Combining Mixture Components for Clustering.

Area of Science:

• Computational statistics
• Data mining
• Machine learning

Background:

• Model-based clustering typically uses multivariate normal distributions and Bayesian Information Criterion (BIC) to determine the number of clusters.
• Overestimation of clusters can occur when non-Gaussian clusters are represented by multiple Gaussian distributions, leading to inaccurate data partitioning.

Purpose of the Study:

• To propose a new method for accurate cluster number determination in model-based clustering.
• To address the issue of overestimating cluster numbers when dealing with non-Gaussian data distributions.

Main Methods:

• A two-stage approach is proposed: first, determine the total number of Gaussian mixture components (K) using BIC.
• Second, hierarchically combine these components based on an entropy criterion to yield soft clusterings.
• An automatic method for selecting the final number of clusters is described using piecewise linear regression on a rescaled entropy plot.

Main Results:

• The proposed method provides a unique soft clustering for each number of clusters up to K.
• Demonstrated effectiveness with simulated data and a real-world flow cytometry dataset.
• The approach successfully mitigates the overestimation of clusters inherent in standard BIC-based methods for non-Gaussian data.

Conclusions:

• The hierarchical clustering approach offers a more accurate way to determine the number of clusters compared to traditional methods.
• This method enhances the reliability of model-based clustering, particularly for datasets with complex cluster structures.
• The technique provides a flexible framework for cluster analysis, allowing for comparison across different numbers of clusters.