  Kernel spectral clustering corresponds to a weighted kernel principal
component analysis problem in a constrained optimization framework. The primal
formulation leads to an eigen-decomposition of a centered Laplacian matrix at
the dual level. The dual formulation allows to build a model on a
representative subgraph of the large scale network in the training phase and
the model parameters are estimated in the validation stage. The KSC model has a
powerful out-of-sample extension property which allows cluster affiliation for
the unseen nodes of the big data network. In this paper we exploit the
structure of the projections in the eigenspace during the validation stage to
automatically determine a set of increasing distance thresholds. We use these
distance thresholds in the test phase to obtain multiple levels of hierarchy
for the large scale network. The hierarchical structure in the network is
determined in a bottom-up fashion. We empirically showcase that real-world
networks have multilevel hierarchical organization which cannot be detected
efficiently by several state-of-the-art large scale hierarchical community
detection techniques like the Louvain, OSLOM and Infomap methods. We show a
major advantage our proposed approach i.e. the ability to locate good quality
clusters at both the coarser and finer levels of hierarchy using internal
cluster quality metrics on 7 real-life networks.
