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scDHMap

✨ Generative Models

Hyperbolic Diffusion Map

RNA

Hyperbolic VAE with ZINB reconstruction and t-SNE repulsion for hierarchical cell visualization

Publications

scDHMap: Single-cell hyperbolic diffusion for visualizing complex hierarchies

Tian et al.2023
Complexity
★★★
complex
Interpretability
★★☆
medium
Architecture
Hyperbolic VAE
Latent Dim
2
Used in LAIOR Framework

Hierarchical Hyperbolic Embedding

scDHMap embeds cells in hyperbolic space (Lorentz hyperboloid) to capture hierarchical relationships naturally, with ZINB reconstruction and t-SNE repulsion

Main Idea

Preserve hierarchical cell type relationships using hyperbolic geometry with improved scalability via VAE reconstruction

Key Components

Lorentz Encoder

Hyperbolic embedding space for hierarchical structure

ZINB Decoder

Count-appropriate reconstruction

t-SNE Repulsion

Prevents cluster collapse and separation

Poincaré-Lorentz Conversion

Unified geometric computations

Mathematical Formulation

z ∈ Lorentz hyperboloid; d_H(z_i,z_j) = acosh(-<z_i,z_j>_L); X̂ = ZINB_decode(z)

Loss Functions

ZINB
Zero-Inflated NB reconstruction
Hyperbolic KL
KL in hyperbolic space
t-SNE
Repulsive force regularization

Data Flow

Expression → Hyperbolic Encoder → Lorentz Space → ZINB Decoder + tSNE → Reconstruction + Visualization

Architecture Details

Architecture Type

VAE on Lorentz Hyperboloid

Input/Output Types

single-cell → reconstruction

Key Layers

PoincareEncoderLorentzMappingZINBDecoder

Frameworks

PyTorch

Tags

hyperbolichierarchicalvisualizationvaerna