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

2024-04-06

AI Summary

This study addresses state identification and abrupt transition early warning in the Indian stock market. We propose a hyperbolic-geometry-based network analysis framework: modeling the market as a heterogeneous scale-free network, we introduce, for the first time, co-clustering embedding and Poincaré disk hyperbolic embedding, integrated with hyperbolic k-means for community detection. A nonparametric discriminant method—Wilcoxon rank-sum test—is developed using hyperbolic distance and shortest-path distance to quantitatively distinguish stable from volatile regimes. Bollinger Bands are further incorporated to enable early state-transition alerts. Experiments demonstrate that hyperbolic clustering improves normalized mutual information (NMI) and adjusted mutual information (AMI) by 18.3% over Euclidean clustering; all seven major market volatility onsets during 2015–2023 are precisely identified, with an average lead time of 2.4 trading days. Moreover, sectoral nodes exhibit pronounced clustering patterns in the hyperbolic radial–angular coordinate system.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Clustering
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• Indian stock market
• network structure
• market prediction

Innovation

• Non-uniform Node Importance
• Curvature-based Embedding
• Market Stability Assessment