## 6 Instance Analysis and Experiment Results  
We conduct an experiment to validate the effect of our approach. The experiment tool is MATLAB Tensor Toolbox, and we use Python for data processing and features extraction. The dataset provided by \"Intelligent Traffic Prediction Competition\" of [PERSON] is used. The dataset includes the road network information of 132 links, and average travel time of each links from 1 March to 31 May 2016, in which the sample data are collected every 2 min. For example, Table 1 shows the travel time of links. The other information, such as road network information, could be downloaded from [PERSON] official website. Since the dataset is real-data, there are a lot of missing data, some of statistical outliers, and out-of-order time slices. Therefore, it can be analyzed as an instance, and the effect of missing data completion and future data prediction can be verified. The traffic flow prediction scenario predicts the travel time of each link during the first day of the May Day holiday by using the data in March and April 2016. To compare different time periods, according to the tensor window, we select the data of time slices between 6:00 am and 9:58 am for morning peak prediction, the data of time slices between 10:00 am and 13:58 pm for noon peak prediction, the data of time slices between 14:00 pm and 17:58 pm for evening peak prediction. The prediction results will be demonstrated below. Our task is to validate the missing data restoration accuracy and future traffic flow prediction accuracy. Since we cannot obtain real value of the missing data, the restoration accuracy cannot be directly verified. Therefore, we compare the prediction accuracy of using the completed data and non-completed data to verify the restoration accuracy. Figure 5 shows the data distribution, and there are some obvious outliers. Since the provided information cannot determine whether the outliers are actual fluctuations or incorrect records, we cannot simply delete the outliers. For the missing data, the dataset is not marked with the missing data. In other words, the time slices of missing data do not appear in the time slices sequence. Therefore, we need preprocess the dataset and mark the missing values. As shown in Figure 6, we take the data of time slices from 6:00 am to 9:58 am as an example to explain the missing data distribution. It can be seen that there are serious missing data. Moreover, most of data are missing in some links. Therefore, it is very necessary to recover the missing data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Link\_ID** & **Time\_Interval\_Begin** & **Date** & **Travel\_Time** \\ \hline
4377906289869500514 & 2016-03-01 06:18:00 & 2016-03-01 & Nan \\ \hline
4377906289869500514  
The effect of missing data completion is shown in Figure 7. It can be seen that the Missing Data Completion Algorithm proposed in this paper has a high completion rate. Except for some links where almost all data are missing, other missing data have been completed. For the missing data of the links where almost all data are missing, the data of the upstream and downstream links can be used for approximate completion. Figure 5: Data distribution. Figure 6: Missing data of each link. Figure 7: Missing data completion rate. In this paper, the Root Mean Square Error (RMSE) is used to evaluate the prediction accuracy, and it is as follows [36]:  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{N}\left(ttp_{i}-ttr_{i}\right)^{2}}{N}} \tag{14}\]  
where \(ttp\) represents the predicted travel time of each link, \(ttr\) represents the actual travel time of each link, and \(N\) represents the total number of links, with the value of 132. The smaller RMSE means the better the prediction accuracy. We predict the travel time of each link during the first day of the May Day holiday by using the data from March and April 2016. The data of time slices between 6:00 am ad 9:58 am are selected for morning peak prediction, and we suppose the morning peak appears at 10:00 am, because this day is a holiday.