2025/01/31 by Vladimir Jaćimović, Jaćimović, Vladimir, Aladin Crnkić +1 · 1 citation
Computer Science · #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.2501.19247
openalex publication_date 2025/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The idea of representations of the data in negatively curved manifolds recently attracted a lot of attention and gave a rise to the new research direction named \it hyperbolic machine learning (ML). In order to unveil the full potential of this new paradigm, efficient techniques for data analysis and statistical modeling in hyperbolic spaces are necessary. In the present paper rigorous mathematical framework for clustering in hyperbolic spaces is established. First, we introduce the k-means clustering in hyperbolic balls, based on the novel definition of barycenter. Second, we present the expectation-maximization (EM) algorithm for learning mixtures of novel probability distributions in hyperbolic balls. In such a way we lay the foundation of unsupervised learning in hyperbolic spaces.