Network Inference and its Application to the Estimation of Crowd Dynamics from IoT Sensors Nikhil Ravi, Raksha Ramakrishna, Hoi-To Wai, Anna Scaglione School of Electrical Computer and Energy Engineering Arizona State University, Tempe, AZ, United States {nravi6, raksha.ramakrishna, htwai, Anna.Scaglione} @asu.edu Abstract—In this paper, we explore the application of system identification techniques to the inference of a model that char- acterizes crowd dynamics, inspired by the social force model proposed by Helbing and Moln´ ar. We focus then on sensor observations of pedestrians’ actions considering that wearables, smart mobile phones and other IoT devices embedded in the environment give significant insights on their expected mobility patterns. Previous work using IoT sensors to uncover social interactions is not based on mathematical models, while most models used for tracking mobility ignore the strong coupling between the model-agents as well as their surroundings. Our aim is to bridge these approaches, by capturing in the data model the swarming behavior of the network, including social interactions. Keywords-non-linear graph filter, network inference, Viterbi training, crowd-dynamics, IoT; I. I NTRODUCTION IoT promises to provide a window for observing individ- uals interacting with their surroundings in real time. In the realms of IoT technology, crowd analysis is typically based on machine vision, and pertains the analysis of crowds from camera networks. With the emergence of the IoT, a long line of algorithms have been proposed to harness sensor data from the sensors embedded in off-the-shelf mobile and IoT devices that people carry with them e.g., [1], [2]. A framework to collect real-time data that captures social interactions among the agents is presented in [3]. Community sensing also leverages the trends in the aggregate data collected from cliques of people who have similar goals (at least in the short term) [2]. Work has also been undertaken to utilize the knowledge of agents’ social relationships to automate the identification cliques of people to participate in group actions, e.g., [4]. The authors in [5] have proposed a paradigm where the concepts of social networking are integrated into the IoT along with a sys- tem architecture required for such a paradigm. The approach taken in this paper towards inference or relationship is very different: specifically, we introduce a crowd-dynamics model that captures social influence and uses a system identification approach and convert the IoT data in a tomographic image of the relative influence each agent exerts on other agents. The model builds on a long history of interdisciplinary research efforts, as surveyed in [6]. Related approaches can roughly This work was supported in part by the National Science Foundation CCF- BSF 1714672 grant. be categorized into flow-based, entity-based and agent-based [7]. These approaches differ in terms of the complexity levels — the flow-based models describe the crowd as a simple, continuous flow of fluid, e.g., [8]; the entity-based models describe each individual in a crowd as homogeneous entities, where the resulting models are similar to a particle system, e.g., [9]; the agent-based models describe each individual in a crowd as an autonomous agent whose movements are decided independently by an agent-specific rule, e.g., [10]. Note that the entity based models have been studied theoretically to analyze emergent swarming behavior, e.g., [11]. The social force model proposed by Helbing and Moln´ ar (HM) is perhaps the most popular entity-based model. The HM model easily accounts for various external effects such as road blocks, walls, etc. The model postulates that the movement of individuals is affected by three forces: a) a self-driving force (to reach his destination) prompting the agent to accelerate to a certain velocity, b) a repulsive force to keep a distance from the others and c) a repulsion force to avoid hitting obstacles, and d) an attractive force towards other pedestrians they may know, as well towards certain sites on the road side (like shops’ displays). However, in practicality a pedestrian doesn’t expe- rience the same level of social force with all the others in the area. To accommodate this, in this paper we parameterize the attractions and repulsions pedestrians experience towards one another by weighted adjacency matrices. It is also worthwhile to mention the recent work in [12] which use an optimization based model for entity-based crowd dynamics. In the context of network inference, a popular problem is inferring the network topology in the form of a binary adja- cency matrix describing the inter-dependency of the agents’ actions. Typically, this problem is studied under the general framework of graphical model inference, e.g., the popular graphical LASSO method [13]. Also related is the literature on network topology recovery from online social networks [14]. The more difficult problem involves network identification, which aims at inferring the exact network dynamics including the strengths of interaction between agents. Recent efforts have been found on the topic, e.g., [15], [16]. An algorithm that estimates the underlying graph to structure and capture the correlations between large number of unstructured time series (like financial data from the stock market) is presented in [17]. Inference of the underlying graphs from data generated by a linear graph-filter is explored in [18]. Non-linear kernel-based 2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 978-1-5386-3512-4/18/$31.00 ©2018 IEEE