Toward Interpretable Imputation: Through Discovering Spatiotemporal Patterns of Urban Metro Flow Data

The rapid growth of the Internet of Things (IoT) has enabled the development of intelligent transportation systems (ITS). However, missing data remains a common issue that hinders the effectiveness of ITS. Although many imputation methods have been proposed to handle missing values, they generally aim to improve the accuracy of final imputation results and often neglect the interpretability of the imputation process. This may cause limited trustworthiness and practical applicability in real-world metro management, where understanding the underlying metro data patterns is essential. To address this gap, this paper conducts an in-depth analysis and mining of the unique spatiotemporal structures inherent in metro flow data, aiming at both accurate and interpretable imputation. Specifically, an orthogonal-autoregression matrix factorization (OAMF) algorithm is proposed to discover two low-dimensional, complete spatial and temporal patterns from high-dimensional, incomplete data. By minimizing reconstruction error associated with these two patterns, OAMF ensures the accuracy of final imputation results. Furthermore, through simultaneous distinctive spatial representations modeling and predictive temporal modeling, OAMF encourages the two patterns with clear physical meaning that captures orthogonal spatial distributions and evolving metro flow trends over time, enabling the interpretability of the imputation process. Additionally, the above explicit temporal modeling further extends OAMF’s ability to predict futures. The proposed OAMF is validated using two real-world datasets. Experimental results demonstrate that OAMF not only extracts interpretable spatiotemporal patterns but also achieves superior accuracy in both imputation and prediction across various missing rates compared to existing methods.