# Predicting Human Location Using Correlated Movements
## 5 Detection of Persons with Correlated Movements
### Behavioral Similarity-Based Method  
Persons \(p\) and \(q\) are said to have similar behavior if they experience a correlated visit behavior pattern, and hence, the location of a person can be estimated by using the other's positional information. The places two people with similar behaviors visit at the same time are denoted as correlated locations. Note that correlated locations may be different. As seen in Table 3, persons \(p\) and \(q\) show a lot of similar behaviors even though they do not encounter each other. For example, person \(p\) exercises at a gym whenever person \(q\) visits a cafe. It is beneficial to measure the behavior similarity between  
Figure 2: A three-dimensional CIS tensor, denoted by **S**. persons because the location of a person can be inferred by using information of another person with a correlated behavioral pattern. For instance, the location of \(p\) at 3 p.m. on day 2 can be predicted using person \(q\)'s location (cafe). Based on this observation, in the BSB method, persons with the highest behavioral correlation are chosen as PCMs. The key difference between the BSB method and friendship-based methods (i.e., CISB and EFB) is as follows. When selecting a PCM, the BSB method does not consider real friendships between people while friendship-based methods extract co-location information to measure the friendships between them. Specifically, in the EFB method, members with the highest number of encounters with a given person are chosen as PCMs. As shown in Table 3, persons \(p\) and \(u\) encounter each other several times (in math class and the laboratory), which indicates a close friendship between them. Therefore, in friendship-based methods, person \(u\) is likely to be chosen as a PCM of person \(p\). Meanwhile, in case of two people with similar behaviors but different correlated locations, a person is not likely to be selected as a PCM of the other person. For example, persons \(p\) and \(q\) have the same behavior of having dinner at 5 p.m. at restaurant B and restaurant C, respectively. Since there is no encounter between people \(p\) and \(q\), in friendship-based methods person \(q\) does not obtain a high enough score to be selected as a person \(p\)'s PCM. On the other hand, the BSB method considers this correlated behavior for choosing PCMs. In the BSB method, a feed-forward neural network (NN), shown in Figure 3, is constructed to evaluate the behavioral similarity between persons \(p\) and \(q\). \(x_{q,t}^{\text{loc}}\) is defined as the location of person \(q\) at time \(t\), while \(x_{t}^{\text{day}}\) and \(x_{t}^{\text{time}}\) are indices of the day and the time slot at time \(t\), respectively. The objective is to learn the underlying conditional probability distribution \(f_{\text{BSB}}(x_{q,t}^{\text{loc}},x_{t}^{\text{day}},x_{t}^{\text{time}})=P(x _{p,t}^{\text{loc}}|x_{q,t}^{\text{loc}},x_{t}^{\text{day}},x_{t}^{\text{time}})\), i.e., the probability mass distribution that person \(p\) stays in a specific location during time slot \(t\) given the spatio-temporal information of person \(q\). Here, the training process is described. First, symbolic location \(x_{q,t}^{\text{loc}}\) is embedded into an \(|\mathbb{L}|\)-dimensional indicator vector using one-hot encoding, because there is no ordinal relationship between locations. Similarly, time slot and day indices (i.e., \(x_{t}^{\text{day}}\) and \(x_{t}^{\text{time}}\), respectively) are also  
Figure 3: Architecture of the neural network for measuring behavioral similarity between persons \(p\) and \(q\) in the BSB method.