Tensor decomposition techniques for analysing time-varying networks

The aim of this Ph.D thesis is the study of time-varying networks via theoretical and data-driven approaches. Networks are natural objects to represent a vast variety of systems in nature, e.g., communication networks (phone calls and e-mails), online social networks (Facebook, Twitter), infrastructural networks, etc. Considering the temporal dimension of networks helps to better understand and predict complex phenomena, by taking into account both the fact that links in the network are not continuously active over time and the potential relation between multiple dimensions, such as space and time. A fundamental challenge in this area is the definition of mathematical models and tools able to capture topological and dynamical aspects and to reproduce properties observed on the real dynamics of networks. Thus, the purpose of this thesis is threefold: 1) we will focus on the analysis of the complex mesoscale patterns, as community like structures and their evolution in time, that characterize time-varying networks; 2) we will study how these patterns impact dynamical processes that occur over the network; 3) we will sketch a generative model to study the interplay between topological and temporal patterns of time-varying networks and dynamical processes occurring over the network, e.g., disease spreading. To tackle these problems, we adopt and extend an approach at the intersection between multi-linear algebra and machine learning: the decomposition of time-varying networks represented as tensors (multi-dimensional arrays). In particular, we focus on the study of Non-negative Tensor Factorization (NTF) techniques to detect complex topological and temporal patterns in the network. We first extend the NTF framework to tackle the problem of detecting anomalies in time-varying networks. Then, we propose a technique to approximate and reconstruct time-varying networks affected by missing information, to both recover the missing values and to reproduce dynamical processes on top of the network. Finally, we focus on the analysis of the interplay between the discovered patterns and dynamical processes. To this aim, we use the NTF as an hint to devise a generative model of time-varying networks, in which we can control both the topological and temporal patterns, to identify which of them has a major impact on the dynamics

Understanding Trust

Several papers study the effect of trust by using the answer to the World Values Survey (WVS) question "Generally speaking, would you say that most people can be trusted or that you can't be too careful in dealing with people?" to measure the level of trust. Glaeser et al. (2000) question the validity of this measure by showing that it is not correlated with senders' behavior in the standard trust game, but only with his trustworthiness. By using a large sample of German households, Fehr et al. (2003) find the opposite result: WVS-like measures of trust are correlated with the sender's behavior, but not with its trustworthiness. In this paper we resolve this puzzle by recognizing that trust has two components: a belief-based one and a preference based one. While the sender's behavior reflects both, we show that WVS-like measures capture mostly the belief-based component, while questions on past trusting behavior are better at capturing the preference component of trust.

Estimating the outcome of spreading processes on networks with incomplete information: a mesoscale approach

Recent advances in data collection have facilitated the access to time-resolved human proximity data that can conveniently be represented as temporal networks of contacts between individuals. While this type of data is fundamental to investigate how information or diseases propagate in a population, it often suffers from incompleteness, which possibly leads to biased conclusions. A major challenge is thus to estimate the outcome of spreading processes occurring on temporal networks built from partial information. To cope with this problem, we devise an approach based on Non-negative Tensor Factorization (NTF) -- a dimensionality reduction technique from multi-linear algebra. The key idea is to learn a low-dimensional representation of the temporal network built from partial information, to adapt it to take into account temporal and structural heterogeneity properties known to be crucial for spreading processes occurring on networks, and to construct in this way a surrogate network similar to the complete original network. To test our method, we consider several human-proximity networks, on which we simulate a loss of data. Using our approach on the resulting partial networks, we build a surrogate version of the complete network for each. We then compare the outcome of a spreading process on the complete networks (non altered by a loss of data) and on the surrogate networks. We observe that the epidemic sizes obtained using the surrogate networks are in good agreement with those measured on the complete networks. Finally, we propose an extension of our framework when additional data sources are available to cope with the missing data problem

Performance Dynamics and Success in Online Games

Online data provide a way to monitor how users behave in social systems like social networks and online games, and understand which features turn an ordinary individual into a successful one. Here, we propose to study individual performance and success in Multiplayer Online Battle Arena (MOBA) games. Our purpose is to identify those behaviors and playing styles that are characteristic of players with high skill level and that distinguish them from other players. To this aim, we study Defense of the ancient 2 (Dota 2), a popular MOBA game. Our findings highlight three main aspects to be successful in the game: (i) players need to have a warm-up period to enhance their performance in the game; (ii) having a long in-game experience does not necessarily translate in achieving better skills; but rather, (iii) players that reach high skill levels differentiate from others because of their aggressive playing strategy, which implies to kill opponents more often than cooperating with teammates, and trying to give an early end to the match