Exploiting the geometry of heterogeneous networks: A case study of the Indian stock market

In this study, we model the Indian stock market as heterogenous scale free network, which is then embedded in a two dimensional hyperbolic space through a machine learning based technique called as coalescent embedding. This allows us to apply the hyperbolic kmeans algorithm on the Poincare disc and the clusters so obtained resemble the original network communities more closely than the clusters obtained via Euclidean kmeans on the basis of well-known measures normalised mutual information and adjusted mutual information. Through this, we are able to clearly distinguish between periods of market stability and volatility by applying non-parametric statistical tests with a significance level of 0.05 to geometric measures namely hyperbolic distance and hyperbolic shortest path distance. After that, we are able to spot significant market change early by leveraging the Bollinger Band analysis on the time series of modularity in the embedded networks of each window. Finally, the radial distance and the Equidistance Angular coordinates help in visualizing the embedded network in the Poincare disc and it is seen that specific market sectors cluster together.