arXiv subjects

Charalampos E. Tsourakakis

Publications and source records attributed to Charalampos E. Tsourakakis.

At least 19 recordsLinked to original sources

arXiv2025

Countering Election Sway: Strategic Algorithms in Friedkin-Johnsen Dynamics

Social influence profoundly impacts individual choices and collective behaviors in politics. In this work, driven by the goal of protecting elections from improper influence, we consider the following scenario: an individual, who has vested interests in political party $Y$, is aware through reliable surveys that parties $X$ and $Y$ are likely to get 50.1\% and 49.9\% of the vote, respectively. Could this individual employ strategies to alter public opinions and consequently invert these polling numbers in favor of party $Y$? We address this question by employing: (i) the Friedkin-Johnsen (FJ) opinion dynamics model, which is mathematically sophisticated and effectively captures the way individual biases and social interactions shape opinions, making it crucial for examining social influence, and (ii) interventions similar to those in Asch's experiments, which involve selecting a group of stooges within the network to spread a specific opinion. We mathematically formalize the aforementioned motivation as an optimization framework and establish that it is NP-hard and inapproximable within any constant factor. We introduce three efficient polynomial-time algorithms. The first two utilize a continuous approach: one employs gradient descent with Huber's estimator to approximate the median, and the other uses a sigmoid threshold influence function. The third utilizes a combinatorial greedy algorithm for targeted interventions. Through comparative analysis against various natural baselines and using real-world data, our results demonstrate that in numerous cases a small fraction of nodes chosen as stooges can significantly sway election outcomes under the Friedkin-Johnsen model.

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arXiv2024

Q-DISCO: Query-Centric Densest Subgraphs in Networks with Opinion Information

Given a network $G=(V,E)$, where each node $v$ is associated with a vector $\boldsymbol{p}_v \in \mathbb{R}^d$ representing its opinion about $d$ different topics, how can we uncover subsets of nodes that not only exhibit exceptionally high density but also possess positively aligned opinions on multiple topics? In this paper we focus on this novel algorithmic question, that is essential in an era where digital social networks are hotbeds of opinion formation and dissemination. We introduce a novel methodology anchored in the well-established densest subgraph problem. We analyze the computational complexity of our formulation, indicating that our problem is NP-hard and eludes practically acceptable approximation guarantees. To navigate these challenges, we design two heuristic algorithms: the first is predicated on the Lagrangian relaxation of our formulation, while the second adopts a peeling algorithm based on the dual of a Linear Programming relaxation. We elucidate the theoretical underpinnings of their performance and validate their utility through empirical evaluation on real-world datasets. Among others, we delve into Twitter datasets we collected concerning timely issues, such as the Ukraine conflict and the discourse surrounding COVID-19 mRNA vaccines, to gauge the effectiveness of our methodology. Our empirical investigations verify that our algorithms are able to extract valuable insights from networks with opinion information.

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arXiv2024

Parallel Motif-Based Community Detection

Community detection is a central task in graph analytics. Given the substantial growth in graph size, scalability in community detection continues to be an unresolved challenge. Recently, alongside established methods like Louvain and Infomap, motif-based community detection has emerged. Techniques like Tectonic are notable for their advanced ability to identify communities by pruning edges based on motif similarity scores and analyzing the resulting connected components. In this study, we perform a comprehensive evaluation of community detection methods, focusing on both the quality of their output and their scalability. Specifically, we contribute an open-source parallel framework for motif-based community detection based on a shared memory architecture. We conduct a thorough comparative analysis of community detection techniques from various families among state-of-the-art methods, including Tectonic, label propagation, spectral clustering, Louvain, LambdaCC, and Infomap on graphs with up to billions of edges. A key finding of our analysis is that motif-based graph clustering provides a good balance between performance and efficiency. Our work provides several novel insights. Interestingly, we pinpoint biases in prior works in evaluating community detection methods using the top 5K groundtruth communities from SNAP only, as these are frequently near-cliques. Our empirical studies lead to rules of thumb threshold picking strategies that can be critical for real applications. Finally, we show that Tectonic can fail to recover two well-separated clusters. To address this, we suggest a new similarity measure based on counts of triangles and wedges (TW) that prevents the over-segmentation of communities by Tectonic.

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arXiv2024

Targeted Least Cardinality Candidate Key for Relational Databases

Functional dependencies (FDs) are a central theme in databases, playing a major role in the design of database schemas and the optimization of queries. In this work, we introduce the {\it targeted least cardinality candidate key problem} (TCAND). This problem is defined over a set of functional dependencies $F$ and a target variable set $T \subseteq V$, and it aims to find the smallest set $X \subseteq V$ such that the FD $X \to T$ can be derived from $F$. The TCAND problem generalizes the well-known NP-hard problem of finding the least cardinality candidate key~\cite{lucchesi1978candidate}, which has been previously demonstrated to be at least as difficult as the set cover problem. We present an integer programming (IP) formulation for the TCAND problem, analogous to a layered set cover problem. We analyze its linear programming (LP) relaxation from two perspectives: we propose two approximation algorithms and investigate the integrality gap. Our findings indicate that the approximation upper bounds for our algorithms are not significantly improvable through LP rounding, a notable distinction from the standard set cover problem. Additionally, we discover that a generalization of the TCAND problem is equivalent to a variant of the set cover problem, named red-blue set cover~\cite{carr1999red}, which cannot be approximated within a sub-polynomial factor in polynomial time under plausible conjectures~\cite{chlamtavc2023approximating}. Despite the extensive history surrounding the issue of identifying the least cardinality candidate key, our research contributes new theoretical insights, novel algorithms, and demonstrates that the general TCAND problem poses complexities beyond those encountered in the set cover problem.

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arXiv2024

A Note on Computing Betweenness Centrality from the 2-core

A central task in network analysis is to identify important nodes in a graph. Betweenness centrality (BC) is a popular centrality measure that captures the significance of nodes based on the number of shortest paths each node intersects with. In this note, we derive a recursive formula to compute the betweenness centralities of a graph from the betweenness centralities of its 2-core.Furthermore, we analyze mathematically the significant impact of removing degree-one nodes on the estimation of betweenness centrality within the context of the popular pivot sampling scheme for Single-Source Shortest Path (SSSP) computations, as described in the Brandes-Pich approach and implemented in widely used software such as NetworkX. We demonstrate both theoretically and empirically that removing degree-1 nodes can reduce the sample complexity needed to achieve better accuracy, thereby decreasing the overall runtime.

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arXiv2024

Wiser than the Wisest of Crowds: The Asch Effect Revisited under Friedkin-Johnsen Opinion Dynamics

In 1907, Sir Francis Galton independently asked 787 villagers to estimate the weight of an ox. Although none of them guessed the exact weight, the average estimate was remarkably accurate. This phenomenon is known as wisdom of crowds. In a clever experiment, Asch employed actors to demonstrate the human tendency to conform to others' opinions. The question we ask is: what would Sir Francis Galton have observed if Asch had interfered by employing actors? Would the wisdom of crowds become even wiser or not? The problem becomes intriguing when considering the inter-connectedness of the villagers, which is the central theme of this work. We examine a scenario where $n$ agents are interconnected and influence each other. The average of their opinions provides an estimator of a certain quality for some unknown quantity. How can one improve or reduce the quality of the original estimator in terms of the MSE by utilizing Asch's strategy of hiring a few stooges? We present a new formulation of this problem, assuming that nodes adjust their opinions according to the Friedkin-Johnsen opinion dynamics. We demonstrate that selecting $k$ stooges for maximizing and minimizing the MSE is NP-hard. We also demonstrate that our formulation is closely related to maximizing or minimizing polarization and show NP-hardness. We propose an efficient greedy heuristic that scales to large networks and test our algorithm on synthetic and real-world datasets. Although MSE and polarization objectives differ, we find in practice that maximizing polarization often yields solutions that are nearly optimal for minimizing the wisdom of crowds in terms of MSE. Our analysis of real-world data reveals that even a small number of stooges can significantly influence the conversation on the war in Ukraine, resulting in a relative increase of the MSE of 207.80% (maximization) or a decrease of 50.62% (minimization).

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arXiv2024

ULTRA-MC: A Unified Approach to Learning Mixtures of Markov Chains via Hitting Times

This study introduces a novel approach for learning mixtures of Markov chains, a critical process applicable to various fields, including healthcare and the analysis of web users. Existing research has identified a clear divide in methodologies for learning mixtures of discrete and continuous-time Markov chains, while the latter presents additional complexities for recovery accuracy and efficiency. We introduce a unifying strategy for learning mixtures of discrete and continuous-time Markov chains, focusing on hitting times, which are well defined for both types. Specifically, we design a reconstruction algorithm that outputs a mixture which accurately reflects the estimated hitting times and demonstrates resilience to noise. We introduce an efficient gradient-descent approach, specifically tailored to manage the computational complexity and non-symmetric characteristics inherent in the calculation of hitting time derivatives. Our approach is also of significant interest when applied to a single Markov chain, thus extending the methodologies previously established by Hoskins et al. and Wittmann et al. We complement our theoretical work with experiments conducted on synthetic and real-world datasets, providing a comprehensive evaluation of our methodology.

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arXiv2024

Markovletics: Methods and A Novel Application for Learning Continuous-Time Markov Chain Mixtures

Sequential data naturally arises from user engagement on digital platforms like social media, music streaming services, and web navigation, encapsulating evolving user preferences and behaviors through continuous information streams. A notable unresolved query in stochastic processes is learning mixtures of continuous-time Markov chains (CTMCs). While there is progress in learning mixtures of discrete-time Markov chains with recovery guarantees [GKV16,ST23,KTT2023], the continuous scenario uncovers unique unexplored challenges. The intrigue in CTMC mixtures stems from their potential to model intricate continuous-time stochastic processes prevalent in various fields including social media, finance, and biology. In this study, we introduce a novel framework for exploring CTMCs, emphasizing the influence of observed trails' length and mixture parameters on problem regimes, which demands specific algorithms. Through thorough experimentation, we examine the impact of discretizing continuous-time trails on the learnability of the continuous-time mixture, given that these processes are often observed via discrete, resource-demanding observations. Our comparative analysis with leading methods explores sample complexity and the trade-off between the number of trails and their lengths, offering crucial insights for method selection in different problem instances. We apply our algorithms on an extensive collection of Lastfm's user-generated trails spanning three years, demonstrating the capability of our algorithms to differentiate diverse user preferences. We pioneer the use of CTMC mixtures on a basketball passing dataset to unveil intricate offensive tactics of NBA teams. This underscores the pragmatic utility and versatility of our proposed framework. All results presented in this study are replicable, and we provide the implementations to facilitate reproducibility.

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arXiv2023

Densest Diverse Subgraphs: How to Plan a Successful Cocktail Party with Diversity

Dense subgraph discovery methods are routinely used in a variety of applications including the identification of a team of skilled individuals for collaboration from a social network. However, when the network's node set is associated with a sensitive attribute such as race, gender, religion, or political opinion, the lack of diversity can lead to lawsuits. In this work, we focus on the problem of finding a densest diverse subgraph in a graph whose nodes have different attribute values/types that we refer to as colors. We propose two novel formulations motivated by different realistic scenarios. Our first formulation, called the densest diverse subgraph problem (DDSP), guarantees that no color represents more than some fraction of the nodes in the output subgraph, which generalizes the state-of-the-art due to Anagnostopoulos et al. (CIKM 2020). By varying the fraction we can range the diversity constraint and interpolate from a diverse dense subgraph where all colors have to be equally represented to an unconstrained dense subgraph. We design a scalable $Ω(1/\sqrt{n})$-approximation algorithm, where $n$ is the number of nodes. Our second formulation is motivated by the setting where any specified color should not be overlooked. We propose the densest at-least-$\vec{k}$-subgraph problem (Dal$\vec{k}$S), a novel generalization of the classic Dal$k$S, where instead of a single value $k$, we have a vector ${\mathbf k}$ of cardinality demands with one coordinate per color class. We design a $1/3$-approximation algorithm using linear programming together with an acceleration technique. Computational experiments using synthetic and real-world datasets demonstrate that our proposed algorithms are effective in extracting dense diverse clusters.

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arXiv2023

Node-Differentially Private Estimation of the Number of Connected Components

We design the first node-differentially private algorithm for approximating the number of connected components in a graph. Given a database representing an $n$-vertex graph $G$ and a privacy parameter $\varepsilon$, our algorithm runs in polynomial time and, with probability $1-o(1)$, has additive error $\widetilde{O}(\frac{Δ^*\ln\ln n}{\varepsilon}),$ where $Δ^*$ is the smallest possible maximum degree of a spanning forest of $G.$ Node-differentially private algorithms are known only for a small number of database analysis tasks. A major obstacle for designing such an algorithm for the number of connected components is that this graph statistic is not robust to adding one node with arbitrary connections (a change that node-differential privacy is designed to hide): every graph is a neighbor of a connected graph. We overcome this by designing a family of efficiently computable Lipschitz extensions of the number of connected components or, equivalently, the size of a spanning forest. The construction of the extensions, which is at the core of our algorithm, is based on the forest polytope of $G.$ We prove several combinatorial facts about spanning forests, in particular, that a graph with no induced $Δ$-stars has a spanning forest of degree at most $Δ$. With this fact, we show that our Lipschitz extensions for the number of connected components equal the true value of the function for the largest possible monotone families of graphs. More generally, on all monotone sets of graphs, the $\ell_\infty$ error of our Lipschitz extensions is nearly optimal.

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arXiv2023

Learning Mixtures of Markov Chains with Quality Guarantees

A large number of modern applications ranging from listening songs online and browsing the Web to using a navigation app on a smartphone generate a plethora of user trails. Clustering such trails into groups with a common sequence pattern can reveal significant structure in human behavior that can lead to improving user experience through better recommendations, and even prevent suicides [LMCR14]. One approach to modeling this problem mathematically is as a mixture of Markov chains. Recently, Gupta, Kumar and Vassilvitski [GKV16] introduced an algorithm (GKV-SVD) based on the singular value decomposition (SVD) that under certain conditions can perfectly recover a mixture of L chains on n states, given only the distribution of trails of length 3 (3-trail). In this work we contribute to the problem of unmixing Markov chains by highlighting and addressing two important constraints of the GKV-SVD algorithm [GKV16]: some chains in the mixture may not even be weakly connected, and secondly in practice one does not know beforehand the true number of chains. We resolve these issues in the Gupta et al. paper [GKV16]. Specifically, we propose an algebraic criterion that enables us to choose a value of L efficiently that avoids overfitting. Furthermore, we design a reconstruction algorithm that outputs the true mixture in the presence of disconnected chains and is robust to noise. We complement our theoretical results with experiments on both synthetic and real data, where we observe that our method outperforms the GKV-SVD algorithm. Finally, we empirically observe that combining an EM-algorithm with our method performs best in practice, both in terms of reconstruction error with respect to the distribution of 3-trails and the mixture of Markov Chains.

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arXiv2022

AntiBenford Subgraphs: Unsupervised Anomaly Detection in Financial Networks

Benford's law describes the distribution of the first digit of numbers appearing in a wide variety of numerical data, including tax records, and election outcomes, and has been used to raise "red flags" about potential anomalies in the data such as tax evasion. In this work, we ask the following novel question: given a large transaction or financial graph, how do we find a set of nodes that perform many transactions among each other that also deviate significantly from Benford's law? We propose the AntiBenford subgraph framework that is founded on well-established statistical principles. Furthermore, we design an efficient algorithm that finds AntiBenford subgraphs in near-linear time on real data. We evaluate our framework on both real and synthetic data against a variety of competitors. We show empirically that our proposed framework enables the detection of anomalous subgraphs in cryptocurrency transaction networks that go undetected by state-of-the-art graph-based anomaly detection methods. Our empirical findings show that our \ab framework is able to mine anomalous subgraphs, and provide novel insights into financial transaction data. The code and the datasets are available at \url{https://github.com/tsourakakis-lab/antibenford-subgraphs}.

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arXiv2021

Dense and well-connected subgraph detection in dual networks

Dense subgraph discovery is a fundamental problem in graph mining with a wide range of applications \cite{gionis2015dense}. Despite a large number of applications ranging from computational neuroscience to social network analysis, that take as input a {\em dual} graph, namely a pair of graphs on the same set of nodes, dense subgraph discovery methods focus on a single graph input with few notable exceptions \cite{semertzidis2019finding,charikar2018finding,reinthal2016finding,jethava2015finding}. In this work, we focus the following problem: given a pair of graphs $G,H$ on the same set of nodes $V$, how do we find a subset of nodes $S \subseteq V$ that induces a well-connected subgraph in $G$ and a dense subgraph in $H$? Our formulation generalizes previous research on dual graphs \cite{Wu+15,WuZLFJZ16,Cui2018}, by enabling the {\em control} of the connectivity constraint on $G$. We propose a novel mathematical formulation based on $k$-edge connectivity, and prove that it is solvable exactly in polynomial time. We compare our method to state-of-the-art competitors; we find empirically that ranging the connectivity constraint enables the practitioner to obtain insightful information that is otherwise inaccessible. Finally, we show that our proposed mining tool can be used to better understand how users interact on Twitter, and connectivity aspects of human brain networks with and without Autism Spectrum Disorder (ASD).

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arXiv2021

On the Power of Edge Independent Graph Models

Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density? In this work we study the limitations of edge independent random graph models, in which each edge is added to the graph independently with some probability. Such models include both the classic Erdös-Rényi and stochastic block models, as well as modern generative models such as NetGAN, variational graph autoencoders, and CELL. We prove that subject to a bounded overlap condition, which ensures that the model does not simply memorize a single graph, edge independent models are inherently limited in their ability to generate graphs with high triangle and other subgraph densities. Notably, such high densities are known to appear in real-world social networks and other graphs. We complement our negative results with a simple generative model that balances overlap and accuracy, performing comparably to more complex models in reconstructing many graph statistics.

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arXiv2021

DeepWalking Backwards: From Embeddings Back to Graphs

Low-dimensional node embeddings play a key role in analyzing graph datasets. However, little work studies exactly what information is encoded by popular embedding methods, and how this information correlates with performance in downstream machine learning tasks. We tackle this question by studying whether embeddings can be inverted to (approximately) recover the graph used to generate them. Focusing on a variant of the popular DeepWalk method (Perozzi et al., 2014; Qiu et al., 2018), we present algorithms for accurate embedding inversion - i.e., from the low-dimensional embedding of a graph G, we can find a graph H with a very similar embedding. We perform numerous experiments on real-world networks, observing that significant information about G, such as specific edges and bulk properties like triangle density, is often lost in H. However, community structure is often preserved or even enhanced. Our findings are a step towards a more rigorous understanding of exactly what information embeddings encode about the input graph, and why this information is useful for learning tasks.

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arXiv2020

Predicting Positive and Negative Links with Noisy Queries: Theory & Practice

Social networks involve both positive and negative relationships, which can be captured in signed graphs. The {\em edge sign prediction problem} aims to predict whether an interaction between a pair of nodes will be positive or negative. We provide theoretical results for this problem that motivate natural improvements to recent heuristics. The edge sign prediction problem is related to correlation clustering; a positive relationship means being in the same cluster. We consider the following model for two clusters: we are allowed to query any pair of nodes whether they belong to the same cluster or not, but the answer to the query is corrupted with some probability $0<q<\frac{1}{2}$. Let $δ=1-2q$ be the bias. We provide an algorithm that recovers all signs correctly with high probability in the presence of noise with $O(\frac{n\log n}{δ^2}+\frac{\log^2 n}{δ^6})$ queries. This is the best known result for this problem for all but tiny $δ$, improving on the recent work of Mazumdar and Saha \cite{mazumdar2017clustering}. We also provide an algorithm that performs $O(\frac{n\log n}{δ^4})$ queries, and uses breadth first search as its main algorithmic primitive. While both the running time and the number of queries for this algorithm are sub-optimal, our result relies on novel theoretical techniques, and naturally suggests the use of edge-disjoint paths as a feature for predicting signs in online social networks. Correspondingly, we experiment with using edge disjoint $s-t$ paths of short length as a feature for predicting the sign of edge $(s,t)$ in real-world signed networks. Empirical findings suggest that the use of such paths improves the classification accuracy, especially for pairs of nodes with no common neighbors.

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arXiv2020

Joint Alignment From Pairwise Differences with a Noisy Oracle

In this work we consider the problem of recovering $n$ discrete random variables $x_i\in \{0,\ldots,k-1\}, 1 \leq i \leq n$ (where $k$ is constant) with the smallest possible number of queries to a noisy oracle that returns for a given query pair $(x_i,x_j)$ a noisy measurement of their modulo $k$ pairwise difference, i.e., $y_{ij} = (x_i-x_j) \mod k$. This is a joint discrete alignment problem with important applications in computer vision, graph mining, and spectroscopy imaging. Our main result is a polynomial time algorithm that learns exactly with high probability the alignment (up to some unrecoverable offset) using $O(n^{1+o(1)})$ queries.

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arXiv2020

Opinion Dynamics with Varying Susceptibility to Persuasion via Non-Convex Local Search

A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, motivated by this fact we propose a new framework for social influence. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another's opinions through an iterative process. Under non-trivial conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to select the resistance of each agent (from some given range) such that the sum of the equilibrium opinions is minimized. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD'18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variation of the problem.

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