proposed method, the cost function for classifier updating and sample importance calculating is defined as a combination of the label fitting loss and manifold smoothness loss. Then, the importance of the pseudo-labeled and unlabeled samples is adaptively calculated by the novel cost. Unlabeled samples with high importance values are pseudo-labeled with their current predictions. In this way, labels are efficiently propagated from the labeled samples to the unlabeled ones in the robust self-paced manner. Experimental results on several benchmark data sets are provided to show the effectiveness of the proposed method.

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  1. Gong C, Tao DC, Maybank SJ, Liu W, Kang GL, Yang J (2016) Multi-modal curriculum learning for semi-supervised image classification. IEEE Trans Image Process 25(7):3249–3260

    Article  MathSciNet  Google Scholar 

  2. Liu CL, Hsaio WH, Lee CH, Chang TS, Kuo TS (2016) Semi-supervised text classification with universum learning. IEEE Trans Cybern 46(2):462–473

    Article  Google Scholar 

  3. Huang H, Feng HL (2012) Gene classification using parameter-free semi-supervised manifold learning. IEEE/ACM Trans Comput Biol Bioinform 9(3):818–827

    Article  Google Scholar 

  4. Reitmaier T, Calma A, Sick B (2015) Transductive active learning—a new semi-supervised learning approach based on iteratively refined generative models to capture structure in data. Inform Sci 293:275–298

    Article  Google Scholar 

  5. Fujino A, Ueda N, Saito K (2008) Semi-supervised learning for a hybrid generative/discriminative classifier based on the maximum entropy principle. IEEE Trans Pattern Anal Mach Intell 30(3):424–437

    Article  Google Scholar 

  6. Maulik U, Chakraborty D (2011) A self-trained ensemble with semisupervised SVM: an application to pixel classification of remote sensing imagery. Pattern Recogn 44(3):615–623

    Article  Google Scholar 

  7. Wu D, Shang MS, Luo X, Xu J, Yan HY, Deng WH, Wang GY (2017) Self-training semi-supervised classification based on density peaks of data. Neurocomputing.

    Article  Google Scholar 

  8. Li M, Zhou ZH (2007) Learning techniques using undiagnosed samples. IEEE Trans Syst Man Cybern Part A 37(6):1088–1098

    Article  Google Scholar 

  9. Xu YK, Qin L, Huang QM (2016) Coupling reranking and structured output SVM co-train for multitarget tracking. IEEE Trans Circuits Syst Video Technol 26(6):1084–1098

    Article  Google Scholar 

  10. Chapelle O, Sindhwani V, Keerthi SS (2008) Optimization techniques for semi-supervised support vector machines. J Mach Learn Res 9:203–233

    MATH  Google Scholar 

  11. Lu ZW, Wang LW (2015) Noise-robust semi-supervised learning via fast sparse coding. Pattern Recogn 48(2):605–612

    Article  Google Scholar 

  12. Zhu X, Ghahramani Z, Lafferty J (2003) Semi-supervised learning using gaussian fields and harmonic functions. In: Proceedings of the 20th international conference on machine learning (ICML2003)

  13. Zhu X, Ghahramani Z (2002) Learning from labeled and unlabeled data with label propagation. Technical Report CMUCALD-02-107, Computer Science Department, Carnegie Mellon University

  14. Zhou D, Bousquet O, Lal T, Weston J, Schökopf B (2014) Learning with local and global consistency. In: Proceedings of the neural information processing systems conference (NIPS 2004)

  15. Belkin M, Sindhwani V, Niyogi P (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399–2434

    MathSciNet  MATH  Google Scholar 

  16. Zhao MY, Jiao LC, Feng J, Liu TY (2014) A simplified low rank and sparse graph for semi-supervised learning. Neurocomputing 140:84–96

    Article  Google Scholar 

  17. Zhuang LS, Zhou ZH, Gao SH, Yin JW, Lin ZC, Ma Y (2017) Label information guided graph construction for semi-supervised learning. IEEE Trans Image Process 26(9):4182–4192

    Article  MathSciNet  Google Scholar 

  18. Chapelle O, Weston J, Schökopf B (2003) Cluster kernels for semisupervised learning. In: Proceedings of the neural information processing systems conference (NIPS2003), pp 585–592

  19. Chapelle O, Scholkopf B, Zien A (2006) Semi-supervised learning. MIT Press, Cambridge

    Book  Google Scholar 

  20. Wang YY, Chen SC, Zhou ZH (2012) New semi-supervised classification method based on modified cluster assumption. IEEE Trans Neural Netw 23(5):689–702

    Article  Google Scholar 

  21. Zhu X (2006) Semi-supervised learning literature survey. Technical Report 1530, Computer Science Department, University of Wisconsin

  22. Kumar M, Packer B, Koller D (2010) Self-paced learning for latent variable models. In: Proceedings of the neural information processing systems conference (NIPS2010), pp 1189–1197

  23. Meng DY, Zhao Q, Jiang L (2017) A theoretical understanding of self-paced learning. Inform Sci 414:319–328

    Article  Google Scholar 

  24. Jiang L, Meng DY, Yu SI, Lan ZZ, Shan SG, Hauptmann A (2014) Self-paced learning with diversity. In: Proceedings of the neural information processing systems conference (NIPS2014)

  25. Zhang DW, Meng DY, Han JW (2017) Co-saliency detection via a self-paced multiple-instance learning framework. IEEE Trans Pattern Anal Mach Intell 39(5):865–878

    Article  Google Scholar 

  26. Lin L, Wang KZ, Meng DY, Zuo WM, Zhang L (2017) Active self-paced learning for cost-effective and progressive face identification. IEEE Trans Pattern Anal Mach Intell.

    Article  Google Scholar 

  27. Supančič III J, Ramanan D (2013) Self-paced learning for long-term tracking. In: IEEE conference on computer vision and pattern recognition (CVPR2013), pp 1189–1197

  28. Kumar M, Turki H, Preston D, Koller D (2011) Learning specific-class segmentation from diverse data. In: IEEE conference on computer vision and pattern recognition (CVPR2011), pp 1800–1807

  29. Yu S et al (2014) Cmu-informedia@ trecvid 2014 multimedia event detection. In: TRECVID video retrieval evaluation workshop

  30. Bengio Y, Louradour J, Collobert R, Weston J (2009) Curriculum learning. In: Proceedings of the 20th international conference on machine learning (ICML2009)

  31. Jiang L, Meng D, Mitamura T, Hauptmann A (2014) Easy samples first: self-paced reranking for zeroexample multimedia search. In: Proceedings of ACM multimedia

  32. Zhao Q, Meng DY, Jiang L, Xie Q, Xu ZB, Hauptmann A (2015) Self-paced learning for matrix factorization. In: Proceedings of AAAI conference on artificial intelligence (AAAI2015)

  33. Bazaraa M, Sherali H, Shetty C (1993) Nonlinear programming—theory and algorithms. Wiley, New York

    MATH  Google Scholar 

  34. Jiang L, Meng DY, Zhao Q, Shan SG, Hauptmann A (2015) Self-paced curriculum learning. In: Proceedings of AAAI conference on artificial intelligence (AAAI2015)

  35. Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68(3):337–404

    Article  MathSciNet  Google Scholar 

  36. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323–2326

    Article  Google Scholar 

  37. Zhao MB, Chow Tommy WS, Wu Z, Zhang Z, Li B (2015) Learning from normalized local and global discriminative information for semi-supervised regression and dimensionality reduction. Inform Sci 324:286–309

    Article  Google Scholar 

  38. Zhao MB, Zhang Z, Chow Tommy WS, Li B (2014) A general soft label based Linear Discriminant Analysis for semi-supervised dimensionality reduction. Neural Netw 55:83–97

    Article  Google Scholar 

  39. Zhao MB, Chow Tommy WS, Zhang Z, Li B (2015) Automatic image annotation via compact graph based semi-supervised learning. Knowl based Syst 76:148–165

    Article  Google Scholar 

  40. Gross R, Baker S, Matthews I (2005) Generic vs. person specific active appearance models. Image Vis Comput 23(11):1080–1093

    Article  Google Scholar 

  41. Samaria FS, Harter AC (1994) Parameterisation of a stochastic model for human face identification. In: Proceedings of the second IEEE workshop on applications of computer vision, pp 138–142

  42. Wang F, Zhang CS (2008) Label propagation through linear neighborhoods. IEEE Trans Knowl Data Eng 20(1):55–67

    Article  Google Scholar 

  43. Zhang HJ, Chow Tommy WS, JonathanWu QM (2016) Organizing books and authors by multilayer SOM. IEEE Trans Neural Netw 27(12):2537–2550

    Article  Google Scholar 

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This work was supported in part by the National Natural Science Foundation (NNSF) of China [Grant Numbers: 61503263, 61772373, 61772374], in part by the Zhejiang Provincial Natural Science Foundation [Grant Numbers: LY15F030011, LY17F030004], in part by the Project of science and technology plans of Wenzhou City [Grant Number: G20160002].

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Correspondence to Mingyu Fan.

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Gu, N., Fan, P., Fan, M. et al. Structure regularized self-paced learning for robust semi-supervised pattern classification. Neural Comput & Applic 31, 6559–6574 (2019).

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