Semi-supervised Sequential Kernel Regression Models with Pairwise Constraints

Abstract

Regression analysis has a long history and switching regression models is a derived form that can output multiple clusters and regression models. Semi-supervision is also useful technique for improving accuracy of regression analysis. However, there is one problem: the results have a strong dependency on the predefined number of clusters. To avoid these drawbacks, we proposed semi-supervised sequential regression models which we call SSSeRM that are related to the algorithm of sequential extractions. In sequential extractions process, one cluster is extracted at a time using a method of noise-detection, and the number of clusters are determinate by automatically. In this paper, we extend the capability of SSSeRM for handling non-linear structures by using kernel methods. Kernel methods can handle non-linear data and we propose two kernel regression algorithms (sequential kernel regression models and semi-supervised sequential kernel regression models) which can output clusters and regression models without defining cluster number. We compare these methods with the ordinary kernel switching regression models and semi-supervised kernel switching regression models and show the effectiveness of the proposed method by using numerical examples.