# Predicting Human Location Using Correlated Movements
## 7 Evaluation Results and Discussion
### Effects of the Number of PCMs  
In this subsection, the number of selected PCMs varies from 1 to 5. As seen in Figure 7b, using location information of one PCM (i.e., \(r=1\)), the PLP model obtains top-1 accuracy of 86.53% with the BSB method compared with 70.92% in case of the MFL model. Meanwhile, the PLP model with EFB, SC, STC, and CISB approaches results in 76.58%, 76.94%, 79.57%, and 76.70% accuracy, respectively.  
It should be emphasized that when adding more PCMs, the performance of the prediction model is generally enhanced. In friendship-based methods (CISB and EFB), this is attributed to the fact that a person usually interacts with multiple PCMs rather than one person during the day. For example, in the morning, person \(p\) encounters co-worker \(q\) at the workplace. At lunch, \(p\) and \(r\) have an appointment at their favorite restaurant. Then, persons \(p\) and \(s\) go to the fitness center to exercise in the afternoon. In other PCMs selection approaches, the performance gain with more PCMs is due to the fact that a person has movement correlation with various PCMs depending on the time of a day. For instance, assume that person \(p\) is a middle-aged man. He may have a similar behavioral pattern with younger co-worker \(q\) during the daytime, whereas after work, he may have behaviors similar to other middle-aged men, rather than with the younger co-workers.  
Moreover, the performance gap between the BSB and friendship-based methods (CISB and EFB) becomes larger as the number of PCMs embedded in the model increases especially in the MIT dataset. This is because selected PCMs of CISB and EFB tend to have more similar encounter patterns with person \(p\) than under the BSB method. To show this, KL divergence [44] is considered to measure similarity between temporal encounter distributions of PCMs and person \(p\). Vector \(q\) denotes the probability distribution of encounters between persons \(p\) and \(q\). The \(i^{\text{th}}\) element of \(q\) represents the probability that persons \(p\) and \(q\) encounter each other during time slot \(i\). Vector \(r\) indicates a distribution of encounters between persons \(p\) and \(r\). The length of \(r\) and \(q\) equals the number of samples for each person. Using KL divergence, the difference between the two probability distributions is given by:  
\[\phi_{q,r}=\sum_{i}q_{i}\log\frac{q_{i}}{r_{i}} \tag{10}\]  
where \(q_{i}\) and \(r_{i}\) are the \(i^{\text{th}}\) elements of vectors \(q\) and \(r\), respectively. If the score from KL divergence is small, encounter distributions between PCMs and person \(p\) are close, which indicates similar movement patterns between PCMs.  
Assume that a mobility prediction model with \(r\) PCMs is considered. If another PCM with highly similar movement patterns to those of the \(r\) existing PCMs is added at input, the location information of the added PCM would not be helpful in predicting location of person \(p\). As shown in Table 7, in cases where the number of selected PCMs is 5, the average value of KL divergence  
Figure 7: Effects of the number of PCMs on the performance of the prediction model in case of (**a**) the MIT dataset and (**b**) Dartmouth dataset.  
between PCMs' patterns of encounters with a person-of-interest is 11.01, 11.03, and 15.19 in EFB, CISB, and BSB methods, respectively. We can also observe from Table 7 that KL divergence values of SC and STC approaches are generally higher than friendship-based ones since SC and STC do not consider encounters between people.  
Lower KL divergence values from EFB and CISB methods indicate that they tend to select PCMs with more similar mobility patterns than the BSB method, and accordingly, movement patterns of the selected PCMs under the BSB method are more divergent than those under EFB/CISB methods. This contributes to a large accuracy gap between the BSB and friendship-based methods. The results also agree with the assumption that correlated locations in the BSB method do not have to be the same places.