Sparse and Robust Multivariate Functional Principal Component Analysis for Passenger Flow Pattern Discovery in Metro Systems

Abstract

Modern metro systems in big cities have accumulated large amounts of passenger transit transaction data via the deployment of automatic fare collection (AFC) devices, which could facilitate a thorough analysis of passenger flow dynamics. To discover the underlying passenger flow patterns over all stations in an entire metro system, this paper proposes a multivariate functional principal component analysis (MFPCA) method. The functional integrity of a single daily passenger flow profile at each station is explicitly utilized, and the complex correlation among a multitude of daily passenger flow profiles from all stations is comprehensively modeled. Moreover, to simultaneously improve the interpretability of eigenvectors and mitigate the sensitivity to outliers, the MFPCA is formulated as a minimization problem with both a sparsity and a robustness penalty term. A computationally efficient algorithm is developed accordingly to obtain the eigenvectors. The superiority of our proposed sparse and robust MFPCA (SRMFPCA) is validated using a Hong Kong Mass Transit Railway (MTR) dataset. The derived sparse and smooth eigenvectors can be well interpreted as empirically meaningful passenger flow patterns. The results of our method can be further used as solid foundations for station clustering, correlation analysis and outlier identification.