Cluster analysis of local convergent sequences of structures1. Issue 4 (26th April 2017) - Nešetřil, Jaroslav; de Mendez, Patrice Ossona
Abstract: The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of a sequence of finite structures we derive an asymptotic clustering. This is achieved by a blend of analytic and geometric techniques, and particularly by a new interpretation of the authors' representation theorem for limits of local convergent sequences, which serves as a guidance for the whole process. Our study may be seen as an effort to describe connectivity structure at the limit (without having a defined explicit limit structure) and to pull this connectivity structure back to the finite structures in the sequence in a continuous way. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 674–728, 2017