| Summary: | 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.
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