Multivariate Functional Clustering with Variable Selection and Application to Sensor Data from Engineering Systems

Zhongnan Jin (), Jie Min (), Yili Hong (), Pang Du () and Qingyu Yang ()
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Zhongnan Jin: Department of Statistics, Virginia Tech, Blacksburg, Virginia 24061
Jie Min: Department of Statistics, Virginia Tech, Blacksburg, Virginia 24061
Yili Hong: Department of Statistics, Virginia Tech, Blacksburg, Virginia 24061
Pang Du: Department of Statistics, Virginia Tech, Blacksburg, Virginia 24061
Qingyu Yang: Department of Industrial and Systems Engineering, Wayne State University, Detroit, Michigan 48202

INFORMS Joural on Data Science, 2024, vol. 3, issue 2, 203-218

Abstract: Multisensor data that track system operating behaviors are widely available nowadays from various engineering systems. Measurements from each sensor over time form a curve and can be viewed as functional data. Clustering of these multivariate functional curves is important for studying the operating patterns of systems. One complication in such applications is the possible presence of sensors whose data do not contain relevant information. Hence, it is desirable for the clustering method to equip with an automatic sensor selection procedure. Motivated by a real engineering application, we propose a functional data clustering method that simultaneously removes noninformative sensors and groups functional curves into clusters using informative sensors. Functional principal component analysis is used to transform multivariate functional data into a coefficient matrix for data reduction. We then model the transformed data by a Gaussian mixture distribution to perform model-based clustering with variable selection. Three types of penalties, the individual, variable, and group penalties, are considered to achieve automatic variable selection. Extensive simulations are conducted to assess the clustering and variable selection performance of the proposed methods. The application of the proposed methods to an engineering system with multiple sensors shows the promise of the methods and reveals interesting patterns in the sensor data.

Keywords: EM algorithm; functional data clustering; functional principal component analysis; Gaussian mixture distribution; group Lasso; signal processing (search for similar items in EconPapers)
Date: 2024
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