A comparison of Pareto sets and Jacobi sets

Abstract

Topological analysis of multifields is an approaches to find meaningful, intrinsic structures in complex data. Methods introduced in previous years were usually evaluated separately or rather informally. However, to aid the decision which method is best suited for a particular kind of data, it is important to compare and put them into context with each other. Using results from optimization mathematics, this paper finds subset and equivalence relations between Jacobi Sets and Pareto Sets and indicates even further relations to Morse decomposition. This is a first step towards the creation of new analysis tools for multifield topology and of new insight about how the topological approaches are connected with each other.