Clustering Tree-structured Data on Manifold
This addresses the challenge of clustering tree-structured data with topological and geometric information for applications like medical imaging, though it appears incremental as it builds on existing manifold and matrix factorization methods.
The authors tackled the problem of clustering tree-structured data by proposing a novel parameterization called the Topology-Attribute matrix, enabling clustering on matrix manifolds, and demonstrated its efficiency and accuracy on simulated data and real retinal images.
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 Fréchet 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.