A graph-based approach to customer segmentation using the RFM model

TL;DR

This paper introduces a novel graph-based customer segmentation method that integrates RFM analysis with max-k-cut optimization, improving computational efficiency and revealing meaningful customer groups.

Contribution

It develops a graph reduction technique and proves equivalence of optimal solutions, enabling efficient segmentation of large customer datasets.

Findings

Effective segmentation of real customer data

Identified distinct customer behavior groups

Reduced computational complexity for large datasets

Abstract

The present article proposes a graph-based approach to customer segmentation, combining the RFM analysis with the classical optimization max-$k$-cut problem. We consider each customer as a vertex of a weighted graph, and the edge weights are given by the distances between the vectors corresponding to the $(R,F,M)$-scores of the customers. We design a procedure to build a reduced graph with fewer vertices and edges, and the customer segmentation is obtained by solving the max-$k$-cut for this reduced graph. We prove that the optimal objective function values of the original and the reduced problems are equal. Additionally, we show that an optimal solution to the original problem can be easily obtained from an optimal solution to the reduced problem, which provides an advantage in dealing with computational complexity in large instances. Applying our methodology to a real customer dataset allowed us to identify distinct behaviors between groups and analyze their meaning and value from a business perspective.