  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.
