  Under any Multiclass Classification (MCC) setting defined by a collection of
labeled point-cloud specified by a feature-set, we extract only stochastic
partial orderings from all possible triplets of point-cloud without explicitly
measuring the three cloud-to-cloud distances. We demonstrate that such a
collective of partial ordering can efficiently compute a label embedding tree
geometry on the Label-space. This tree in turn gives rise to a predictive
graph, or a network with precisely weighted linkages. Such two multiscale
geometries are taken as the coarse scale information content of MCC. They
indeed jointly shed lights on explainable knowledge on why and how labeling
comes about and facilitates error-free prediction with potential multiple
candidate labels supported by data. For revealing within-label heterogeneity,
we further undergo labeling naturally found clusters within each point-cloud,
and likewise derive multiscale geometry as its fine-scale information content
contained in data. This fine-scale endeavor shows that our computational
proposal is indeed scalable to a MCC setting having a large label-space.
Overall the computed multiscale collective of data-driven patterns and
knowledge will serve as a basis for constructing visible and explainable
subject matter intelligence regarding the system of interest.
