Tensor-Train-Based Incremental High Order Dominant Z-Eigen Decomposition for Multi-Modal Intelligent Transportation Prediction

Transportation big data generated from various Internet of Things devices have the feature of muti-source and heterogeneous. To efficiently represent and analyze these ubiquitous transportation big data, tensor and tensor-based data analysis methods have been widely adopted in recent years. As a tensor-based machine learning method, high-order dominant Z-eigen decomposition (HODZED) in multivariate multi-order Markov model is suitable for multi-modal transportation prediction. However, massive transportation data are usually generated in a streaming way and the transportation system requires frequent updates. To avoid recalculating the history data and provide immediate prediction, we propose a tensor train (TT) based incremental HODZED (TT-IHODZED) method. Concretely, we first present an incremental HODZED (IHODZED) method to update the dominant Z-eigentensor in multivariate multi-order Markov model. Then, TT-based tensor operations are adopted to IHODZED to speed up calculations, especially the repeated Einstein products. Furthermore, to solve the TT-based high-order linear equations in TT-IHODZED method, we also propose a TT-based biconjugate gradient stabilized (TT-HOBiCGS) algorithm. Experimental results based on real-world and synthetic datasets show that, compared to HODZED method, TT-IHODZED significantly improves computation efficiency up to 10 times while keeping the same or even better prediction accuracy.