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

ArXiv ID: 2404.04710 “View on arXiv”

Authors: Unknown

Abstract

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.

Keywords: Hyperbolic Embedding, Network Analysis, Scale-Free Network, Market Stability, Machine Learning, Equity (Stocks)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including hyperbolic geometry, non-parametric statistical tests, and machine learning embeddings (coalescent embedding, hyperbolic k-means), indicating high math complexity. Empirical rigor is substantial with specific datasets (CNX500, 2017-2021), windowed backtesting (Bollinger Bands on modularity), and robust validation (NMI/AMI scores, p-values), making it backtest-ready.

  flowchart TD
    A["Research Goal: Model Indian Stock Market Geometry"] --> B["Construct Scale-Free Network"]
    B --> C["Hyperbolic Embedding<br>Poincaré Disc"]
    C --> D["Clustering<br>Hyperbolic vs Euclidean K-Means"]
    D --> E{"Market Regime Analysis"}
    E --> F["Stable vs Volatile<br>Period Detection"]
    E --> G["Sector Visualization"]
    F --> H["Early Warning:<br>Bollinger Bands on Modularity"]