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
2107082801 2082729696 2149801387 2139964991
We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: a) when the overlay topology is clustered, and h) when a client re-issues the same query while its horizon does not change much. For construction, we argue that an expander can he maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is hounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead. This paper reports on a novel technique for literature indexing and searching in a mechanized library system. The notion of relevance is taken as the key concept in the theory of information retrieval and a comparative concept of relevance is explicated in terms of the theory of probability. The resulting technique called “Probabilistic Indexing,” allows a computing machine, given a request for information, to make a statistical inference and derive a number (called the “relevance number”) for each document, which is a measure of the probability that the document will satisfy the given request. The result of a search is an ordered list of those documents which satisfy the request ranked according to their probable relevance. The paper goes on to show that whereas in a conventional library system the cross-referencing (“see” and “see also”) is based solely on the “semantical closeness” between index terms, statistical measures of closeness between index terms can be defined and computed. Thus, given an arbitrary request consisting of one (or many) index term(s), a machine can elaborate on it to increase the probability of selecting relevant documents that would not otherwise have been selected. Finally, the paper suggests an interpretation of the whole library problem as one where the request is considered as a clue on the basis of which the library system makes a concatenated statistical inference in order to provide as an output an ordered list of those documents which most probably satisfy the information needs of the user. 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. We consider a finite random walk on a weighted graph G; we show that the fraction of time spent in a set of vertices A converges to the stationary probability @math with error probability exponentially small in the length of the random walk and the square of the size of the deviation from @math . The exponential bound is in terms of the expansion of G and improves previous results of [D. Aldous, Probab. Engrg. Inform. Sci., 1 (1987), pp. 33--46], [L. Lovasz and M. Simonovits, Random Structures Algorithms , 4 (1993), pp. 359--412], [M. Ajtai, J. Komlos, and E. Szemeredi, Deterministic simulation of logspace, in Proc. 19th ACM Symp. on Theory of Computing, 1987]. We show that taking the sample average from one trajectory gives a more efficient estimate of @math than the standard method of generating independent sample points from several trajectories. Using this more efficient sampling method, we improve the algorithms of Jerrum and Sinclair for approximating the number of perfect matchings in a dense graph and for approximating the partition function of a ferromagnetic Ising system, and we give an efficient algorithm to estimate the entropy of a random walk on an unweighted graph.