Mixtures of multivariate power exponential distributions

Area of Science:

• Statistics
• Machine Learning
• Data Clustering

Background:

• Model-based clustering often focuses on heavy-tails and skewness.
• Existing distributions may not adequately capture varying tail-weight and peakedness simultaneously.

Purpose of the Study:

• Introduce an expanded family of multivariate power exponential distributions.
• Develop a flexible distribution capable of modeling diverse data characteristics.
• Enhance model-based clustering with improved distributional assumptions.

Main Methods:

• Proposed a parsimonious family of models using eigen-decomposition of the scale matrix.
• Developed a generalized expectation-maximization algorithm.
• Combined convex optimization (minorization-maximization) with accelerated line search on the Stiefel manifold.

Main Results:

• Demonstrated the utility of the proposed distribution family.
• Illustrated model performance using both synthetic (toy) and benchmark datasets.
• Showcased the ability to fit data with varying tail-weight and peakedness.

Conclusions:

• The proposed multivariate power exponential distribution family offers a flexible approach to model-based clustering.
• The developed algorithm efficiently estimates model parameters.
• These models provide a valuable tool for analyzing complex, real-world data structures.