Convergence analysis of binary relation inference networks

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Convergence analysis of binary relation inference networks

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Two methods for studying the consistency problems of a class of binary relation inference networks are described. One method is derived using the mathematical concepts of energy function (Et) and delta energy function (ΔEt), where both functions have closely related geometrical interpretations. By properly formulating ΔEt as matrix quadratic form, network convergence is shown to be directly related to the matrix property of negative semidefiniteness. The other method, which can be applied in either a discrete-time or continuous-time framework, is based on studying the eigenvalue problem for an associated state-space model of the inference network. The merits and limitations of the proposed methods are discussed, with reference to several specific examples.

Inspec keywords: convergence; eigenvalues and eigenfunctions; inference mechanisms; state-space methods; matrix algebra; computational geometry

Other keywords: matrix quadratic form; network convergence; eigenvalue; state-space model; delta energy function; geometrical interpretations; convergence analysis; binary relation inference networks

Subjects: Computational geometry; Algebra; Artificial intelligence (theory)

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