Seminar: Signal Processing and Systems
Learning Latent Hierarchies in High-Dimensional Data Using Hyperbolic Geometry and Tree-Wasserstein Distance
Date:
February,05,2025
Start Time:
13:30 - 14:30
Location:
506, Zisapel Building
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Lecturer:
Ya-Wei Eileen Lin
Research Areas:
| Finding meaningful representations and distances of hierarchical data is an important task in many fields. In this talk, I will discuss how hyperbolic geometry and tree-Wasserstein distance (TWD) can be used to learn latent hierarchies in high-dimensional data. I will begin by introducing a method for hierarchical representation learning that integrates hyperbolic and diffusion geometry to recover the latent hierarchical structure underlying data samples. Next, I will present a new perspective on TWD, designed for data with a latent feature hierarchy, where the focus shifts to the hierarchical structure of features rather than embedding samples in hyperbolic space. Unlike the typical use of TWD to reduce Wasserstein distance computations, this approach uses its tree structure to reveal the hidden feature hierarchy. In the final part of the talk, I will address the challenge of jointly learning hierarchical structures for both data samples and features. I will introduce an iterative, unsupervised method that uses TWD to construct trees for both samples and features. The proposed algorithm converges and scales well to high-dimensional data. This approach also integrates seamlessly with hyperbolic graph convolutional neural networks (HGCNs), improving performance in link prediction and node classification tasks.
Ph.D. Under the supervision of Prof. Ronen Talmon.
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