Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation

作     者：Chamroukhi, Faicel 

作者机构：Univ Toulon & Var F-83957 La Garde France Aix Marseille Univ F-13397 Marseille France Lab Paul Painleve Villeneuve Dascq France 

出 版 物：《JOURNAL OF CLASSIFICATION》 (分类杂志)

年 卷 期：2016年第33卷第3期

页      面：374-411页

核心收录：

学科分类：0402[教育学-心理学(可授教育学、理学学位）] 07[理学] 08[工学] 0701[理学-数学] 

基　　金：FUI-SYCIE Project 

主　　题：Model-based clustering Functional data analysis Optimal curve segmentation Mixture models Piecewise regression EM algortihm CEM algorithm 

摘      要：This paper introduces a novel mixture model-based approach to the simultaneous clustering and optimal segmentation of functional data, which are curves presenting regime changes. The proposed model consists of a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches to learning the model parameters: the first is an estimation approach which maximizes the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm, then yielding a fuzzy partition of the curves into K clusters obtained at convergence by maximizing the posterior cluster probabilities. The second is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification expectation-maximization (CEM) algorithm. The optimal curve segmentation is performed by using dynamic programming. In the classification approach, both the curve clustering and the optimal segmentation are performed simultaneously as the CEM learning proceeds. We show that the classification approach is a probabilistic version generalizing the deterministic K-means-like algorithm proposed in Hbrail, Hugueney, Lechevallier, and Rossi (2010). The proposed approach is evaluated using simulated curves and real-world curves. Comparisons with alternatives including regression mixture models and the K-means-like algorithm for piecewise regression demonstrate the effectiveness of the proposed approach.