MATROIDAL REPRESENTATION FOR THE ADJACENCY GRAPHS FAMILY BUILT ON A SET OF KNOWLEDGE PATTERNS

Vsevolod Oparin, Andrey A. Filchenkov , Sirotkin Alexander Vladimirovich

2010 , VOLUME 10, NUMBER 4 ( JULY-AUGUST )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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MATROIDAL REPRESENTATION FOR THE ADJACENCY GRAPHS FAMILY BUILT ON A SET OF KNOWLEDGE PATTERNS

V. Oparin, A. A. Filchenkov, A. V. Sirotkin

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Abstract

The paper considers a problem appeared in machine learning of uncertain knowledge patterns bases represented as algebraic Bayesian networks. The problem is to build an adjacency graph as a representation of a global (secondary) structure of such a network using its primary structure. Under the given primary structure of an algebraic Bayesian network, the corresponding adjacency graphs family can be characterized with a special matroid. It leads to further results: the sets of minimal adjacency graphs and non-reducible join graphs are equal; a minimal adjacency graph can be built with a greedy algorithm; the vertices number of minimal adjacency graph can be expressed with the vertices number of maximal adjacency graph and the matroid rank.

Keywords: knowledge patterns bases, algebraic Bayesian networks, machine learning, global structure, matroid, adjacency graph

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