A Novel Approach to Topological Graph Theory with R-K Diagrams and Gravitational Wave Analysis. (arXiv:2201.06923v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Roy_A/0/1/0/all/0/1">Animikh Roy</a> (University of Sussex, UK), <a href="http://arxiv.org/find/astro-ph/1/au:+Kesselman_A/0/1/0/all/0/1">Andor Kesselman</a> (Pathr.ai, USA)
Graph Theory and Topological Data Analytics, while powerful, have many
drawbacks related to their sensitivity and consistency with TDA & Graph Network
Analytics. In this paper, we aim to propose a novel approach for encoding
vectorized associations between data points for the purpose of enabling smooth
transitions between Graph and Topological Data Analytics. 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 self-expressive, event-driven unique topological signatures
which we have referred as Roy-Kesselman Diagrams or R-K Diagrams with
persistent homology, which emerge from filter-based encodings of R-K Models.
The validity and impact of this approach were tested specifically on
high-dimensional raw and derived measures of Gravitational Wave Data from the
latest LIGO datasets published by the LIGO Open Science Centre along with
testing a generalized approach for a non-scientific use-case, which has been
demonstrated using the Tableau Superstore Sales dataset. We believe the
findings of our work will lay the foundation for many future scientific and
engineering applications of stable, high-dimensional data analysis with the
combined effectiveness of Topological Graph Theory transformations.
Graph Theory and Topological Data Analytics, while powerful, have many
drawbacks related to their sensitivity and consistency with TDA & Graph Network
Analytics. In this paper, we aim to propose a novel approach for encoding
vectorized associations between data points for the purpose of enabling smooth
transitions between Graph and Topological Data Analytics. 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 self-expressive, event-driven unique topological signatures
which we have referred as Roy-Kesselman Diagrams or R-K Diagrams with
persistent homology, which emerge from filter-based encodings of R-K Models.
The validity and impact of this approach were tested specifically on
high-dimensional raw and derived measures of Gravitational Wave Data from the
latest LIGO datasets published by the LIGO Open Science Centre along with
testing a generalized approach for a non-scientific use-case, which has been
demonstrated using the Tableau Superstore Sales dataset. We believe the
findings of our work will lay the foundation for many future scientific and
engineering applications of stable, high-dimensional data analysis with the
combined effectiveness of Topological Graph Theory transformations.
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