HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clustering
This addresses the challenge of hierarchical clustering and tree-fitting in applications like NLP and genomics, offering a novel denoising approach for noisy data.
The paper tackles the problem of fitting tree-metrics to noisy data that deviates from tree structures, proposing HyperAid to denoise data in hyperbolic spaces and showing it outperforms existing methods with an average improvement of 125.94% over Neighbor Joining on real-world datasets.
The problem of fitting distances by tree-metrics has received significant attention in the theoretical computer science and machine learning communities alike, due to many applications in natural language processing, phylogeny, cancer genomics and a myriad of problem areas that involve hierarchical clustering. Despite the existence of several provably exact algorithms for tree-metric fitting of data that inherently obeys tree-metric constraints, much less is known about how to best fit tree-metrics for data whose structure moderately (or substantially) differs from a tree. For such noisy data, most available algorithms perform poorly and often produce negative edge weights in representative trees. Furthermore, it is currently not known how to choose the most suitable approximation objective for noisy fitting. Our contributions are as follows. First, we propose a new approach to tree-metric denoising (HyperAid) in hyperbolic spaces which transforms the original data into data that is ``more'' tree-like, when evaluated in terms of Gromov's $δ$ hyperbolicity. Second, we perform an ablation study involving two choices for the approximation objective, $\ell_p$ norms and the Dasgupta loss. Third, we integrate HyperAid with schemes for enforcing nonnegative edge-weights. As a result, the HyperAid platform outperforms all other existing methods in the literature, including Neighbor Joining (NJ), TreeRep and T-REX, both on synthetic and real-world data. Synthetic data is represented by edge-augmented trees and shortest-distance metrics while the real-world datasets include Zoo, Iris, Glass, Segmentation and SpamBase; on these datasets, the average improvement with respect to NJ is $125.94\%$.