Piecewise Linear Regression Based on Plane Clustering

Abstract

Piecewise linear regressions have shown many successful applications in image denoising, signal process, and data mining fields. In essence, they attempt to seek multiple linear functions (piecewise/stepwise function) to fit the given scatter data points by various methodologies, typically point-centered clustering methods, such as ${k}$ -means or fuzzy c means. Obviously, it is reasonable that plane-centered clustering is more suitable for capturing the linearities in data. In this paper, we propose an efficient piecewise linear regression method based on ${k}$ -plane clustering, termed as PlrPC. The proposed method first partitions the data into multiple plane-centered clusters and then analytically compute corresponding piecewise linear functions. Compared with the state-to-the-art linear regressors, the advantages of the PlrPC lie in fourfold: 1) it is generated from plane clustering, which is truly coincident with geometrical intuition; 2) to fuse the linear characteristics into plane clustering, a new implicit regression method is proposed; 3) a new plane jump method is proposed to detect the number of clusters, and; 4) the leading problem can be solved by ordinary eigenvalue problems. The experimental results will show the aforesaid characters on some artificial and some benchmark datasets.