## 4 Numerical Studies
### Simulation Results  
Based on the analysis of similarity profiles, we found the following results. At first, different user pairs are shown that are at specific locations of the same time span. For calculating mobility similarities among different user pairs at different time intervals, data of the users are selected from the USC traces available in the dataset. Figures 1-3 show different pairs of users who are found at the same location at the same time interval. The following histograms show the similarities of different user pairs on different days of the week.  
The users are from the same data set that we used for experiments. In these histograms, the number of user pairs is taken as a function of similarity showing the behavioral similarity of different days of mobile users. The result was a co-occurrence matrix having no null value and combinations of visited locations for both users. Then we deployed the SVD technique on the co-occurrence matrix for a normalized output. Each similarity value was calculated for different days and plotted respectively. The experiment was performed to show that the SAA approach is a deep analysis (on a daily basis) of similar behavior. Figures 1-3 show the deep analysis of different pairs of users that are calculated at the  
Figure 3: Similarity analysis during different days, (**a**) On Friday, and (**b**) On Saturday. Similarity shows that these users are found on the same location during the same time frame.  
Figure 2: Similarity analysis during different days, (**a**) On Monday, (**b**) On Tuesday, (**c**) On Wednesday, and (**d**) On Thursday. Similarity shows that these users are found on the same location during the same time frame.  
same location at the same time interval. The following histograms show the similarities of different user pairs on different days of the week. The users are from the same data set that we used for experiments. In these histograms, the number of user pairs is taken as a function of similarity showing the behavioral similarity of different days of mobile users.  
The data set was divided based on each day i.e., for seven days a week. For each day, we used iterator tools to bring the data in sorted form, i.e., all combinations were extracted. The locations visited by both users \(x\) and \(y\) were sorted and their co-occurrences were recorded. After recording multiple co-occurrences, we removed the redundant information and only unique location IDs were extracted. We used iterator tools that were function-creating iterations for efficient looping and redundant information using groups by command.  
For weekends, i.e., Saturday and Sunday, the lowest similarity reached zero and the highest similarities were 0.000020 and 0.00008 as the number of active users was quite less due to the absence of academic activity. In Figure 4, we compared the similarity characteristics of those users who have common mobility behaviors based on location and time. The comparative analysis of 7 days shows a very high similarity on Monday.  
The comparison results show a similar pattern with the increased number of similarity-user pairs in SAA as shown in Figure 4. The \(x\)-axis shows similarity and the \(y\)-axis shows user pairs.  
The graph given in Figure 5 shows the comparison of our purposed mode SAA with the existing work. The existing approach uses longitudinal wireless activity sessions and assigns more than one access point to a building and considered a different location. Whereas our model is based on location and time with one access point to each building, and the building is considered as one location. To capture more mobility patterns, we used the co-occurrence matrix. The comparison results also show that the proposed model SAA is 33% more efficient than the existing approach. The comparison results are based on (a one-week) dataset.  
Figure 4: Similarity analysis of all 7 days of a week.