Flexible Bivariate Beta Mixture Model: A Probabilistic Approach for Clustering Complex Data Structures

TL;DR

The paper introduces the Flexible Bivariate Beta Mixture Model (FBBMM), a novel probabilistic clustering method capable of handling complex, irregular data structures more effectively than traditional algorithms like k-means and GMM.

Contribution

It proposes the FBBMM, leveraging bivariate beta distributions and advanced optimization techniques, to improve clustering of nonconvex and irregular data shapes.

Findings

FBBMM outperforms traditional clustering methods on synthetic datasets.

FBBMM demonstrates superior accuracy on real-world complex data.

The method is validated with extensive experiments and available as open-source code.

Abstract

Clustering is essential in data analysis and machine learning, but traditional algorithms like $k$-means and Gaussian Mixture Models (GMM) often fail with nonconvex clusters. To address the challenge, we introduce the Flexible Bivariate Beta Mixture Model (FBBMM), which utilizes the flexibility of the bivariate beta distribution to handle diverse and irregular cluster shapes. Using the Expectation Maximization (EM) algorithm and Sequential Least Squares Programming (SLSQP) optimizer for parameter estimation, we validate FBBMM on synthetic and real-world datasets, demonstrating its superior performance in clustering complex data structures, offering a robust solution for big data analytics across various domains. We release the experimental code at https://github.com/yung-peng/MBMM-and-FBBMM.