Abstract
In this paper, we consider semi-supervised regression problem. The proposed method can be divided into two steps. In the first step, a number of variants of clustering partition are obtained with some clustering algorithm working on both labeled and unlabeled data. Weighted co-association matrix is calculated using the results of partitioning. It is known that this matrix satisfies Mercer’s condition, so it can be used as a kernel for a kernel-based regression algorithm. In the second step, we use the obtained matrix as kernel to construct the decision function based on labelled data. With the use of probabilistic model, we prove that the probability that the error is significant converges to its minimum possible value as the number of elements in the cluster ensemble tends to infinity. Output of the method applied to a real set of data is compared with the results of popular regression methods that use a standard kernel and have all the data labelled. In noisy conditions the proposed method showed higher quality, compared with support vector regression algorithm with standard kernel.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amemiya, T.: Generalized least squares theory. In: Advanced Econometrics. Harvard University Press (1985)
Henderson, D.J., Parmeter, C.F.: Applied Nonparametric Econometrics. Cambridge University Press, New York (2015)
Maronna, R., Martin, D., Yohai, V.: Robust Statistics: Theory and Methods. Wiley, Hoboken (2006)
Zhu, X.: Semi-supervised learning literature survey. Technical report, Department of Computer Science, University of Wisconsin, Madison, no. 1530, pp. 35–36 (2008)
Ghosh, J., Acharya, A.: Cluster ensembles. Wiley Interdiscip. Rev.: Data Min. Knowl. Discov. 1(5), 305–315 (2011)
Vega-Pons, S., Ruiz-Shulclope, J.: A survey of clustering ensemble algorithms. IJPRAI 25(3), 337–372 (2011)
Fred, A., Jain, A.: Combining multiple clusterings using evidence accumulation. IEEE Trans. Pattern Anal. Mach. Intell. 27, 835–850 (2005)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Berikov, V., Karaev, N., Tewari, A.: Semi-supervised classification with cluster ensemble. In: Proceedings of 2017 International Multi-conference on Engineering, Computer and Information Sciences (SIBIRCON), Novosibirsk, Russia, 18–22 September 2017, pp. 245–250. IEEE (2017)
Dua, D., Karra Taniskidou, E.: UCI machine learning repository. School of Information and Computer Science, University of California, Irvine, CA (2017). http://archive.ics.uci.edu/ml
Yeh, I.-C.: Modeling of strength of high performance concrete using artificial neural networks. Cem. Concr. Res. 28(12), 1797–1808 (1998)
Acknowledgment
The article was prepared according to the scientific research program “Mathematical methods of pattern recognition and prediction” in the Sobolev Institute of mathematics SB RAS. The research was partly supported by RFBR grant 18-07-00600 and partly by the Russian Ministry of Science and Higher Education under the 5-100 Excellence Programme. We also want to express our gratitude to the reviewers, as their comments helped us to fill the missing and outlined areas for further research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Berikov, V., Vinogradova, T. (2018). Regression Analysis with Cluster Ensemble and Kernel Function. In: van der Aalst, W., et al. Analysis of Images, Social Networks and Texts. AIST 2018. Lecture Notes in Computer Science(), vol 11179. Springer, Cham. https://doi.org/10.1007/978-3-030-11027-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-11027-7_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11026-0
Online ISBN: 978-3-030-11027-7
eBook Packages: Computer ScienceComputer Science (R0)