Merge Tree

Merge trees are hierarchical representations of data, particularly useful for visualizing and analyzing scalar fields and multi-variate data. Current research focuses on developing efficient algorithms for comparing and manipulating merge trees, including neural network architectures like Merge Tree Neural Networks (MTNNs) and auto-encoders tailored to the Wasserstein metric space of merge trees. These advancements aim to improve the speed and accuracy of topological data analysis, enabling applications in diverse fields ranging from scientific visualization to data compression and dimensionality reduction. The development of robust metrics, such as the universal ℓ^p-metric, further enhances the rigor and applicability of merge tree analysis.