Countrywide arrhythmia: emergency event detection using mobile phone data

Abstract

Large scale social events that involve violence may have dramatic political, economic and social consequences. These events may result in higher crime rates, spreading of infectious diseases, economic crises, and even in migration phenomena (e.g., refugees across borders or internally displaced people). Hence, researchers have started using mobile phone data for developing tools to identify such emergency events in real time. In our paper, we apply a stochastic model, namely a Markov modulated Poisson process, for spatio-temporal detection of hourly and daily behavioral anomalies. We use the call volumes collected from an entire geographic region. Our work is based on the assumption that people tend to make calls when extraordinary events take place. We validate our methodology using a dataset of mobile phone records and events (emergency and non-emergency) from the Republic of Côte d’Ivoire. Our results show that we can successfully capture anomalous calling patterns associated with violent events, riots, as well as social non-emergency events such as holidays, sports events. Moreover, call volume changes also show significant temporal and spatial differences depending on the type of an event. Our results provide insights for the long-term goal of developing a real-time event detection system based on mobile phone data.

Appendix

A.1 Derivation of Markov modulated Poisson process

In this section we present how we implement the Markov modulated Poisson process in order to detect anomalous events.

The model is represented as a two state Markov chain, with a normal call behavior state $z{(t)} = 0$ and an abnormal call behavior state $z{(t)} = 1$, as shown in Figure 8. The transitions between the states are defined with a transition probability matrix $M_{z}$ in Equation (6), which is time independent but dependent on previous transition probabilities

$$\begin{aligned}& z(t)= \textstyle\begin{cases} 1, & \text{if there is an event in time } t,\\ 0, & \text{otherwise}, \end{cases}\displaystyle \end{aligned}$$

(6)

$$\begin{aligned}& M_{z} = \begin{pmatrix} {1-z_{0}} & z_{1} \\ z_{0} & {1 - z_{1}} \end{pmatrix}. \end{aligned}$$

(7)

Figure 8

Event transition state diagram.

Our observations are denoted as $N(t)$, and hidden variables are as follows: the amount of calls in a normal call pattern $N_{0}(t)$, the amount of calls initiated because of an anomalous event $N_{E}(t)$ and the transition probabilities of events $z(t)$ as in Equation (7). The definition of $N^{k}(t)$ for a cell tower k is given by the summation of hidden variables $N^{k}_{0}(t)$ and $N^{k}_{E}(t)$, as shown in Equation (8)

$$ N^{k}(t) = N^{k}_{0}(t) + N^{k}_{E}(t). $$

(8)

We assume that the number of calls are generated through a heterogeneous Poisson distribution $\operatorname{Pois}(N,\lambda(t))$, with the rate value that is a function of time $\lambda(t)$, as shown in Equation (9). Changes in the count data are modeled taking into account the periodicity depending on the day and on the hour of the day. In Appendix A.1.1, this property is used to calculate the posterior distributions

$$\begin{aligned} \operatorname{Pois}\bigl(N;\lambda(t)\bigr) = e^{-\lambda(t)} \bigl(\lambda(t)^{N} / N!\bigr). \end{aligned}$$

(9)

The normal call pattern of a cell tower k is dependent on the day (i) of the week ($\delta^{k}_{i}$) and the hour (j) of the day $\eta ^{k}_{j,i}$, and $\lambda^{k}_{0}$ represents the average rate of cell towers in one week. We can formulate the rate function of the Poisson distribution $\lambda^{k}(t)$ as the product of the initial rate $\lambda ^{k}_{0}$, the daily effect $\delta^{k}_{i}$, and the hourly effects $\eta ^{k}_{j, i}$, Equation (10). Plate notation is used to depict the repeating form of the data, as shown in Figure 9

$$\begin{aligned} \lambda^{k}(t) = \lambda^{k}_{0} \delta^{k}_{d(t)} \eta^{k}_{d(t),h(t)}. \end{aligned}$$

(10)

Figure 9

The graphical model to understand hour of day and day of week effect, taken from [ 11 ].

Conjugate prior ensures that the posterior distribution is coming from the same family of the prior distribution. Hence, our model becomes tractable and it can be written in closed form. Random variables δ, η, denoting the day of the week and the hour of the day, are coming from a multinomial distribution as shown in Equation (11) and the conjugate prior is selected as Dirichlet distribution in Equation (12)

$$\begin{aligned}& \begin{aligned} &\sum_{i=1}^{7} { \delta_{i}} = 7, \\ &\sum_{i=1}^{D} {\nu_{j,i}} = {D} \quad \forall j, \end{aligned} \end{aligned}$$

(11)

$$\begin{aligned}& \begin{aligned} &\lambda_{0} \sim\Gamma\bigl( \lambda;a^{L},b^{L}\bigr), \\ &\frac{1}{7} [ \delta_{1},\ldots,\delta_{7}] \sim Dir \bigl(\alpha^{d}_{1}\cdots\alpha^{d}_{7} \bigr), \\ &\frac{1}{D}[\eta_{j,i},\ldots,\eta_{j,D}] \sim Dir \bigl(\alpha^{h}_{1}\cdots\alpha ^{h}_{D} \bigr). \end{aligned} \end{aligned}$$

(12)

In the right side of Figure 9, $z_{(t-1)}$, $z_{(t)}$ and $z_{(t+1)}$ show the time series properties of the event transitions. $N_{0}(t)$ and $N_{E}(t)$ are hidden variables, and $N(t)$ is our observation

$$\begin{aligned} &z_{0} \sim\beta\bigl(z;a_{0}^{Z},0^{Z} \bigr), \end{aligned}$$

(13)

$$\begin{aligned} &z_{1} \sim\beta\bigl(z;a_{1}^{Z},b_{1}^{Z} \bigr), \end{aligned}$$

(14)

$$\begin{aligned} &N_{E}(t)= \textstyle\begin{cases} 0, & z(t) = 0,\\ P(N;\lambda(t)), & z(t) = 1, \end{cases}\displaystyle \end{aligned}$$

(15)

$$\begin{aligned} &\lambda(t) \sim\Gamma\bigl(\lambda; a^{E}, b^{E} \bigr). \end{aligned}$$

(16)

Event probabilities can be sampled through the densities of a normal event $P(N;\gamma)$ times the probability of having an anomalous event $\gamma(t)$ as shown in Equation (17)

$$ \int{P(N;\gamma)\Gamma\bigl(\gamma;a^{E},b^{E} \bigr)} = Nbin \biggl(N;a^{E}, \frac{b^{E}}{1+b^{E}}\biggr). $$

(17)

The hyper parameters of Gamma Distribution Γ, $a^{E}$ and $b^{E}$ in Equation (16) set the distribution’s sharpness or smoothness between the transition states $Z_{0}$ and $Z_{1}$. In traumatic events, the transition generates a sharp peak. Estimation of these two parameters are shown in Appendix A.1.1.

A.1.1 Inference and parameter estimation

In our model, we need to estimate the parameters for the Gamma distribution $\Gamma(\gamma;a^{E},b^{E})$ in order to model the probability of an anomalous event $p(z(t)^{k} | N(t)^{k})$. Let us assume $\{ N_{0}(t), N_{E}(t), z(t)\}$ are given. Then, we may estimate the parameters of the distribution by computing the maximum likelihood [43], given that all other variables are conditionally independent. However, as in Figure 9, only $N(t)$ is observed, without separation into $N_{0}(t)$ and $N_{E}(t)$. The rest of the parameters, including $z(t)$, are estimated from the observations. Since we do not know when a social or emergency event takes place, we estimate the parameters of the model with the information we obtained. In that respect, we take one cell tower, which is known for having an associated event, and calculate the deviation from the mean value of the hour of the day $\eta^{k}_{j, i}$, and day of the week $\delta^{k}_{i}$ from the observation, as in Equation (3). After tuning these parameters for a single cell tower, we apply them to all $N_{E}(t)$ in the dataset. We exclude the cell tower that is used for calculating the hyper parameters from the evaluation set. Since the model may be sensitive to the selection of hyper parameters, this selection is important for the evaluation of the model. We recommend the selection of a cell tower that represents the average rate function of the all cell towers. Furthermore, the selected antenna should have a number of observed events, so that the rate change can be quantified. The duration of the experiment is not important if the data can represent the normal behavior of the cell tower, which corresponds to the mean value of the call volume in our case.

A.2 Event lists

In Table 3 and 4 we list emergency and social non-emergency events, gathered from a variety of public sources (e.g., Armed Conflict Location and Event Data Project, United Nations Council and International Crisis Group reports, local and international news). The cell towers IDs in the event region are given for the analyzed data period.

Table 3 List of emergency and social non emergency events. MMPP and baseline results columns show the detected events with ‘X’ and the undetected ones with ‘-’. Specifically, we use ‘E’ for emergency events and ‘S’ for social non emergency events. For the emergency events not gathered from UN reports [ 62 ] we cite the source

Table 4 List of emergency and social non emergency events. MMPP and baseline results columns show the detected events with ‘X’ and the undetected ones with ‘-’. Specifically, we use ‘E’ for emergency events and ‘S’ for social non emergency events. For the emergency events not gathered from UN reports [ 62 ] we cite the source