Proximity Networks and Semi-Metric Behavior
Luis Rocha, School of Informatics, IUB
January 24th, 2005 | 6-7p | LI 001
Fuzzy graphs are weighted graphs whose edges are characterized by weights in the unit interval.
We discuss a particular type of fuzzy graphs which are reflexive and symmetrical (undirected) and
are known as proximity graphs. We discuss how we build such graphs from co-occurrence data
extracted from several electronic resources, and use them to represent knowledge in an associative
manner. We show that such distributed knowledge representations are useful for information
retrieval, text mining, and knowledge discovery tasks which we have applied to recommendation
systems, social network analysis, and knowledge discovery in Biology.
In the second part of this talk, we investigate the transitivity of proximity networks. The transitive
closure of a proximity network is a similarity network. The most traditional way of obtaining the
transitive closure of a fuzzy graph is with the max-min matrix operation. We have been
investigating a more demanding type of closure which is based on a distance transformation of the
proximity network. Using an inverse function, from the proximity graphs we produce distance
graphs. We show that most distance graphs obtained this way violate the triangle inequality
expected of Euclidean distances. Non-Euclidean distance functions are known as a semi-metric.
The metric closure of the semi-metric distance graphs establishes a type of transitive closure which
is more demanding than the traditional max-min closure.
Finally, we show that the semi-metric closure of co-occurrence proximity graphs obtained from
various electronic resources, can be used for identifying specific implicit associations in the graph,
and thus useful to identify trends in communities associated with the sets of documents from where
associations were extracted. We exemplify this process of knowledge discovery in various realworld examples.
Today, January 24th, 2005 | 6-7p | Main Library 001