Clustering compositional data using Dirichlet mixture model.

Area of Science:

• Statistics
• Data Mining
• Machine Learning

Background:

• Compositional data analysis (CoDa) often requires data transformations for standard clustering methods.
• Existing clustering algorithms may struggle with the unique constraints of compositional data, such as the unit sum property.

Purpose of the Study:

• To propose and evaluate a model-based clustering method specifically designed for compositional data.
• To address the limitations of existing methods by directly handling the unit sum constraint without transformations.

Main Methods:

• Development of a mixture model utilizing the Dirichlet distribution to accommodate compositional data.
• Implementation of a modified hard Expectation-Maximization (EM) algorithm to prevent empty clusters and ensure convergence.
• Rigorous simulation studies across various dimensions, cluster numbers, and overlap levels.

Main Results:

• The proposed Dirichlet mixture model demonstrated robust performance in clustering simulated compositional data.
• Comparative analysis showed the new method outperforming popular algorithms like KMeans, Gaussian Mixture Models (GMM), and Partition Around Medoids (PAM).
• Successful application to real-world datasets from business/marketing and physical sciences, highlighting its practical utility.

Conclusions:

• The Dirichlet mixture model offers a powerful and effective approach for clustering compositional data.
• The modified hard EM algorithm successfully overcomes convergence issues, making the method reliable.
• This approach provides a valuable alternative for analyzing compositional data without prior transformations.