Bayesian Nonparametric Clustering for Positive Definite Matrices.

Area of Science:

• Computer Vision
• Machine Learning
• Bayesian Nonparametrics

Background:

• Symmetric Positive Definite (SPD) matrices are crucial data descriptors in computer vision tasks like object tracking and diffusion tensor imaging.
• Traditional soft-clustering algorithms require pre-specifying the number of clusters, posing challenges for large datasets.
• Existing Dirichlet process (DP) models are unsuitable for SPD matrices due to their non-Euclidean Riemannian manifold geometry.

Purpose of the Study:

• To propose a novel DP mixture model specifically designed for clustering SPD matrices.
• To address the scalability and accuracy limitations of current clustering methods for SPD data.

Main Methods:

• Developed a novel DP mixture model framework for SPD matrices.
• Utilized the log-determinant divergence as the dissimilarity measure.
• Leveraged the connection between log-determinant divergence and the Wishart distribution to derive a model based on the Wishart-Inverse-Wishart conjugate pair.

Main Results:

• The proposed model demonstrates scalability with increasing dataset size.
• Achieved superior clustering accuracy compared to state-of-the-art parametric and nonparametric algorithms.
• Successfully applied the model to various computer vision applications.

Conclusions:

• The novel DP mixture model provides an effective and scalable solution for clustering SPD matrices.
• This framework advances nonparametric Bayesian methods for complex data structures in computer vision.