Convergence analysis of binary relation inference networks

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 (E_t) and delta energy function (ΔE_t), where both functions have closely related geometrical interpretations. By properly formulating ΔE_t 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