Rapid and Precise Topological Comparison with Merge Tree Neural Networks
Yu Qin Brittany Terese Fasy Carola Wenk Brian Summa
Merge trees are a valuable tool in scientific visualization of scalar fields;
however, current methods for merge tree comparisons are computationally
expensive, primarily due to the exhaustive matching between tree nodes. To
address this challenge, we introduce the merge tree neural networks (MTNN), a
learned neural network model designed for merge tree comparison. The MTNN
enables rapid and high-quality similarity computation. We first demonstrate how
graph neural networks (GNNs), which emerged as an effective encoder for graphs,
can be trained to produce embeddings of merge trees in vector spaces that
enable efficient similarity comparison. Next, we formulate the novel MTNN model
that further improves the similarity comparisons by integrating the tree and
node embeddings with a new topological attention mechanism. We demonstrate the
effectiveness of our model on real-world data in different domains and examine
our model's generalizability across various datasets. Our experimental analysis
demonstrates our approach's superiority in accuracy and efficiency. In
particular, we speed up the prior state-of-the-art by more than 100x on the
benchmark datasets while maintaining an error rate below 0.1%.