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

This article focuses on developing a clustering method for multivariate functional data that simultaneously performs variable (sensor) selection, motivated by engineering systems with multisensor data streams. The proposed approach applies functional principal component analysis (FPCA) to reduce dimensionality, followed by model-based clustering using Gaussian mixture distributions with three types of penalty terms—individual, variable, and group penalties—to automatically identify and remove noninformative sensors. An expectation-maximization (EM) algorithm is employed for parameter estimation, and a modified adjusted Bayesian information criterion (BIC) guides hyperparameter selection, including the number of clusters and penalty parameters. Simulation studies demonstrate that all penalties effectively perform clustering and variable selection, with the group penalty showing superior performance in accuracy and sensor selection. Application to a real engineering system with 42 sensors illustrates the method’s ability to reduce sensor dimensionality and reveal meaningful operating patterns, highlighting its potential utility in sensor scheduling and decision-making in engineering and other multivariate functional data contexts.