mlsanityData to 14 Oct 2026

Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning

arXiv 2305.18962 ↗First posted 30 May 2023cs.LGcited by 18

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Abstract (arXiv)

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 23 of its 79 references that are in the map. First posted on arXiv 30 May 2023.

Builds on

23 of 79 references.

References · 23

  1. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  2. 2018Hyperbolic Neural Networkscited by 402
  3. 2019Hyperbolic Graph Convolutional Neural Networkscited by 402
  4. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 265
  5. 2019Hyperbolic Image Embeddingscited by 221
  6. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 206
  7. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 156
  8. 2019Mixed-curvature Variational Autoencoderscited by 86
  9. 2020From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clusteringcited by 65
  10. 2015A cost function for similarity-based hierarchical clusteringcited by 63
  11. 2017Neural Embeddings of Graphs in Hyperbolic Spacecited by 58
  12. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 47
11 more
  1. 2020Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embeddingcited by 36
  2. 2022Hyperbolic Deep Reinforcement Learningcited by 25
  3. 2017Hyperbolic Representation Learning for Fast and Efficient Neural Question Answeringcited by 23
  4. 2021Diffusion Earth Mover's Distance and Distribution Embeddingscited by 18
  5. 2020Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloudcited by 14
  6. 2015Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discoverycited by 10
  7. 2019Spectral-Spatial Diffusion Geometry for Hyperspectral Image Clusteringcited by 10
  8. 2017Data-Driven Tree Transforms and Metricscited by 5
  9. 2022Log-Euclidean Signatures for Intrinsic Distances Between Unaligned Datasetscited by 5
  10. 2018Co-manifold learning with missing datacited by 3
  11. 2016On the Diffusion Geometry of Graph Laplacians and Applicationscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 7; 2025: 6; 2026: 3.

18 papers.

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  1. 2024Hyperbolic Geometric Latent Diffusion Model for Graph Generationcited by 20
  2. 2025Hyperbolic Safety-Aware Vision-Language Modelscited by 17
  3. 2024Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wassersteincited by 12
  4. 2025Hyperbolic Diffusion Recommender Modelcited by 9
  5. 2025Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embeddingcited by 8
  6. 2023SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across Statescited by 5
  7. 2024DiffKillR: Killing and Recreating Diffeomorphisms for Cell Annotation in Dense Microscopy Imagescited by 5
  8. 2024Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchycited by 5
  9. 2025Unsupervised Graph Clustering with Deep Structural Entropycited by 4
  10. 2024Accelerating hyperbolic t-SNEcited by 3
  11. 2024Metric Convolutions: A Unifying Theory to Adaptive Image Convolutionscited by 3
  12. 2025Learning Protein-Ligand Binding in Hyperbolic Spacecited by 2
6 more
  1. 2026Emotion Collider: Dual Hyperbolic Mirror Manifolds for Sentiment Recovery via Anti Emotion Reflectioncited by 2
  2. 2024On Probabilistic Pullback Metrics for Latent Hyperbolic Manifoldscited by 1
  3. 2026Harnessing Data Asymmetry: Manifold Learning in the Finsler Worldcited by 1
  4. 2023Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hullscited by 0
  5. 2025Learning Eigenstructures of Unstructured Data Manifoldscited by 0
  6. 2026HSG: Hyperbolic Scene Graphcited by 0