Clustering of tree-structured data

Tree-structured data conveys both topological and geometrical information, which is strongly non-Euclidean and thus need be considered on manifold for parameterization and analysis. To address this problem and perform tree-structured data clustering, a novel parameterization method using the Topology-Attribute matrix (T-A matrix) is proposed which could enable tree analysis on matrix manifold. Then a nonnegative matrix factorization (NMF) method with structure constraint from trees is developed to mine the subspace of tree-structured data, which we call meta-tree space. The clustering task is conducted in the meta-tree space based on the concept of Fréchet mean. The proposed method is evaluated using both simulated data and real retinal images.