Clustering Tree-Structured Data on Manifold.

Area of Science:

• Data Science
• Computational Geometry
• Topology

Background:

• Tree-structured data possess both topological and geometrical properties.
• Analysis often requires non-Euclidean spaces for accurate parameterization.
• Existing methods may not fully capture the complexity of such data.

Purpose of the Study:

• To propose a novel parameterization for tree-structured data.
• To enable data clustering directly on a matrix manifold.
• To develop an accurate and efficient clustering framework for tree-structured data.

Main Methods:

• Introduction of the Topology-Attribute matrix (T-A matrix) for data representation.
• Incorporation of structural constraints into non-negative matrix factorization (NMF).
• Meta-tree decomposition and analysis within a cone space using Fréchet mean.

Main Results:

• The T-A matrix facilitates clustering on a matrix manifold.
• A novel framework, TAMBAC (Topology-Attribute matrix based clustering), was developed.
• The method demonstrated efficiency and accuracy on simulated and real retinal image data.

Conclusions:

• The T-A matrix provides an effective way to parameterize tree-structured data.
• The TAMBAC framework offers a robust solution for clustering complex tree data.
• The approach shows promise for applications in image analysis and other fields.