Abstract
Kernel Minimum Squared Error (KMSE) has been receiving much attention in data mining and pattern recognition in recent years. Generally speaking, training a KMSE classifier, which is a kind of supervised learning, needs sufficient labeled examples. However, there are usually a large amount of unlabeled examples and few labeled examples in real world applications. In this paper, we introduce a semi-supervised KMSE algorithm, called Laplacian regularized KMSE (LapKMSE), which explicitly exploits the manifold structure. We construct a p nearest neighbor graph to model the manifold structure of labeled and unlabeled examples. Then, LapKMSE incorporates the structure information of labeled and unlabeled examples in the objective function of KMSE by adding a Laplacian regularized term. As a result, the labels of labeled and unlabeled examples vary smoothly along the geodesics on the manifold. Experimental results on several synthetic and real-world datasets illustrate the effectiveness of our algorithm.
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References
Muller, K.-R., Mika, S., Ratsch, G., Tsuda, S., Scholkopf, B.: An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks 12(2), 181–202 (2001)
Scholkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2001)
Ruiz, A., de Teruel, P.E.L.: Nonlinear kernel-based statistical pattern analysis. IEEE Transactions on Neural Networks 12(1), 16–32 (2001)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge University Press (2000)
Suykens, J.A.K., Vandewalle, J.: Least squares support vector machine classifiers. Neural Processing Letters 9(3), 293–300 (1999)
Schlkopf, B., Smola, A.J., Müller, K.R.: Kernel principal component analysis. Advances in Kernel Methods: Support Vector Learning, 327–352 (1999)
Mika, S., Ratsch, G., Weston, J., Scholkopf, B., Mullers, K.R.: Fisher discriminant analysis with kernels. In: Proceedings of the 1999 IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing IX, pp. 41–48 (1999)
Xu, J., Zhang, X., Li, Y.: Regularized kernel forms of minimum squared error method. Frontiers of Electrical and Electronic Engineering in China 1, 1–7 (2006)
Xu, J., Zhang, X., Li, Y.: Kernel mse algorithm: A unified framework for KFD, LS-SVM and KRR . In: Proceedings of International Joint Conference on Neural Networks, pp. 1486–1491 (2001)
Gan, H., Sang, N., Huang, R., Tong, X., Dan, Z.: Using clustering analysis to improve semi-supervised classification. Neurocomputing 101, 290–298 (2013)
Belkin, M., Niyogi, P., Sindhwani, V.: Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. The Journal of Machine Learning Research 7, 2399–2434 (2006)
Cai, D., He, X., Han, J.: Semi-supervised discriminant analysis. In: Proceeding of the IEEE 11th International Conference on Computer Vision, ICCV (2007)
Chapelle, O., Scholkopf, B., Zien, A.: Semi-Supervised Learning. MIT Press, Cambridge (2006)
Zhu, X.: Semi-supervised learning literature survey. Technical Report 1530, Computer Sciences, University of Wisconsin-Madison (2005)
Frank, A., Asuncion, A.: UCI machine learning repository (2010)
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Gan, H., Sang, N., Chen, X. (2013). Semi-supervised Kernel Minimum Squared Error Based on Manifold Structure. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_33
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DOI: https://doi.org/10.1007/978-3-642-39065-4_33
Publisher Name: Springer, Berlin, Heidelberg
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