Title: Deep Hyperbolic Hierarchical Clustering
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Hyperbolic Geometry, Deep Clustering, Hierarchical Clustering, Representation Learning, Unsupervised Learning, Lowest Common Ancestor (LCA)

Abstract: Hierarchical clustering is a cornerstone of unsupervised learning, yet it has been a neglected method in modern deep learning. To enable deep hierarchical clustering, the unique geometry of hyperbolic space offers an ideal setting, renowned for its ability to embed tree-like structures with minimal distortion. However, prior attempts have been hampered by significant limitations, including geometric rigidity, a lack of scalability to large datasets, and imprecise formulations of key operations.
This paper introduces a novel deep hyperbolic clustering framework that directly addresses these shortcomings through three key advancements. First, we present a generalized and rectified definition of the hyperbolic lowest common ancestor for both the Poincaré Ball and the Lorentz models of arbitrary curvature. Second, to address the critical issue of scalability, we employ a deep encoder that learns clusters in an exceptionally low-dimensional space compared to state of the art Euclidean methods. This makes our approach highly efficient and feasible for large-scale datasets. Finally, we introduce HoroPCA++, an improved and numerically stable dimensionality reduction technique for more faithful and lower distorted visualizations of the resulting hierarchies.

TL;DR: A scalable deep framework for hyperbolic clustering that corrects the LCA definition for theoretical robustness, enables large-scale learning with a deep encoder, and improves visualization using HoroPCA++.