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

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. History: Kwok Tsui served as the senior editor for this article. Funding: The research by J. Min and Y. Hong was partially supported by the National Science Foundation [Grant CMMI-1904165] to Virginia Tech. The work by Y. Hong was partially supported by the Virginia Tech College of Science Research Equipment Fund. Data Ethics & Reproducibility Note: The original dataset is proprietary and cannot be shared. The full code to replicate the results in this paper, based on summary statistics of the original data, is available at https://github.com/jiem3/MultiFuncClustering . The code applied to a simplified version is available at https://codeocean.com/capsule/4041000/tree/v1 , which covers the data analysis and part of the simulation scenarios with a single dataset under each scenario using a fixed set of hyperparameters, for reducing computation time, and at https://doi.org/10.1287/ijds.2022.0034 .