Data identification can be sometimes formulated as a problem of identifying points in Euclidean space satisfying a given set of algebraic relations. A key question then is to identify sufficient conditions for observations to guarantee the identifiability of the points. In this work we propose a new general framework for capturing the identifiability problem when a set of algebraic relations has a combinatorial structure and develops tools to analyze the impact of the underlying combinatorics on the local or global identifiability of points. Our framework is built on the language of graph rigidity, where the measurements are Euclidean distances between two points, but applicable in the generality of hypergraphs with arbitrary algebraic measurements.

The talk is based on a joint work with James Cruickshank, Fatemeh Mohammadi, and Anthony Nixon.