# Clustering Tree-structured Data on Manifold

arXiv: https://arxiv.org/abs/1507.05532 · HTML: https://mlsanity.com/paper/1507.05532/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2015.

## Built on by (most cited first, 2 of 2)

- [Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects](https://mlsanity.com/paper/2606.10212/) (2026)
- [Consistent Spectral Clustering in Hyperbolic Spaces](https://mlsanity.com/paper/2409.09304/) (2024)

## Abstract (arXiv)

Tree-structured data usually contain both topological and geometrical information, and are necessarily considered on manifold instead of Euclidean space for appropriate data parameterization and analysis. In this study, we propose a novel tree-structured data parameterization, called Topology-Attribute matrix (T-A matrix), so the data clustering task can be conducted on matrix manifold. We incorporate the structure constraints embedded in data into the negative matrix factorization method to determine meta-trees from the T-A matrix, and the signature vector of each single tree can then be extracted by meta-tree decomposition. The meta-tree space turns out to be a cone space, in which we explore the distance metric and implement the clustering algorithm based on the concepts like Fr'echet mean. Finally, the T-A matrix based clustering (TAMBAC) framework is evaluated and compared using both simulated data and real retinal images to illustrate its efficiency and accuracy.