Curve Clustering via Pairwise Directions Estimation

This article concerns the cluster analysis of curve response data with multi-dimensional covariates. A novel clustering approach based on dimension reduction to group curves with similar patterns without requiring a prespecified parametric model is introduced. The proposed method can be applied to analyze regularly or irregularly observed curve data. Instead of being driven by cost optimization, the clustering problem is shifted to explore the mean functions and basis patterns in data from the geometric viewpoint. For implementing a data-driven function search, the method of pairwise directions estimation (PDE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf {PDE}$$\end{document}) (Lue Journal of Statistical Computation and Simulation 89, 776-794 2019) is applied. The benefit of using geometric information from the PDE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf {PDE}$$\end{document} is highlighted. The proposed method is on the basis of the squared prediction error to achieve optimal cluster membership prediction. Our proposal can not only obtain higher cluster qualities in clustering but also enhance the interpretation of cluster structure. Several simulation examples are conducted, and comparisons are made with nine methods. Applications to two real datasets are also presented for illustration.