# Transfer Learning: Video Prediction and Spatiotemporal Urban Traffic Forecasting +
## 4 Experimental Results  
### Data Set  
The performance of the discussed models was estimated on the basis of the large real-world data set, obtained from the archive of Minnesota Department of Transportation (MnDoT). The complete data set includes information for 40 weeks (1 January-8 October 2017) from 2676 detectors, deployed in the city center of Minneapolis. Detectors were uniformly distributed over the analyzed roads with a mean distance of 270 m. For calculation purposes, 100 detectors were randomly sampled from the complete data set for further analysis. A map of the case study area with the spatial distribution of the complete data set and the research sample is presented in Figure 3.  
The original data set includes information on traffic flow volumes, temporarily aggregated by 30-s periods. The executed data preprocessing routines include:  
* Lane detectors' values are aggregated by road.
* Values are aggregated in 5-min time intervals, widely used for short-term traffic forecasting.  
Figure 3: Case study area—complete data set (**blue circles**) and research sample (**red circles**).  
* Median traffic values are calculated for the first 30 weeks for every 5-min time interval and node, and used as periodical patterns of traffic flows.
* Obtained periodical patterns are subtracted from the flow values for the latest 10 weeks of the data set. As a result, we obtained detrended time series that are used for model training and testing. Thus, the models are focused on the forecasting of deviations from regular traffic conditions (in video prediction, this operation corresponds to the removal of a static background scene).
* Outliers are identified using detector- and time period-specific interquartile ranges. The selected threshold value is selected as 0.01 and is fairly small, so only wrong observations are filtered out, while real traffic values for congested conditions are kept in place. The identified outliers are marked as missed values.
* Linear interpolation is utilized for the imputation of missed values; detectors with more than 4 h of missed values in a row are excluded from the final data set.
* 100 detectors are randomly sampled from the complete data set for computational reasons.  
As a result, the preprocessed data set includes a complete 10-week time series (20,160 observations) for 100 detectors that represent deviations from regular traffic conditions. The data set is supplemented by a matrix of travel times between detectors, estimated using acting speed limits.  
Spatial characteristics of the research sample are presented in Figure 4.  
Figure 4a represents a graph of the spatial neighborhood, constructed for 10-min travel times (unconnected vertices correspond to the entrance points of the research road segment, which are not reachable from other nodes). Figure 4b represents the s-curved distribution of reachable nodes by travel time: percentage of nodes, reachable from a given spatial location within a specified time period under uncongested traffic conditions. The form of the curve closely matches for the complete data set and our research sample, so the characteristics of the sample spatial graph are similar to the complete one. Figure 4c contains a heatmap of the spatial Laplacian matrix, which is used for GCNN convolutions. The graph vertices are ordered by their geographical coordinates for better information on the spatial structure; zero-valued Laplacian rows and columns were excluded from the heatmap for smoother representation of the spatial graph structure.