Group centrality is an extension of the classical notion of centrality for individuals, to make it applicable to sets of them. We perform a SWOT (strengths, weaknesses, opportunities and threats) analysis of the use of group centrality in semantic networks, for different centrality notions: degree, closeness, betweenness, giving prominence to random walks. Among our main results stand out the relevance and NP-hardness of the problem of finding the most central set in a semantic network for an specific centrality measure.
Random Walks and Semantic Networks. The motivation to address random walk centrality comes from works that have used the notion of random walks and related it with semantics. The work of @cite_11 compares the functioning of the human mind when searching for memories with a random walk in a semantic network, as both present a similar behavior. They conclude that these results can help clarify the possible mechanisms that could account for PageRank predicting the prominence of words in semantic memory. @cite_7 use random walks to determine the semantic relatedness of two elements. In particular, they use a personalized PageRank algorithm with a custom teleport vector. They conclude that random walk combined with personalized PageRank is a feasible and potentially fruitful mean of computing semantic relatedness for words and texts. @cite_15 introduce a new measure of lexical relatedness based on the divergence of the stationary distributions computed using random walks over graphs extracted from WordNet. All these works have been valuable sources of inspiration for our method.
@cite_15 @cite_7 @cite_11
2149801387 2144597083
Many systems for tasks such as question answering, multi-document summarization, and information retrieval need robust numerical measures of lexical relatedness. Standard thesaurus-based measures of word pair similarity are based on only a single path between those words in the thesaurus graph. By contrast, we propose a new model of lexical semantic relatedness that incorporates information from every explicit or implicit path connecting the two words in the entire graph. Our model uses a random walk over nodes and edges derived from WordNet links and corpus statistics. We treat the graph as a Markov chain and compute a word-specific stationary distribution via a generalized PageRank algorithm. Semantic relatedness of a word pair is scored by a novel divergence measure, ZKL, that outperforms existing measures on certain classes of distributions. In our experiments, the resulting relatedness measure is the WordNet-based measure most highly correlated with human similarity judgments by rank ordering at = .90. The concept of pagerank was first started as a way for determining the ranking of Web pages by Web search engines. Based on relations in interconnected networks, pagerank has become a major tool for addressing fundamental problems arising in general graphs, especially for large information networks with hundreds of thousands of nodes. A notable notion of pagerank, introduced by Brin and Page and denoted by PageRank, is based on random walks as a geometric sum. In this paper, we consider a notion of pagerank that is based on the (discrete) heat kernel and can be expressed as an exponential sum of random walks. The heat kernel satisfies the heat equation and can be used to analyze many useful properties of random walks in a graph. A local Cheeger inequality is established, which implies that, by focusing on cuts determined by linear orderings of vertices using the heat kernel pageranks, the resulting partition is within a quadratic factor of the optimum. This is true, even if we restrict the volume of the small part separated by the cut to be close to some specified target value. This leads to a graph partitioning algorithm for which the running time is proportional to the size of the targeted volume (instead of the size of the whole graph). In this paper, we analyze the efficiency of Monte Carlo methods for incremental computation of PageRank, personalized PageRank, and similar random walk based methods (with focus on SALSA), on large-scale dynamically evolving social networks. We assume that the graph of friendships is stored in distributed shared memory, as is the case for large social networks such as Twitter. For global PageRank, we assume that the social network has n nodes, and m adversarially chosen edges arrive in a random order. We show that with a reset probability of e, the expected total work needed to maintain an accurate estimate (using the Monte Carlo method) of the PageRank of every node at all times is [EQUATION]. This is significantly better than all known bounds for incremental PageRank. For instance, if we naively recompute the PageRanks as each edge arrives, the simple power iteration method needs [EQUATION] total time and the Monte Carlo method needs O(mn e) total time; both are prohibitively expensive. We also show that we can handle deletions equally efficiently. We then study the computation of the top k personalized PageRanks starting from a seed node, assuming that personalized PageRanks follow a power-law with exponent α q ln n random walks starting from every node for large enough constant q (using the approach outlined for global PageRank), then the expected number of calls made to the distributed social network database is O(k (R(1-α) α)). We also present experimental results from the social networking site, Twitter, verifying our assumptions and analyses. The overall result is that this algorithm is fast enough for real-time queries over a dynamic social network. In this paper, we analyze the efficiency of Monte Carlo methods for incremental computation of PageRank, personalized PageRank, and similar random walk based methods (with focus on SALSA), on large-scale dynamically evolving social networks. We assume that the graph of friendships is stored in distributed shared memory, as is the case for large social networks such as Twitter. For global PageRank, we assume that the social network has @math nodes, and @math adversarially chosen edges arrive in a random order. We show that with a reset probability of @math , the total work needed to maintain an accurate estimate (using the Monte Carlo method) of the PageRank of every node at all times is @math . This is significantly better than all known bounds for incremental PageRank. For instance, if we naively recompute the PageRanks as each edge arrives, the simple power iteration method needs @math total time and the Monte Carlo method needs @math total time; both are prohibitively expensive. Furthermore, we also show that we can handle deletions equally efficiently. We then study the computation of the top @math personalized PageRanks starting from a seed node, assuming that personalized PageRanks follow a power-law with exponent @math random walks starting from every node for large enough constant @math (using the approach outlined for global PageRank), then the expected number of calls made to the distributed social network database is @math . We also present experimental results from the social networking site, Twitter, verifying our assumptions and analyses. The overall result is that this algorithm is fast enough for real-time queries over a dynamic social network. Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time @math , assuming performing a random walk step and sampling from a distribution with bounded support take constant time. The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms. We present an efficient local clustering algorithm that finds cuts by performing a sweep over a heat kernel pagerank vector, using the heat kernel pagerank approximation algorithm as a subroutine. Specifically, we show that for a subset @math of Cheeger ratio @math , many vertices in @math may serve as seeds for a heat kernel pagerank vector which will find a cut of conductance @math . The human mind has a remarkable ability to store a vast amount of information in memory, and an even more remarkable ability to retrieve these experiences when needed. Understanding the representations and algorithms that underlie human memory search could potentially be useful in other information retrieval settings, including internet search. Psychological studies have revealed clear regularities in how people search their memory, with clusters of semantically related items tending to be retrieved together. These findings have recently been taken as evidence that human memory search is similar to animals foraging for food in patchy environments, with people making a rational decision to switch away from a cluster of related information as it becomes depleted. We demonstrate that the results that were taken as evidence for this account also emerge from a random walk on a semantic network, much like the random web surfer model used in internet search engines. This offers a simpler and more unified account of how people search their memory, postulating a single process rather than one process for exploring a cluster and one process for switching between clusters. This study focuses on computations on large graphs (e.g., the web-graph) where the edges of the graph are presented as a stream. The objective in the streaming model is to use small amount of memory (preferably sub-linear in the number of nodes n) and a few passes. In the streaming model, we show how to perform several graph computations including estimating the probability distribution after a random walk of length l, mixing time, and the conductance. We estimate the mixing time M of a random walk in O(nα+Mα√n+√Mn α) space and O(√Mα) passes. Furthermore, the relation between mixing time and conductance gives us an estimate for the conductance of the graph. By applying our algorithm for computing probability distribution on the web-graph, we can estimate the PageRank p of any node up to an additive error of √ep in O(√M α) passes and O(min(nα + 1 e √M α + 1 e Mα, αn√Mα + 1 e √M α)) space, for any α ∈ (0, 1]. In particular, for e = M n, by setting α = M--1 2, we can compute the approximate PageRank values in O(nM--1 4) space and O(M3 4) passes. In comparison, a standard implementation of the PageRank algorithm will take O(n) space and O(M) passes. Relational inference is a crucial technique for knowledge base population. The central problem in the study of relational inference is to infer unknown relations between entities from the facts given in the knowledge bases. Two popular models have been put forth recently to solve this problem, which are the latent factor models and the random-walk models, respectively. However, each of them has their pros and cons, depending on their computational efficiency and inference accuracy. In this paper, we propose a hierarchical random-walk inference algorithm for relational learning in large scale graph-structured knowledge bases, which not only maintains the computational simplicity of the random-walk models, but also provides better inference accuracy than related works. The improvements come from two basic assumptions we proposed in this paper. Firstly, we assume that although a relation between two entities is syntactically directional, the information conveyed by this relation is equally shared between the connected entities, thus all of the relations are semantically bidirectional. Secondly, we assume that the topology structures of the relation-specific subgraphs in knowledge bases can be exploited to improve the performance of the random-walk based relational inference algorithms. The proposed algorithm and ideas are validated with numerical results on experimental data sampled from practical knowledge bases, and the results are compared to state-of-the-art approaches. Ranking on image search has attracted considerable attentions. Many graph-based algorithms have been proposed to solve this problem. Despite their remarkable success, these approaches are restricted to their separated image networks. To improve the ranking performance, one effective strategy is to work beyond the separated image graph by leveraging fruitful information from manual semantic labeling (i.e., tags) associated with images, which leads to the technique of co-ranking images and tags, a representative method that aims to explore the reinforcing relationship between image and tag graphs. The idea of co-ranking is implemented by adopting the paradigm of random walks. However, there are two problems hidden in co-ranking remained to be open: the high computational complexity and the problem of out-of-sample. To address the challenges above, in this paper, we cast the co-ranking process into a Bregman divergence optimization framework under which we transform the original random walk into an equivalent optimal kernel matrix learning problem. Enhanced by this new formulation, we derive a novel extension to achieve a better performance for both in-sample and out-of-sample cases. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of our approach. Link prediction is a fundamental problem in social network analysis. The key technique in unsupervised link prediction is to find an appropriate similarity measure between nodes of a network. A class of wildly used similarity measures are based on random walk on graph. The traditional random walk (TRW) considers the link structures by treating all nodes in a network equivalently, and ignores the centrality of nodes of a network. However, in many real networks, nodes of a network not only prefer to link to the similar node, but also prefer to link to the central nodes of the network. To address this issue, we use maximal entropy random walk (MERW) for link prediction, which incorporates the centrality of nodes of the network. First, we study certain important properties of MERW on graph @math by constructing an eigen-weighted graph G. We show that the transition matrix and stationary distribution of MERW on G are identical to the ones of TRW on G. Based on G, we further give the maximal entropy graph Laplacians, and show how to fast compute the hitting time and commute time of MERW. Second, we propose four new graph kernels and two similarity measures based on MERW for link prediction. Finally, to exhibit the power of MERW in link prediction, we compare 27 various link prediction methods over 3 synthetic and 8 real networks. The results show that our newly proposed MERW based methods outperform the state-of-the-art method on most datasets. Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider quantum walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example of a typical walk, the Hadamard walk''''. In particular, we show that after @math time steps, the probability distribution on the line induced by the Hadamard walk is almost uniformly distributed over the interval @math . This implies that the same walk defined on the circle mixes in linear time. This is in direct contrast with the quadratic mixing time for the corresponding classical walk. We conclude by indicating how our techniques may be applied to more general graphs. In this paper, we introduce a WordNetbased measure of semantic relatedness by combining the structure and content of WordNet with co–occurrence information derived from raw text. We use the co–occurrence information along with the WordNet definitions to build gloss vectors corresponding to each concept in WordNet. Numeric scores of relatedness are assigned to a pair of concepts by measuring the cosine of the angle between their respective gloss vectors. We show that this measure compares favorably to other measures with respect to human judgments of semantic relatedness, and that it performs well when used in a word sense disambiguation algorithm that relies on semantic relatedness. This measure is flexible in that it can make comparisons between any two concepts without regard to their part of speech. In addition, it can be adapted to different domains, since any plain text corpus can be used to derive the co–occurrence information. Assessing the navigability of interconnected networks (transporting information, people, or goods) under eventual random failures is of utmost importance to design and protect critical infrastructures. Random walks are a good proxy to determine this navigability, specifically the coverage time of random walks, which is a measure of the dynamical functionality of the network. Here, we introduce the theoretical tools required to describe random walks in interconnected networks accounting for structure and dynamics inherent to real systems. We develop an analytical approach for the covering time of random walks in interconnected networks and compare it with extensive Monte Carlo simulations. Generally speaking, interconnected networks are more resilient to random failures than their individual layers per se, and we are able to quantify this effect. As an application––which we illustrate by considering the public transport of London––we show how the efficiency in exploring the multiplex critically depends on layers’ topology, interconnection strengths, and walk strategy. Our findings are corroborated by data-driven simulations, where the empirical distribution of check-ins and checks-out is considered and passengers travel along fastest paths in a network affected by real disruptions. These findings are fundamental for further development of searching and navigability strategies in real interconnected systems. Most current semantic segmentation methods rely on fully convolutional networks (FCNs). However, their use of large receptive fields and many pooling layers cause low spatial resolution inside the deep layers. This leads to predictions with poor localization around the boundaries. Prior work has attempted to address this issue by post-processing predictions with CRFs or MRFs. But such models often fail to capture semantic relationships between objects, which causes spatially disjoint predictions. To overcome these problems, recent methods integrated CRFs or MRFs into an FCN framework. The downside of these new models is that they have much higher complexity than traditional FCNs, which renders training and testing more challenging. In this work we introduce a simple, yet effective Convolutional Random Walk Network (RWN) that addresses the issues of poor boundary localization and spatially fragmented predictions with very little increase in model complexity. Our proposed RWN jointly optimizes the objectives of pixelwise affinity and semantic segmentation. It combines these two objectives via a novel random walk layer that enforces consistent spatial grouping in the deep layers of the network. Our RWN is implemented using standard convolution and matrix multiplication. This allows an easy integration into existing FCN frameworks and it enables end-to-end training of the whole network via standard back-propagation. Our implementation of RWN requires just 131 additional parameters compared to the traditional FCNs, and yet it consistently produces an improvement over the FCNs on semantic segmentation and scene labeling. We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time - the expected time required to visit every node in a graph at least once - and we show that for a large collection of interesting graphs, running many random walks in parallel yields a speed-up in the cover time that is linear in the number of parallel walks. We demonstrate that an exponential speed-up is sometimes possible, but that some natural graphs allow only a logarithmic speed-up. A problem related to ours (in which the walks start from some probablistic distribution on vertices) was previously studied in the context of space efficient algorithms for undirected s-t-connectivity and our results yield, in certain cases, an improvement upon some of the earlier bounds. We investigate random walks on complex networks and derive an exact expression for the mean firstpassage time (MFPT) between two nodes. We introduce for each node the random walk centrality C, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction. Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random walks are useful but have drawbacks. Random vertex sampling may require too many resources (time, bandwidth, or money). Random walks, which normally require fewer resources per sample, can suffer from large estimation errors in the presence of disconnected or loosely connected graphs. In this work we propose a new m-dimensional random walk that uses m dependent random walkers. We show that the proposed sampling method, which we call Frontier sampling, exhibits all of the nice sampling properties of a regular random walk. At the same time, our simulations over large real world graphs show that, in the presence of disconnected or loosely connected components, Frontier sampling exhibits lower estimation errors than regular random walks. We also show that Frontier sampling is more suitable than random vertex sampling to sample the tail of the degree distribution of the graph. Personalized PageRank expresses link-based page quality around userselected pages in a similar way as PageRank expresses quality over the entire web. Existing personalized PageRank algorithms can, however, serve online queries only for a restricted choice of pages. In this paper we achieve full personalization by a novel algorithm that precomputes a compact database; using this database, it can serve online responses to arbitrary user-selected personalization. The algorithm uses simulated random walks; we prove that for a fixed error probability the size of our database is linear in the number of web pages. We justify our estimation approach by asymptotic worst-case lower bounds: we show that on some sets of graphs, exact personalized PageRank values can only be obtained from a database of size quadratic in the number of vertices. Furthermore, we evaluate the precision of approximation experimentally on the Stanford WebBase graph. A local graph partitioning algorithm finds a cut near a specified starting vertex, with a running time that depends largely on the size of the small side of the cut, rather than the size of the input graph. In this paper, we present a local partitioning algorithm using a variation of PageRank with a specified starting distribution. We derive a mixing result for PageRank vectors similar to that for random walks, and show that the ordering of the vertices produced by a PageRank vector reveals a cut with small conductance. In particular, we show that for any set C with conductance and volume k, a PageRank vector with a certain starting distribution can be used to produce a set with conductance O ( k ). We present an improved algorithm for computing approximate PageRank vectors, which allows us to find such a set in time proportional to its size. In particular, we can find a cut with conductance at most o , whose small side has volume at least 2b, in time O ( 2^b ^2 m o^2 ) where m is the number of edges in the graph. By combining small sets found by this local partitioning algorithm, we obtain a cut with conductance o and approximately optimal balance in time O ( m ^4 m o^2 ). Abstract We consider random walks in dynamic random environments given by Markovian dynamics on Z d . We assume that the environment has a stationary distribution μ and satisfies the Poincare inequality w.r.t. μ . The random walk is a perturbation of another random walk (called “unperturbed”). We assume that also the environment viewed from the unperturbed random walk has stationary distribution μ . Both perturbed and unperturbed random walks can depend heavily on the environment and are not assumed to be finite-range. We derive a law of large numbers, an averaged invariance principle for the position of the walker and a series expansion for the asymptotic speed. We also provide a condition for non-degeneracy of the diffusion, and describe in some details equilibrium and convergence properties of the environment seen by the walker. All these results are based on a more general perturbative analysis of operators that we derive in the context of L 2 - bounded perturbations of Markov processes by means of the so-called Dyson–Phillips expansion.