BGMM (Beta-Gaussian Mixture Model) Documentation

🔍 Overview

BGMM is a clustering algorithm that jointly models two types of data using Gaussian and Beta distributions. It is especially useful when integrating expression data (continuous, real-valued) and binding probability data (ranged in (0,1)).

⚙️ Class Definition

Class Name: BGMM

This class implements the EM algorithm to jointly fit Gaussian and Beta mixture components.

class BGMM:
    def __init__(self, n_components: int = 3, max_iter: int = 100, tol: float = 1e-5):
        ...

📋 Parameters

Parameter	Type	Default	Description
`n_components`	int	3	Number of clusters
`max_iter`	int	100	Maximum number of EM iterations
`tol`	float	1e-5	Log-likelihood convergence threshold

🚀 Usage Examples

from soft_clustering._bgmm._bgmm import BGMM
import numpy as np

# Generate synthetic data
Xg = np.concatenate([
    np.random.normal(0, 1, 50),
    np.random.normal(5, 1, 50)
])
Xb = np.concatenate([
    np.random.beta(2, 5, 50),
    np.random.beta(5, 2, 50)
])

model = BGMM(n_components=2, max_iter=100)
model.fit(Xg, Xb)

print("Labels:", model.predict())
print("Memberships:", model.predict_proba())

📥 Input / 📤 Output

Input to fit(Xg, Xb):
- Xg (np.ndarray): Gaussian data (shape: N)
- Xb (np.ndarray): Beta data (shape: N), values should be in (0,1)
Returns:
- Membership probabilities: predict_proba()
- Cluster assignments: predict()

🛠️ Methods

fit(Xg, Xb): Runs the EM algorithm on mixed Gaussian + Beta data
predict_proba(): Returns posterior membership probabilities (N x K)
predict(): Returns hard cluster labels (N,)

📝 Implementation Notes

Uses EM algorithm to jointly update Gaussian and Beta parameters
Gaussian updates via standard weighted mean/variance
Beta updates via method-of-moments estimation
Numerically stable and interpretable for multi-modal biological data

📚 Reference

This implementation is based on:
“BGMM: A Beta-Gaussian Mixture Model for Clustering Genes with Multiple Data Sources”
by Liang et al.