Novel Pattern Identification Means for Networks and Tabular Data based upon Lie Groups

The author previously derived a decomposition of the generators of the general linear group GL(n) in n dimensions into Abelian A(n) and Markov Type MT(n²-1) Lie algebras where the MT generates all Markov Transformations preserving the sum of coordinates when nonnegative combinations are used giving a Markov monoid (MM). He then showed that all networks, as defined by a square matrix C of non-negative connections among nodes are isomorphic to this MM. The resulting MM has columns that can be interpreted as probability distributions supporting n^th order Renyi entropy which give spectral curves supporting network expansions and a distance function between networks. The eigenvalues of the MM are shown to define novel network clusters where the eigenvectors define the contributions of each node to each cluster. We then showed that tabular data tables can be transformed into two networks, allowing novel pattern identification to also be performed on numerical tables as well as general networks. We have performed this analysis on networks of internet traffic and on tables of medical patients and their properties (blood …). It is suggested that these algorithms (ported to an AWS server) offer novel pattern recognition methods for Big Data for both networks and tabular numerical data.