knowledge patterns bases, algebraic Bayesian networks, machine learning, global structure, matroid, adjacency graph " />

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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