Improving Comparability of Temporal Evolution in 2D Embeddings of Ensemble Data

Ensemble data refers to a set of simulations or measurements of the same phenomenon conducted under different settings such as varying control parameters of the simulation.When the data capture changes over time, the main analysis task is to compare the temporal evolution of the ensemble members.For a global analysis of the ensemble's temporal evolution, the data can be embedded in a 2D visual space, where each ensemble member is visualized by a 2D curve.For the embedding, the dissimilarities of the states of the ensemble members at different points in time shall be represented by the distances of the respective points in the 2D embedding.This goal is achieved by minimizing the stress functional of Multidimensional Scaling (MDS).However, direct visual comparison of the embedded curves can be complicated due to their non-trivial geometry.We propose an algorithm for the simplification of curve geometries in 2D MDS embeddings of ensemble data, where the target shape of a selected reference curve can be chosen by the user.We transform the original embedding in a controllable way consistent with the MDS stress functional.Thus, we improve the comparability of curves representing individual ensemble members, while minimizing the loss in accuracy of presented data dissimilarities.We perform several tests demonstrating the benefits of the proposed method, present our findings, and discuss numerical aspects of the algorithm.