Few-to-few Cross-domain Object Matching
; Proceedings of The 3rd International Workshop on Advanced Methodologies for Bayesian Networks, PMLR 73:176-187, 2017.
Cross-domain object matching refers to the task of inferring unknown alignment between objects in two data collections that do not have a shared data representation. In recent years several methods have been proposed for solving the special case that assumes each object is to be paired with exactly one object, resulting in a constrained optimization problem over permutations. A related problem formulation of cluster matching seeks to match a cluster of objects in one data set to a cluster of objects in the other set, which can be considered as many-to-many extension of cross-domain object matching and can be solved without explicit constraints. In this work we study the intermediate region between these two special cases, presenting a range of Bayesian inference algorithms that work also for few-to-few cross-domain object matching problems where constrained optimization is necessary but the optimization domain is broader than just permutations.