Topological Analysis of Credit Data: Preliminary Findings

Abstract

Intuitively, similar customers should have similar credit risk. Capturing this similarity is often attempted using Euclidean distances between customer features and predicting credit default via logistic regression. Here we explore the use of topological data analysis for describing this similarity. In particular, persistent homology algorithms provide summaries of point clouds which relate to their topology. This approach has been shown to be useful in many applications but to the best of our knowledge, applying topological data analysis to prediction of credit risk is novel. We develop a pipeline which is based on the topological analysis of neighbourhoods of customers, with the neighbourhoods determined by a geometric network construction. We find a modest signal using three data sets from the Lending Club, and the Japan Credit Screening data set. The Cleveland oncological data set is used to validate the pipeline. The results have high variance, but they indicate that including such topological features could improve credit risk prediction when used as additional explanatory variable in a logistic regression.