BIGCLAM (Cluster Affiliation Model for Big Networks) Documentation

🔍 Overview

BIGCLAM is an overlapping community detection algorithm based on non-negative matrix factorization. It models edge formation as a function of shared community affiliations and scales well to large networks.

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⚙️ Class Definition

Class Name: BIGCLAM This class implements the BIGCLAM model with coordinate gradient ascent and non-negative membership updates.

class BIGCLAM:
    def __init__(self, n_nodes: int, n_communities: int, max_iter: int = 100, learning_rate: float = 0.01):
        ...

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📋 Parameters

Parameter	Type	Default	Description
n_nodes	int	—	Number of nodes in the graph
n_communities	int	—	Number of latent communities
max_iter	int	100	Maximum number of training iterations
learning_rate	float	0.01	Learning rate for gradient updates

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🚀 Usage Examples

from soft_clustering._bigclam._bigclam import BIGCLAM
import numpy as np

adj = np.array([
    [0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0],
    [0, 1, 0, 1, 0, 0],
    [0, 0, 1, 0, 1, 0],
    [0, 0, 0, 1, 0, 1],
    [0, 0, 0, 0, 1, 0]
])

model = BIGCLAM(n_nodes=6, n_communities=2)
model.fit(adj)
F = model.get_membership()
print(F)

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📥 Input / 📤 Output

• Input to fit(adj):

  • adj (np.ndarray): Symmetric binary adjacency matrix (n x n)

• Returns:

  • Membership matrix F (n x k) via get_membership()

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🛠️ Methods

• fit(adj): Fits the BIGCLAM model to the input graph

• get_membership(): Returns the learned non-negative node-community matrix

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📝 Implementation Notes

• Updates use block coordinate ascent

• Gradients computed with respect to edge and non-edge pairs

• Model enforces non-negativity of community affiliations

• Easily scales to large networks

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📚 Reference

This implementation is based on:
“Overlapping Community Detection at Scale: A Nonnegative Matrix Factorization Approach”
by J. Yang and J. Leskovec (2013).