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Register a new userGrammar-Based Random Walkers in Semantic Networks
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Added by
Marko A. Rodriguez
Publication date
2008
fields
Informatics Engineering
and research's language is
English
Authors
Marko A. Rodriguez
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Semantic networks qualify the meaning of an edge relating any two vertices. Determining which vertices are most central in a semantic network is difficult because one relationship type may be deemed subjectively more important than another. For this reason, research into semantic network metrics has focused primarily on context-based rankings (i.e. user prescribed contexts). Moreover, many of the current semantic network metrics rank semantic associations (i.e. directed paths between two vertices) and not the vertices themselves. This article presents a framework for calculating semantically meaningful primary eigenvector-based metrics such as eigenvector centrality and PageRank in semantic networks using a modified version of the random walker model of Markov chain analysis. Random walkers, in the context of this article, are constrained by a grammar, where the grammar is a user defined data structure that determines the meaning of the final vertex ranking. The ideas in this article are presented within the context of the Resource Description Framework (RDF) of the Semantic Web initiative.
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A geodesic is the shortest path between two vertices in a connected network. The geodesic is the kernel of various network metrics including radius, diameter, eccentricity, closeness, and betweenness. These metrics are the foundation of much network research and thus, have been studied extensively in the domain of single-relational networks (both in their directed and undirected forms). However, geodesics for single-relational networks do not translate directly to multi-relational, or semantic networks, where vertices are connected to one another by any number of edge labels. Here, a more sophisticated method for calculating a geodesic is necessary. This article presents a technique for calculating geodesics in semantic networks with a focus on semantic networks represented according to the Resource Description Framework (RDF). In this framework, a discrete walker utilizes an abstract path description called a grammar to determine which paths to include in its geodesic calculation. The grammar-based model forms a general framework for studying geodesic metrics in semantic networks.
Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and cover time are known. However, many recent applications such as search engines and recommender systems involve multiple random walkers on complex networks. In this work, based on numerical simulations, we show that the fraction of nodes of scale-free network not visited by $W$ random walkers in time $t$ has a stretched exponential form independent of the details of the network and number of walkers. This leads to a power-law relation between nodes not visited by $W$ walkers and by one walker within time $t$. The problem of finding the distinct nodes visited by $W$ walkers, effectively, can be reduced to that of a single walker. The robustness of the results is demonstrated by verifying them on four different real-world networks that approximately display scale-free structure.
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive constraints. We can then, for instance, use state of the art SAT solvers and profit from their advanced features like fast unit propagation, clause learning, and conflict-based search heuristics. This approach holds promise for solving combinatorial problems in scheduling, rostering, and configuration, as well as problems in more diverse areas like bioinformatics, software testing and natural language processing. In addition, decomposition may be an effective method to propagate other global constraints.
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a context-free grammar respectively. Taking advantage of the fixed length of the constraint, we give an algorithm to transform a context-free grammar into an automaton. We then study the use of minimization techniques to reduce the size of such automata and speed up propagation. We show that minimizing such automata after they have been unfolded and domains initially reduced can give automata that are more compact than minimizing before unfolding and reducing. Experimental results show that such transformations can improve the size of rostering problems that we can model and run.
The human ability to flexibly reason using analogies with domain-general content depends on mechanisms for identifying relations between concepts, and for mapping concepts and their relations across analogs. Building on a recent model of how semantic relations can be learned from non-relational word embeddings, we present a new computational model of mapping between two analogs. The model adopts a Bayesian framework for probabilistic graph matching, operating on semantic relation networks constructed from distributed representations of individual concepts and of relations between concepts. Through comparisons of model predictions with human performance in a novel mapping task requiring integration of multiple relations, as well as in several classic studies, we demonstrate that the model accounts for a broad range of phenomena involving analogical mapping by both adults and children. We also show the potential for extending the model to deal with analog retrieval. Our approach demonstrates that human-like analogical mapping can emerge from comparison mechanisms applied to rich semantic representations of individual concepts and relations.
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