Here we propose an online method to explore the multiway nature of urban spaces data for outlier detection based on higher-order singular value tensor decomposition. Our proposal has two sequential steps: (i) the offline modeling step, where we model the outliers detection problem as a system; and (ii) the online modeling step, where the projection distance of each data vector is decomposed by a multidimensional method as new data arrives and an outlier statistical index is calculated. We used real data gathered and streamed by urban sensors from three cities in Finland, chosen during a continuous time interval: Helsinki, Tuusula, and Lohja. The results showed greater efficiency for the online method of detection of outliers when compared to the offline approach, in terms of accuracy between a range of 8.5% to 10% gain. We observed that online detection of outliers from real-time monitoring through the sliding window becomes a more adequate approach once it achieves better accuracy.
Keywords: HOSVD; MPCA; multiway analysis; online monitoring; outlier detection; smart cities.