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Missingness and corruption are common problems for real-world traffic data. How to accurately perform imputation and prediction based on incomplete or even sparse traffic data becomes a critical research question in intelligent transportation systems. Low-rank matrix factorization (MF) is a common solution for the general missing value imputation problem. To better characterize and encode the strong spatial and temporal consistency in traffic data, existing work has introduced flexible spatial/temporal Gaussian process (GP) priors to model the latent factors in MF framework, which also allows us to perform kriging for unseen locations and virtual sensors. However, learning the hyperparameters in GP kernels remains a challenging task. In this paper, we present a Bayesian kernelized matrix factorization (BKMF) model with an efficient Markov chain Monte Carlo (MCMC) sampling algorithm for model inference. By learning the kernel hyperparameters from their marginal posteriors through a slice sampling treatment and updating the latent factors alternatively with Gibbs sampling, we achieve a fully Bayesian model for the spatiotemporally kernelized (i.e., GP prior regularized) MF framework. We apply BKMF on both imputation and kriging tasks, and our results demonstrate the superiority of BKMF compared with state-of-the-art spatiotemporal models. In addition, we also explore the effects of different GP kernels in characterizing networked spatiotemporal traffic state data. [ABSTRACT FROM AUTHOR]

Spatiotemporal traffic time series (e.g., traffic volume/speed) collected from sensing systems are often incomplete with considerable corruption and large amounts of missing values, preventing users from harnessing the full power of the data. Missing data imputation has been a long-standing research topic and critical application for real-world intelligent transportation systems. A widely applied imputation method is low-rank matrix/tensor completion; however, the low-rank assumption only preserves the global structure while ignores the strong local consistency in spatiotemporal data. In this paper, we propose a low-rank autoregressive tensor completion (LATC) framework by introducing temporal variation as a new regularization term into the completion of a third-order (sensor $\times $ time of day $\times $ day) tensor. The third-order tensor structure allows us to better capture the global consistency of traffic data, such as the inherent seasonality and day-to-day similarity. To achieve local consistency, we design the temporal variation by imposing an autoregressive model for each time series with coefficients as learnable parameters. Different from previous spatial and temporal regularization schemes, the minimization of temporal variation can better characterize temporal generative mechanisms beyond local smoothness, allowing us to deal with more challenging scenarios such as “blackout” missing. To solve the optimization problem in LATC, we introduce an alternating minimization scheme that estimates the low-rank tensor and autoregressive coefficients iteratively. We conduct extensive numerical experiments on several real-world traffic data sets, and our results demonstrate the effectiveness of LATC in diverse missing scenarios. [ABSTRACT FROM AUTHOR]

Objective: This study proposes a new parametric time-frequency conditional Granger causality (TF-CGC) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source electroencephalogram (EEG) signals to reveal dynamic interaction patterns in oscillatory neocortical sensorimotor networks. Methods: The Geweke's spectral measure is combined with the time-varying autoregressive with exogenous input (TVARX) modeling approach, which uses multiwavelet-based ultra-regularized orthogonal least squares (UROLS) algorithm, aided by adjustable prediction error sum of squares (APRESS), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves, but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems. Results: The proposed method is validated on two simulations, and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cortical networks. Conclusion: Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks. Significance: The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition. [ABSTRACT FROM AUTHOR]