Hyperbolic 2D Stochastic Gradient Descent

This example demonstrates how to use the Stochastic Gradient Descent (SGD) layout algorithm with hyperbolic 2D drawings.

Basic Hyperbolic SGD Example

import networkx as nx
import egraph as eg
import matplotlib.pyplot as plt
import numpy as np

# Create a graph from NetworkX
nx_graph = nx.les_miserables_graph()
graph = eg.Graph()
indices = {}
for u in nx_graph.nodes:
    indices[u] = graph.add_node(u)
for u, v in nx_graph.edges:
    graph.add_edge(indices[u], indices[v], (u, v))

# Create a hyperbolic drawing using the factory method
drawing = eg.DrawingHyperbolic2d.initial_placement(graph)

# Create a random number generator with a seed for reproducibility
rng = eg.Rng.seed_from(0)

# Create a SparseSgd instance using the builder pattern
sgd = eg.SparseSgd().h(50).build(graph, lambda _: 0.3, rng)

# Create a scheduler for the SGD algorithm
scheduler = sgd.scheduler(
    100,  # number of iterations
    0.1,  # eps: eta_min = eps * min d[i, j] ^ 2
)

# Define a step function for the scheduler
def step(eta):
    sgd.shuffle(rng)
    sgd.apply(drawing, eta)

# Run the scheduler
scheduler.run(step)

# Extract node positions
pos = {u: (drawing.x(i), drawing.y(i)) for u, i in indices.items()}

# Visualize with NetworkX and Matplotlib
fig, ax = plt.subplots(figsize=(10, 10))

# Draw the Poincaré disk boundary
circle = plt.Circle((0, 0), 1, fill=False, color='gray', linestyle='--')
ax.add_patch(circle)

# Draw the graph
nx.draw(nx_graph, pos, ax=ax, node_size=50)

# Set equal aspect ratio and limits
ax.set_xlim(-1.1, 1.1)
ax.set_ylim(-1.1, 1.1)
ax.set_aspect('equal')

Working with Hyperbolic Distances

When working with hyperbolic space, it’s important to understand that distances are different from Euclidean space. The hyperbolic distance formula in the Poincaré disk model can be calculated using the positions of nodes.