Graph Theory and Topological Data Analytics (TDA), while powerful, have many drawbacks related to their sensitivity and consistency with TDA & Graph Network Analytics. In this paper we demonstrate a novel approach for overcoming drawbacks of consistent frameworks for Graph and Topological Analysis by encoding vectorized associations between data points for the purpose of enabling smooth transitions between Graph and TDA. We conclusively reveal effective ways of converting such vectorized associations to simplicial complexes representing micro-states in a Phase-Space, resulting in filter specific, Homotopic, Event-Driven Topological Signatures which have been referred as “Roy-Kesselman (R-K) Diagrams” with Persistent Homology. They arise out of filter-based encodings of “(R-K) Models”. 

We have also built a computational framework called the “R-K Pipeline” which can be applied for different analytical purposes via the “R-K Toolkit” available on Github. This would enable filter-based ML Driven models for unique topological signature identification and classification problems. The validity and impact of this approach were tested specifically on high-dimensional (parameter specific) raw and derived measures from the latest LIGO datasets published by the GW Open Science Center along with a generalized approach for a non-scientific use-case, which was tested and demonstrated using the Tableau Superstore Sales Dataset.

The application of this above novel technique of Topological-Graph Analytics with Roy-Kesselman (R-K) diagrams can be used for the efficient and automated classification of Binary Merger Signals from LIGO data and other Multi-messenger data streams for event-based classification of compact-binary mergers, aiding the search for Primordial Black Hole Dark Matter and enabling template-based classification of binary BH-BH, BH-NS, NS-NS mergers. This work focuses on noise-filtering, using topological techniques such as isometric (Loss-less) compression (of high-dimensional data), for efficient encoding of intrinsic physical parameters of compact binary-mergers. It also enables effective ways to automate the segregation and classification of such GW signals using R-K Models. This pipeline and methodology could be scaled to obtain all significant parameters for more confident compact binary merger classifications over the years, using Multi-Messenger Data-streams.