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Alberto Pepe deleted file The_trivial_intersection_method.tex
about 11 years ago
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The trivial intersection method of identifying the degree of similarity between two graph structures can be extended. Other algorithms, such as those based on a spreading activation within a semantic graph \cite{spread:collins1975,inform:cohen1987,search:crestani2000,grammar:rodriguez2008} can be used as a more fuzzy and probabilistic means of determining the relative ``semantic distance" between two graphs \cite{semdist:delugach1993}. Spreading activation methods are more analogous to the connectionist paradigm of cognitive science than the symbolic methods of artificial intelligence research \cite{rumelhart:conn1993}. The purpose of a spreading activation algorithm is to determine which resources in a semantic graph are most related to some other set of resources. In general, a spreading activation algorithm diffuses an energy distribution over a graph starting from a set of resources and proceeding until a predetermined number of steps have been taken or the energy decays to some $\epsilon \approx 0$. (Note: In many ways this is analagous to finding the primary eigenvector of the graph using the power method. However, the energy vector at time step $1$ only has values for the source resources, the energy vector is decayed on each iteration, and finally, only so many iterations are executed as a steady state distribution is not desired.) Those resources that received the most energy flow during the spreading activation process are considered the most similar to the set of source resources. With respect to the particular example at hand, the energy diffusion would start at the resources in $H$ and the results would be compared with resources of $T_x$ and $T_y$. If the set of resource in $T_x$ received more energy than those in $T_y$, then the dilated triple $T_x$ is considered more representative of the context of $H$. (Note: Spreading activation on a semantic graph is complicated as edges have labels. A framework that makes use of this fact to perform arbitrary path traversals through a semantic graph is presented in \cite{grammar:rodriguez2008}.)
