Regression Analysis with Cluster Ensemble and Kernel Function
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.
KeywordsRegression analysis Cluster analysis Ensemble clustering Kernel methods
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.
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