This paper presents a new graph-based approach that induces synsets using synonymy dictionaries and word embeddings. First, we build a weighted graph of synonyms extracted from commonly available resources, such as Wiktionary. Second, we apply word sense induction to deal with ambiguous words. Finally, we cluster the disambiguated version of the ambiguous input graph into synsets. Our meta-clustering approach lets us use an efficient hard clustering algorithm to perform a fuzzy clustering of the graph. Despite its simplicity, our approach shows excellent results, outperforming five competitive state-of-the-art methods in terms of F-score on three gold standard datasets for English and Russian derived from large-scale manually constructed lexical resources.
(CW) @cite_11 is a clustering algorithm for weighted graphs that can be considered as a special case of MCL with a simplified class update step. At each iteration, the labels of all the nodes are updated according to the majority labels among the neighboring nodes. The algorithm has a meta-parameter that controls graph weights that can be set to three values: (1) sums over the neighborhood's classes; (2) downgrades the influence of a neighboring node by its degree or by (3) of its degree.
@cite_11
1987302197
Given a network of interconnected nodes, each with a given initial value, we develop a distributed strategy that enables some or all of the nodes to calculate any arbitrary function of these initial values, despite the presence of some malicious (or faulty) nodes. Our scheme utilizes a linear iterative strategy where, at each time-step, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We consider a node to be malicious if, instead of following the predefined linear iterative strategy, it updates its value arbitrarily at each time-step (perhaps by conspiring and coordinating with other malicious nodes). When there are up to f malicious nodes, we show that any node in the network is guaranteed to be able to calculate any arbitrary function of all initial node values if the graph of the network is at least (2f +1)-connected. Specifically, we show that under this condition, the nodes can calculate their desired functions after running the linear iteration for a finite number of time- steps (upper bounded by the number of nodes in the network) using almost any set of weights (i.e., for all weights except for a set of measure zero). Our approach treats the problem of fault-tolerant distributed consensus, where all nodes have to calculate the same function despite the presence of faulty or malicious nodes, as a special case. Distributed averaging describes a class of network algorithms for the decentralized computation of aggregate statistics. Initially, each node has a scalar data value, and the goal is to compute the average of these values at every node (the so-called average consensus problem). Nodes iteratively exchange information with their neighbors and perform local updates until the value at every node converges to the initial network average. Much previous work has focused on algorithms where each node maintains and updates a single value; every time an update is performed, the previous value is forgotten. Convergence to the average consensus is achieved asymptotically. The convergence rate is fundamentally limited by network connectivity, and it can be prohibitively slow on topologies such as grids and random geometric graphs, even if the update rules are optimized. In this paper, we provide the first theoretical demonstration that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms. We focus on the case where the local predictor is a linear combination of the node's current and previous values (i.e., two memory taps), and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighboring nodes. We derive the optimal mixing parameter for combining the predictor with the neighbors' values, and conduct a theoretical analysis of the improvement in convergence rate that can be achieved using this acceleration methodology. For a chain topology on N nodes, this leads to a factor of N improvement over standard consensus, and for a two-dimensional grid, our approach achieves a factor of ?N improvement. Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2-length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with a minimum span. The L(h, k)-labelling problem has intensively been studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previously published literature, looking at the problem with a graph algorithmic approach. It is an update of a previous survey written by the same author. We introduce and study the reverse voter model, a dynamics for spin variables similar to the well‐known voter dynamics. The difference is in the way neighbors influence each other: once a node is selected and one among its neighbors chosen, the neighbor is made equal to the selected node, while in the usual voter dynamics the update goes in the opposite direction. The reverse voter dynamics is studied analytically, showing that on networks with degree distribution decaying as k−v, the time to reach consensus is linear in the system size N for all v > 2. The consensus time for link‐update voter dynamics is computed as well. We verify the results numerically on a class of uncorrelated scale‐free graphs. We analyze the structure of random graphs generated by the geographical threshold model. The model is a generalization of random geometric graphs. Nodes are distributed in space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. We show how the degree distribution, percolation and connectivity transitions, clustering coefficient, and diameter relate to the threshold value and weight distribution. We give bounds on the threshold value guaranteeing the presence or absence of a giant component, connectivity and disconnectivity of the graph, and small diameter. Finally, we consider the clustering coefficient for nodes with a given degree l, finding that its scaling is very close to 1 l when the node weights are exponentially distributed. Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the values of its neighbors. We introduce the Metropolis weights, a simple choice for the averaging weights used in each step. We show that with these weights, the values at every node converge to the average, provided the innitely occurring communication graphs are jointly connected. We address the average consensus problem for a distributed system whose components (nodes) can exchange information via interconnections (links) that form an arbitrary, strongly connected but possibly directed, topology (graph). Specifically, we discuss how the nodes can asymptotically reach average consensus (i.e., obtain the average of their initial values) with linear-iterative algorithms in which each node updates its value using a weighted linear combination of its own value and the values of neighboring nodes. In the process, the strategies we develop allow the nodes to adapt their weights in a distributed fashion, so that asymptotically they obtain a doubly stochastic weight matrix, which is useful for many algorithms that utilize linear- or nonlinear-iterative schemes to perform various estimation and optimization tasks. A broad class of data, ranging from similarity networks, workflow networks to protein networks, can be modeled as graphs with data values as vertex labels. Both vertex labels and neighbors could be dirty for various reasons such as typos or erroneous reporting of results in scientific experiments. Neighborhood constraints, specifying label pairs that are allowed to appear on adjacent vertices in the graph, are employed to detect and repair erroneous vertex labels and neighbors. In this paper, we study the problem of repairing vertex labels and neighbors to make graphs satisfy neighborhood constraints. Unfortunately, the problem is generally hard, which motivates us to devise approximation methods for repairing and identify interesting special cases (star and clique constraints) that can be efficiently solved. First, we propose several label repairing approximation algorithms including greedy heuristics, contraction method and an approach combining both. The performances of algorithms are also analyzed for the special case. Moreover, we devise a cubic-time constant-factor graph repairing algorithm with both label and neighbor repairs (given degree-bounded instance graphs). Our extensive experimental evaluation on real data demonstrates the effectiveness of eliminating frauds in several types of application networks. We consider the problem of distributed function calculation in the presence of faulty or malicious agents. In particular, we consider a setup where each node has an initial value and the goal is for (a subset of) the nodes to calculate a function of these values in a distributed manner. We focus on linear iterative strategies for function calculation, where each node updates its value at each time-step to be a weighted average of its own previous value and those of its neighbors; after a sufficiently large number of time-steps, each node is expected to have enough information to calculate the desired function of the initial node values. We study the susceptibility of such strategies to misbehavior by some nodes in the network; specifically, we consider a node to be malicious if it updates its value arbitrarily at each time-step, instead of following the predefined linear iterative strategy. If the connectivity of the network topology is 2f or less, we show that it is possible for a set of f malicious nodes to conspire in a way that makes it impossible for a subset of the other nodes in the network to correctly calculate an arbitrary function of all node values. Our analysis is constructive, in that it provides a specific scheme for the malicious nodes to follow in order to obfuscate the network in this fashion. We consider the problem of topology recognition in wireless (radio) networks modeled as undirected graphs. Topology recognition is a fundamental task in which every node of the network has to output a map of the underlying graph i.e., an isomorphic copy of it, and situate itself in this map. In wireless networks, nodes communicate in synchronous rounds. In each round a node can either transmit a message to all its neighbors, or stay silent and listen. At the receiving end, a node @math hears a message from a neighbor @math in a given round, if @math listens in this round, and if @math is its only neighbor that transmits in this round. Nodes have labels which are (not necessarily different) binary strings. The length of a labeling scheme is the largest length of a label. We concentrate on wireless networks modeled by trees, and we investigate two problems. What is the shortest labeling scheme that permits topology recognition in all wireless tree networks of diameter @math and maximum degree @math ? What is the fastest topology recognition algorithm working for all wireless tree networks of diameter @math and maximum degree @math , using such a short labeling scheme? We are interested in deterministic topology recognition algorithms. For the first problem, we show that the minimum length of a labeling scheme allowing topology recognition in all trees of maximum degree @math is @math . For such short schemes, used by an algorithm working for the class of trees of diameter @math and maximum degree @math , we show almost matching bounds on the time of topology recognition: an upper bound @math , and a lower bound @math , for any constant @math . In local community detection by seed expansion a single cluster concentrated around few given query nodes in a graph is discovered in a localized way. Conductance is a popular objective function used in many algorithms for local community detection. Algorithms that directly optimize conductance usually add or remove one node at a time to find a local optimum. This amounts to fix a specific neighborhood structure over clusters. A natural way to avoid the problem of choosing a specific neighborhood structure is to use a continuous relaxation of conductance. This paper studies such a continuous relaxation of conductance. We show that in this setting continuous optimization leads to hard clusters. We investigate the relation of conductance with weighted kernel k-means for a single cluster, which leads to the introduction of a weighted kernel 1-mean objective function, called -conductance, where is a parameter which influences the size of the community. Conductance is obtained by setting to 0. Two algorithms for local optimization of -conductance based on the expectation maximization and the projected gradient descend method are developed, called EMc and PGDc, respectively. We show that for =0 EMc corresponds to gradient descend with an infinite step size at each iteration. We design a procedure to automatically select a value for . Performance guarantee for these algorithms is proven for a class of dense communities centered around the seeds and well separated from the rest of the network. On this class we also prove that our algorithms stay localized. A comparative experimental analysis on networks with ground-truth communities is performed using state-of-the-art algorithms based on the graph diffusion method. Our experiments indicate that EMc and PGDc stay localized and produce communities most similar to the ground. In this paper we describe several new clustering algorithms for nodes in a mobile ad hoc network. We propose to combine two known approaches into a single clustering algorithm which considers connectivity as a primary criterion and lower ID as secondary criterion for selecting cluster heads. The goal is to minimize the number of clusters, which results in dominating sets of smaller sizes (this is important for applications in broadcasting and Bluetooth formation). We also describe algorithms for modifying cluster structure in the presence of topological changes. Next, we generalize the cluster definition so that a cluster contains all nodes that are at a distance of at most k hops from the cluster head. The efficiency of four clustering algorithms (k-lowestID and k-CONID, k=1 and k=2) is tested by measuring the average number of created clusters, the number of border nodes, and the cluster size in random unit graphs. The most interesting experimental result is stability of the ratio of the sum of CHs and border nodes in the set. It was constantly 60-70 for 1-lowestID and 46-56 for 1-ConID, for any value of n (number of nodes) and d (average node degree). Similar conclusions and similar number were obtained for k=2. We also proposed a unified framework for most existing and new clustering algorithms where a properly defined weight at each node is the only difference in the algorithm. Finally, we propose a framework for generating random unit graphs with obstacles. In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph. Coalescing random walks can be used to achieve consensus in distributed networks, and is the basis of the self-stabilizing mutual exclusion algorithm of Israeli and Jalfon. Let G=(V,E), be an undirected, connected n vertex graph with m edges. Let C(n) be the expected time for all particles to coalesce, when initially one particle is located at each vertex of an n vertex graph. We study the problem of bounding the coalescence time C(n) for general classes of graphs. Our main result is that C(n)= O(1 (1-lambda_2))*((log n)^4 +n A)), where lambda_2 is the absolute value of the second largest eigenvalue of the transition matrix of the random walk, A= (sum d^2(v)) (d^2 n), d(v) is the degree of vertex v, and d is the average node degree. The parameter A is an indicator of the variability of node degrees. Thus 1 <= A =O(n), with A=1 for regular graphs. We study deterministic, distributed algorithms for two weak variants of the standard graph coloring problem. We consider defective colorings, i.e., colorings where nodes of a color class may induce a graph of maximum degree d for some parameter d>0. We also look at colorings where a minimum number of multi-chromatic edges is required. For an integer k>0, we call a coloring k-partially proper if every node v has at least min k,deg(v) neighbors with a different color. We show that for all d∈ 1,...,Δ , it is possible to compute a O(Δ2 d2)-coloring with defect d in time O(log*n) where Δ is the largest degree of the network graph. Similarly, for all k∈ 1,...,Δ , a k-partially proper O(k2)-coloring can be computed in O(log*n) rounds. As an application of our weak defective coloring algorithm, we obtain a faster deterministic algorithm for the standard vertex coloring problem on graphs with moderate degrees. We show that in time O(Δ+log*n), a (Δ+1)-coloring can be computed, a task for which the best previous algorithm required time O(Δ*log(Δ) + log*n). The same result holds for the problem of computing a maximal independent set. We present a new multi-class graph-based transduction algorithm. Examples are associated with vertices in an undirected weighted graph and edge weights correspond to a similarity measure between examples. Typical algorithms in such a setting perform label propagation between neighbours, ignoring the quality, or estimated quality, in the labeling of various nodes. We introduce an additional quantity of confidence in label assignments, and learn them jointly with the weights, while using them to dynamically tune the influence of each vertex on its neighbours. We cast learning as a convex optimization problem, and derive an efficient iterative algorithm for solving it. Empirical evaluations on seven NLP data sets demonstrate our algorithm improves over other state-of-the-art graph-based transduction algorithms. In this paper, we review a recently developed class of algorithms that solve global problems in unit distance wireless networks by means of local algorithms. A local algorithm is one in which any node of a network only has information on nodes at distance at most k from itself, for a constant k. For example, given a unit distance wireless network N, we want to obtain a planar subnetwork of N by means of an algorithm in which all nodes can communicate only with their neighbors in N, perform some operations, and then halt. We review algorithms for obtaining planar subnetworks, approximations to minimum weight spanning trees, Delaunay triangulations, and relative neighbor graphs. Given a unit distance wireless network N, we present new local algorithms to solve the following problems:1.Calculate small dominating sets (not necessarily connected) of N. 2.Extract a bounded degree planar subgraph H of N and obtain a proper edge coloring of H with at most 12 colors. The second of these algorithms can be used in the channel assignment problem. We consider a network of distributed sensors, where where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximum-likelihood estimate of the parameters. This scheme doesn't involve explicit point-to-point message passing or routing; instead, it diffuses information across the network by updating each node's data with a weighted average of its neighbors' data (they maintain the same data structure). At each step, every node can compute a local weighted least-squares estimate, which converges to the global maximum-likelihood solution. This scheme is robust to unreliable communication links. We show that it works in a network with dynamically changing topology, provided that the infinitely occurring communication graphs are jointly connected. The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered structure. Specifically we assume that nodes possess latent attributes drawn from a general compact space and edges between two nodes are randomly generated and labeled according to some unknown distribution as a function of their latent attributes. Our goal is then to infer the edge label distributions from a partially observed network. We propose a computationally efficient spectral algorithm and show it allows for asymptotically correct inference when the average node degree could be as low as logarithmic in the total number of nodes. Conversely, if the average node degree is below a specific constant threshold, we show that no algorithm can achieve better inference than guessing without using the observations. As a byproduct of our analysis, we show that our model provides a general procedure to construct random graph models with a spectrum asymptotic to a pre-specified eigenvalue distribution such as a power-law distribution. Summary form only given. The XTC ad-hoc network topology control algorithm introduced shows three main advantages over previously proposed algorithms. First, it is extremely simple and strictly local. Second, it does not assume the network graph to be a unit disk graph; XTC proves correct also on general weighted network graphs. Third, the algorithm does not require availability of node position information. Instead, XTC operates with a general notion of order over the neighbors' link qualities. In the special case of the network graph being a unit disk graph, the resulting topology proves to have bounded degree, to be a planar graph, and - on average-case graphs - to be a good spanner. In a seminal paper, Bar- (1992) considered broadcasting in radio networks whose nodes know only their own label and labels of their neighbors. They claimed a linear lower bound on the time of deterministic broadcasting in such radio networks, by constructing a class of graphs of diameter 3, with the property that every broadcasting algorithm requires linear time on one of these graphs. Due to a subtle error in the argument, this result is incorrect. We construct an algorithm that broadcasts in logarithmic time on all graphs from the work of Bar- Moreover, we show how to broadcast in sublinear time on all n-node graphs of diameter o(log log n). On the other hand, we construct a class of graphs of diameter 4, such that every broadcasting algorithm requires time spl Omega (4 spl radic n) on one of these graphs. In view of the randomized algorithm, running in expected time O(D log n + log sup 2 n) on all n-node graphs of diameter D, our lower bound gives the first correct proof of an exponential gap between determinism and randomization in the time of radio broadcasting.