MBMM (Multivariate Beta Mixture Model) Documentation

🔍 Overview

MBMM is a probabilistic soft clustering algorithm using mixtures of multivariate Beta distributions. Each feature is modeled independently with a Beta distribution. It is especially effective when features are constrained to the range (0,1).

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⚙️ Class Definition

Class Name: MBMM This class implements the EM algorithm for estimating parameters of Beta mixtures across multiple dimensions.

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

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📋 Parameters

Parameter	Type	Default	Description
n_components	int	3	Number of clusters/components in the mixture
max_iter	int	100	Maximum number of iterations in the EM algorithm
tol	float	1e-5	Convergence threshold on log-likelihood

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🚀 Usage Examples

from soft_clustering._mbmm._mbmm import MBMM
import numpy as np

# Create synthetic beta-distributed data
X1 = np.random.beta(2, 5, size=(50, 2))
X2 = np.random.beta(5, 2, size=(50, 2))
X = np.vstack([X1, X2])

model = MBMM(n_components=2, max_iter=100)
model.fit(X)

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

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📥 Input / 📤 Output

• Input to fit(X):

  • X (np.ndarray): Input data (N x D), all features must be in the range (0,1)

• Returns:

  • Membership probabilities: predict_proba() → array of shape (N x K)

  • Hard labels: predict() → array of shape (N,)

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🛠️ Methods

• fit(X): Fits the MBMM model using EM algorithm

• predict_proba(): Returns the membership probability matrix

• predict(): Returns hard cluster labels

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📝 Implementation Notes

• Each dimension is modeled independently with a Beta distribution

• Parameters estimated via method of moments in M-step

• Log-likelihood used for convergence checking

• Input data must be scaled to (0,1)

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📚 Reference

1. Kim, K., & Tewari, A. (2024). Multivariate Beta Mixture Model: Probabilistic Clustering with Flexible Cluster Shapes.