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Charalampos E. Tsourakakis

Publications and source records attributed to Charalampos E. Tsourakakis.

At least 37 records · Page 2Linked to original sources
arXiv2020

Node Embeddings and Exact Low-Rank Representations of Complex Networks

Low-dimensional embeddings, from classical spectral embeddings to modern neural-net-inspired methods, are a cornerstone in the modeling and analysis of complex networks. Recent work by Seshadhri et al. (PNAS 2020) suggests that such embeddings cannot capture local structure arising in complex networks. In particular, they show that any network generated from a natural low-dimensional model cannot be both sparse and have high triangle density (high clustering coefficient), two hallmark properties of many real-world networks. In this work we show that the results of Seshadhri et al. are intimately connected to the model they use rather than the low-dimensional structure of complex networks. Specifically, we prove that a minor relaxation of their model can generate sparse graphs with high triangle density. Surprisingly, we show that this same model leads to exact low-dimensional factorizations of many real-world networks. We give a simple algorithm based on logistic principal component analysis (LPCA) that succeeds in finding such exact embeddings. Finally, we perform a large number of experiments that verify the ability of very low-dimensional embeddings to capture local structure in real-world networks.

cs.LG↗
arXiv2020

Finding Densest $k$-Connected Subgraphs

Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an edge-weighted undirected graph $G=(V,E,w)$, we are asked to find $S\subseteq V$ that maximizes the density $d(S)$, i.e., half the weighted average degree of the induced subgraph $G[S]$. This problem can be solved exactly in polynomial time and well-approximately in almost linear time. However, a densest subgraph has a structural drawback, namely, the subgraph may not be robust to vertex/edge failure. Indeed, a densest subgraph may not be well-connected, which implies that the subgraph may be disconnected by removing only a few vertices/edges within it. In this paper, we provide an algorithmic framework to find a dense subgraph that is well-connected in terms of vertex/edge connectivity. Specifically, we introduce the following problems: given a graph $G=(V,E,w)$ and a positive integer/real $k$, we are asked to find $S\subseteq V$ that maximizes the density $d(S)$ under the constraint that $G[S]$ is $k$-vertex/edge-connected. For both problems, we propose polynomial-time (bicriteria and ordinary) approximation algorithms, using classic Mader's theorem in graph theory and its extensions.

cs.DS↗
arXiv2019

Flowless: Extracting Densest Subgraphs Without Flow Computations

We propose a simple and computationally efficient method for dense subgraph discovery, which is a classic problem both in theory and in practice. It is well known that dense subgraphs can have strong correlation with structures of interest in real-world networks across various domains ranging from social networks to biological systems [Gionis and Tsourakakis `15]. For the densest subgraph problem, Charikar's greedy algorithm [Asashiro `00, Charikar `00] is very simple, and can typically find result of quality much better than the provable factor 2-approximation, which makes it very popular in practice. However, it is also known to give suboptimal output in many real-world examples. On the other hand, finding the exact optimal solution requires the computation of maximum flow. Despite the existence of highly optimized maximum flow solvers, such computation still incurs prohibitive computational costs for the massive graphs arising in modern data science applications. We devise an iterative algorithm which naturally generalizes the greedy algorithm of Charikar. Our algorithm draws insights from the iterative approaches from convex optimization, and also exploits the dual interpretation of the densest subgraph problem. We have empirical evidence that our algorithm is much more robust against the structural heterogeneities in real-world datasets, and converges to the optimal subgraph density even when the simple greedy algorithm fails. On the other hand, in instances where Charikar's algorithm performs well, our algorithm is able to quickly verify its optimality. Furthermore, we demonstrate that our method is significantly faster than the maximum flow based exact optimal algorithm. We conduct experiments on datasets from broad domains, and our algorithm achieves $\sim$145$\times$ speedup on average to find subgraphs whose density is at least 90\% of the optimal value.

cs.DS↗
arXiv2019

Optimal Learning of Joint Alignments with a Faulty Oracle

We consider the following problem, which is useful in applications such as joint image and shape alignment. The goal is to recover $n$ discrete variables $g_i \in \{0, \ldots, k-1\}$ (up to some global offset) given noisy observations of a set of their pairwise differences $\{(g_i - g_j) \bmod k\}$; specifically, with probability $\frac{1}{k}+δ$ for some $δ> 0$ one obtains the correct answer, and with the remaining probability one obtains a uniformly random incorrect answer. We consider a learning-based formulation where one can perform a query to observe a pairwise difference, and the goal is to perform as few queries as possible while obtaining the exact joint alignment. We provide an easy-to-implement, time efficient algorithm that performs $O\big(\frac{n \lg n}{k δ^2}\big)$ queries, and recovers the joint alignment with high probability. We also show that our algorithm is optimal by proving a general lower bound that holds for all non-adaptive algorithms. Our work improves significantly recent work by Chen and Candés \cite{chen2016projected}, who view the problem as a constrained principal components analysis problem that can be solved using the power method. Specifically, our approach is simpler both in the algorithm and the analysis, and provides additional insights into the problem structure.

cs.DS↗
arXiv2019

TwitterMancer: Predicting Interactions on Twitter Accurately

This paper investigates the interplay between different types of user interactions on Twitter, with respect to predicting missing or unseen interactions. For example, given a set of retweet interactions between Twitter users, how accurately can we predict reply interactions? Is it more difficult to predict retweet or quote interactions between a pair of accounts? Also, how important is time locality, and which features of interaction patterns are most important to enable accurate prediction of specific Twitter interactions? Our empirical study of Twitter interactions contributes initial answers to these questions. We have crawled an extensive dataset of Greek-speaking Twitter accounts and their follow, quote, retweet, reply interactions over a period of a month. We find we can accurately predict many interactions of Twitter users. Interestingly, the most predictive features vary with the user profiles, and are not the same across all users. For example, for a pair of users that interact with a large number of other Twitter users, we find that certain "higher-dimensional" triads, i.e., triads that involve multiple types of interactions, are very informative, whereas for less active Twitter users, certain in-degrees and out-degrees play a major role. Finally, we provide various other insights on Twitter user behavior. Our code and data are available at https://github.com/twittermancer/. Keywords: Graph mining, machine learning, social media, social networks

cs.SI↗
arXiv2019

Novel Dense Subgraph Discovery Primitives: Risk Aversion and Exclusion Queries

In the densest subgraph problem, given a weighted undirected graph $G(V,E,w)$, with non-negative edge weights, we are asked to find a subset of nodes $S\subseteq V$ that maximizes the degree density $w(S)/|S|$, where $w(S)$ is the sum of the edge weights induced by $S$. This problem is a well studied problem, known as the {\em densest subgraph problem}, and is solvable in polynomial time. But what happens when the edge weights are negative? Is the problem still solvable in polynomial time? Also, why should we care about the densest subgraph problem in the presence of negative weights? In this work we answer the aforementioned question. Specifically, we provide two novel graph mining primitives that are applicable to a wide variety of applications. Our primitives can be used to answer questions such as "how can we find a dense subgraph in Twitter with lots of replies and mentions but no follows?", "how do we extract a dense subgraph with high expected reward and low risk from an uncertain graph"? We formulate both problems mathematically as special instances of dense subgraph discovery in graphs with negative weights. We study the hardness of the problem, and we prove that the problem in general is NP-hard. We design an efficient approximation algorithm that works well in the presence of small negative weights, and also an effective heuristic for the more general case. Finally, we perform experiments on various real-world uncertain graphs, and a crawled Twitter multilayer graph that verify the value of the proposed primitives, and the practical value of our proposed algorithms. The code and the data are available at \url{https://github.com/negativedsd}.

cs.SI↗
arXiv2018

Opinion Dynamics with Varying Susceptibility to Persuasion

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, we adopt a popular model for social opinion dynamics, and we formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility lead to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization and show its efficacy at finding target-sets that optimize the sum of opinions compared on real world networks, including a Twitter network with real opinion estimates.

cs.SI↗
arXiv2018

Learning Networks from Random Walk-Based Node Similarities

Digital presence in the world of online social media entails significant privacy risks. In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i.e., commute times) or personalized PageRank scores. Using these similarities, the attacker's goal is to infer as much information as possible about the underlying network, including any remaining unknown pairwise node similarities and edges. For the effective resistance metric, we show that with just a small subset of measurements, the attacker can learn a large fraction of edges in a social network, even when the measurements are noisy. We also show that it is possible to learn a graph which accurately matches the underlying network on all other effective resistances. This second observation is interesting from a data mining perspective, since it can be expensive to accurately compute all effective resistances. As an alternative, our graphs learned from just a subset of approximate effective resistances can be used as surrogates in a wide range of applications that use effective resistances to probe graph structure, including for graph clustering, node centrality evaluation, and anomaly detection. We obtain our results by formalizing the graph learning objective mathematically, using two optimization problems. One formulation is convex and can be solved provably in polynomial time. The other is not, but we solve it efficiently with projected gradient and coordinate descent. We demonstrate the effectiveness of these methods on a number of social networks obtained from Facebook. We also discuss how our methods can be generalized to other random walk-based similarities, such as personalized PageRank. Our code is available at https://github.com/cnmusco/graph-similarity-learning.

cs.SI↗
arXiv2018

Risk-Averse Matchings over Uncertain Graph Databases

A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an uncertain, weighted (hyper)graph, how can we efficiently find a (hyper)matching with high expected reward, and low risk? This problem naturally arises in the context of several important applications, such as online dating, kidney exchanges, and team formation. We introduce a novel formulation for finding matchings with maximum expected reward and bounded risk under a general model of uncertain weighted (hyper)graphs that we introduce in this work. Our model generalizes probabilistic models used in prior work, and captures both continuous and discrete probability distributions, thus allowing to handle privacy related applications that inject appropriately distributed noise to (hyper)edge weights. Given that our optimization problem is NP-hard, we turn our attention to designing efficient approximation algorithms. For the case of uncertain weighted graphs, we provide a $\frac{1}{3}$-approximation algorithm, and a $\frac{1}{5}$-approximation algorithm with near optimal run time. For the case of uncertain weighted hypergraphs, we provide a $Ω(\frac{1}{k})$-approximation algorithm, where $k$ is the rank of the hypergraph (i.e., any hyperedge includes at most $k$ nodes), that runs in almost (modulo log factors) linear time. We complement our theoretical results by testing our approximation algorithms on a wide variety of synthetic experiments, where we observe in a controlled setting interesting findings on the trade-off between reward, and risk. We also provide an application of our formulation for providing recommendations of teams that are likely to collaborate, and have high impact.

cs.DS↗
arXiv2017

Minimizing Polarization and Disagreement in Social Networks

The rise of social media and online social networks has been a disruptive force in society. Opinions are increasingly shaped by interactions on online social media, and social phenomena including disagreement and polarization are now tightly woven into everyday life. In this work we initiate the study of the following question: given $n$ agents, each with its own initial opinion that reflects its core value on a topic, and an opinion dynamics model, what is the structure of a social network that minimizes {\em polarization} and {\em disagreement} simultaneously? This question is central to recommender systems: should a recommender system prefer a link suggestion between two online users with similar mindsets in order to keep disagreement low, or between two users with different opinions in order to expose each to the other's viewpoint of the world, and decrease overall levels of polarization? Our contributions include a mathematical formalization of this question as an optimization problem and an exact, time-efficient algorithm. We also prove that there always exists a network with $O(n/ε^2)$ edges that is a $(1+ε)$ approximation to the optimum. For a fixed graph, we additionally show how to optimize our objective function over the agents' innate opinions in polynomial time. We perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization. We find that there is a lot of space to reduce both polarization and disagreement in real-world networks; for instance, on a Reddit network where users exchange comments on politics, our methods achieve a $\sim 60\,000$-fold reduction in polarization and disagreement.

cs.SI↗
arXiv2016

Predicting Signed Edges with $O(n^{1+o(1)} \log{n})$ Queries

Social networks and interactions in social media involve both positive and negative relationships. Signed graphs capture both types of relationships: positive edges correspond to pairs of "friends", and negative edges to pairs of "foes". The {\em edge sign prediction problem}, which aims to predict whether an interaction between a pair of nodes will be positive or negative, is an important graph mining task for which many heuristics have recently been proposed \cite{leskovec2010predicting,leskovec2010signed}. Motivated by social balance theory, we model the edge sign prediction problem as a noisy correlation clustering problem with two clusters. We are allowed to query each 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 $c=\frac{1}{2}-q$ be the gap. We provide an algorithm that recovers the clustering with high probability in the presence of noise for any constant gap $c$ with $O(n^{1+\tfrac{1}{\log\log{n}}}\log{n})$ queries. Our algorithm uses simple breadth first search as its main algorithmic primitive. Finally, we provide a novel generalization to $k \geq 3$ clusters and prove that our techniques can recover the clustering if the gap is constant in this generalized setting.

cs.DS↗
arXiv2016

ADAGIO: Fast Data-aware Near-Isometric Linear Embeddings

Many important applications, including signal reconstruction, parameter estimation, and signal processing in a compressed domain, rely on a low-dimensional representation of the dataset that preserves {\em all} pairwise distances between the data points and leverages the inherent geometric structure that is typically present. Recently Hedge, Sankaranarayanan, Yin and Baraniuk \cite{hedge2015} proposed the first data-aware near-isometric linear embedding which achieves the best of both worlds. However, their method NuMax does not scale to large-scale datasets. Our main contribution is a simple, data-aware, near-isometric linear dimensionality reduction method which significantly outperforms a state-of-the-art method \cite{hedge2015} with respect to scalability while achieving high quality near-isometries. Furthermore, our method comes with strong worst-case theoretical guarantees that allow us to guarantee the quality of the obtained near-isometry. We verify experimentally the efficiency of our method on numerous real-world datasets, where we find that our method ($<$10 secs) is more than 3\,000$\times$ faster than the state-of-the-art method \cite{hedge2015} ($>$9 hours) on medium scale datasets with 60\,000 data points in 784 dimensions. Finally, we use our method as a preprocessing step to increase the computational efficiency of a classification application and for speeding up approximate nearest neighbor queries.

stat.ML↗
arXiv2016

Scalable Betweenness Centrality Maximization via Sampling

Betweenness centrality is a fundamental centrality measure in social network analysis. Given a large-scale network, how can we find the most central nodes? This question is of key importance to numerous important applications that rely on betweenness centrality, including community detection and understanding graph vulnerability. Despite the large amount of work on designing scalable approximation algorithms for betweenness centrality, estimating it on large-scale networks remains a computational challenge. In this paper, we study the Betweenness Centrality Maximization problem: given a graph $G=(V,E)$ and a positive integer $k$, find a set $S^* \subseteq V$ that maximizes betweenness centrality subject to the cardinality constraint $|S^*| \leq k$. We present an efficient randomized algorithm that provides a $(1-1/e-ε)$-approximation with high probability, where $ε>0$. Our results improve the current state-of-the-art result by Yoshida~\cite{yoshida2014almost}. Furthermore, we provide theoretical evidence for the validity of a crucial assumption in the literature of betweenness centrality estimation, namely that in real-world networks $O(|V|^2)$ shortest paths pass through the top-$k$ central nodes, where $k$ is a constant. On the experimental side, we perform an extensive experimental analysis of our method on real-world networks, demonstrate its accuracy and scalability, and study different properties of central nodes. Finally, we provide three graph mining applications of our method.

cs.SI↗
arXiv2015

Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams

While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a problem which lies at the core of many graph mining applications called {\em densest subgraph problem}. We develop an algorithm that achieves time- and space-efficiency for this problem simultaneously. It is one of the first of its kind for graph problems to the best of our knowledge. In a graph $G = (V, E)$, the "density" of a subgraph induced by a subset of nodes $S \subseteq V$ is defined as $|E(S)|/|S|$, where $E(S)$ is the set of edges in $E$ with both endpoints in $S$. In the densest subgraph problem, the goal is to find a subset of nodes that maximizes the density of the corresponding induced subgraph. For any $ε>0$, we present a dynamic algorithm that, with high probability, maintains a $(4+ε)$-approximation to the densest subgraph problem under a sequence of edge insertions and deletions in a graph with $n$ nodes. It uses $\tilde O(n)$ space, and has an amortized update time of $\tilde O(1)$ and a query time of $\tilde O(1)$. Here, $\tilde O$ hides a $O(\poly\log_{1+ε} n)$ term. The approximation ratio can be improved to $(2+ε)$ at the cost of increasing the query time to $\tilde O(n)$. It can be extended to a $(2+ε)$-approximation sublinear-time algorithm and a distributed-streaming algorithm. Our algorithm is the first streaming algorithm that can maintain the densest subgraph in {\em one pass}. The previously best algorithm in this setting required $O(\log n)$ passes [Bahmani, Kumar and Vassilvitskii, VLDB'12]. The space required by our algorithm is tight up to a polylogarithmic factor.

cs.DS↗
arXiv2014

Streaming Graph Partitioning in the Planted Partition Model

The sheer increase in the size of graph data has created a lot of interest into developing efficient distributed graph processing frameworks. Popular existing frameworks such as Graphlab and Pregel rely on balanced graph partitioning in order to minimize communication and achieve work balance. In this work we contribute to the recent research line of streaming graph partitioning \cite{stantonstreaming,stanton,fennel} which computes an approximately balanced $k$-partitioning of the vertex set of a graph using a single pass over the graph stream using degree-based criteria. This graph partitioning framework is well tailored to processing large-scale and dynamic graphs. In this work we introduce the use of higher length walks for streaming graph partitioning and show that their use incurs a minor computational cost which can significantly improve the quality of the graph partition. We perform an average case analysis of our algorithm using the planted partition model \cite{condon2001algorithms,mcsherry2001spectral}. We complement the recent results of Stanton \cite{stantonstreaming} by showing that our proposed method recovers the true partition with high probability even when the gap of the model tends to zero as the size of the graph grows. Furthermore, among the wide number of choices for the length of the walks we show that the proposed length is optimal. Finally, we conduct experiments which verify the value of the proposed method.

cs.DS↗
arXiv2014

A Novel Approach to Finding Near-Cliques: The Triangle-Densest Subgraph Problem

Many graph mining applications rely on detecting subgraphs which are near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand the densest subgraph problem (DSP) which maximizes the average degree over all subgraphs is solvable in polynomial time but for many networks fails to find subgraphs which are near-cliques. On the other hand, formulations that are geared towards finding near-cliques are NP-hard and frequently inapproximable due to connections with the Maximum Clique problem. In this work, we propose a formulation which combines the best of both worlds: it is solvable in polynomial time and finds near-cliques when the DSP fails. Surprisingly, our formulation is a simple variation of the DSP. Specifically, we define the triangle densest subgraph problem (TDSP): given $G(V,E)$, find a subset of vertices $S^*$ such that $τ(S^*)=\max_{S \subseteq V} \frac{t(S)}{|S|}$, where $t(S)$ is the number of triangles induced by the set $S$. We provide various exact and approximation algorithms which the solve the TDSP efficiently. Furthermore, we show how our algorithms adapt to the more general problem of maximizing the $k$-clique average density. Finally, we provide empirical evidence that the TDSP should be used whenever the output of the DSP fails to output a near-clique.

cs.DS↗
arXiv2013

Modeling Intratumor Gene Copy Number Heterogeneity using Fluorescence in Situ Hybridization data

Tumorigenesis is an evolutionary process which involves a significant number of genomic rearrangements typically coupled with changes in the gene copy number profiles of numerous cells. Fluorescence in situ hybridization (FISH) is a cytogenetic technique which allows counting copy numbers of genes in single cells. The study of cancer progression using FISH data has received considerably less attention compared to other types of cancer datasets. In this work we focus on inferring likely tumor progression pathways using publicly available FISH data. We model the evolutionary process as a Markov chain in the positive integer cone Z_+^g where g is the number of genes examined with FISH. Compared to existing work which oversimplifies reality by assuming independence of copy number changes, our model is able to capture dependencies. We model the probability distribution of a dataset with hierarchical log-linear models, a popular probabilistic model of count data. Our choice provides an attractive trade-off between parsimony and good data fit. We prove a theorem of independent interest which provides necessary and sufficient conditions for reconstructing oncogenetic trees. Using this theorem we are able to capitalize on the wealth of inter-tumor phylogenetic methods. We show how to produce tumor phylogenetic trees which capture the dynamics of cancer progression. We validate our proposed method on a breast tumor dataset.

q-bio.QM↗