# A Weight-based Information Filtration Algorithm for Stock-Correlation Networks

## TL;DR

This paper introduces a new weight-based filtering algorithm called proportional degree (PD) for stock-correlation networks, which produces more homogeneous and robust clusters compared to the existing PMFG method.

## Contribution

The paper proposes the PD algorithm for filtering stock correlation data, demonstrating its advantages over PMFG in producing homogeneous, well-clustered, and robust networks.

## Key findings

- PD network shows better homogeneity with respect to cliques.
- Partition of PD network aligns more closely with spectral clustering.
- Clusters in PD network are more robust to random edge removal.

## Abstract

Several algorithms have been proposed to filter information on a complete graph of correlations across stocks to build a stock-correlation network. Among them the planar maximally filtered graph (PMFG) algorithm uses $3n-6$ edges to build a graph whose features include a high frequency of small cliques and a good clustering of stocks. We propose a new algorithm which we call proportional degree (PD) to filter information on the complete graph of normalised mutual information (NMI) across stocks. Our results show that the PD algorithm produces a network showing better homogeneity with respect to cliques, as compared to economic sectoral classification than its PMFG counterpart. We also show that the partition of the PD network obtained through normalised spectral clustering (NSC) agrees better with the NSC of the complete graph than the corresponding one obtained from PMFG. Finally, we show that the clusters in the PD network are more robust with respect to the removal of random sets of edges than those in the PMFG network.