OPTIMIZATION OF TRUST PROPAGATION ON HILBERT SPACE IN COMPLEX NETWORKS

Keywords: hilbert space, embedding, operator, trust propagation, optimization

This paper introduces a Hilbert space formulation of trust propa-

gation and develops an optimization framework for estimating global

trust states in complex networks. Trust interactions are modeled using

a bounded linear operator defined on the Hilbert space of node trust

vectors. The global trust inference problem is formulated as a varia-

tional optimization problem whose solution represents the equilibrium

trust configuration of the network. The proposed framework guarantees

existence and uniqueness of optimal trust states under mild spectral con-

ditions. An eﬃcient iterative algorithm is derived using gradient-based

optimization in Hilbert space. Preliminary experiments on simulated

networks demonstrate the stability and convergence of the proposed ap-

proach compared with classical propagation models.