Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

André Luiz Corrêa Vianna Filho, Leonardo de Lima, Mariana Kleina

TL;DR

The paper addresses customer segmentation by leveraging RFM scores within a max-$k$-cut formulation on a graph whose vertices represent customers and whose edge weights are the Manhattan distances between $(R,F,M)$-scores. A reduced graph $G'$ is constructed by merging identical $(R,F,M)$-scores, yielding at most $n' \le T^3$ vertices (with $T=5$, $n' \le 125$), and the authors prove that the optimal objective value of the original problem equals that of the reduced problem, enabling exact solution transfer via a mapping procedure. The method is validated on the Online Retail II dataset, showing that solving on $G'$ is feasible for large $n$ and that the resulting clusterings (notably $k=2$ and $k=4$) yield meaningful business insights, with $k=4$ offering richer segmentation from a practical perspective. This work demonstrates how graph reduction coupled with a max-$k$-cut formulation can scale exact segmentation to thousands of customers while preserving optimality, providing actionable customer groups for targeted marketing.

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.

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

TL;DR

The paper addresses customer segmentation by leveraging RFM scores within a max--cut formulation on a graph whose vertices represent customers and whose edge weights are the Manhattan distances between -scores. A reduced graph is constructed by merging identical -scores, yielding at most vertices (with , ), and the authors prove that the optimal objective value of the original problem equals that of the reduced problem, enabling exact solution transfer via a mapping procedure. The method is validated on the Online Retail II dataset, showing that solving on is feasible for large and that the resulting clusterings (notably and ) yield meaningful business insights, with offering richer segmentation from a practical perspective. This work demonstrates how graph reduction coupled with a max--cut formulation can scale exact segmentation to thousands of customers while preserving optimality, providing actionable customer groups for targeted marketing.

Abstract

The present article proposes a graph-based approach to customer segmentation, combining the RFM analysis with the classical optimization max--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 -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--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.
Paper Structure (11 sections, 2 theorems, 5 equations, 1 figure, 7 tables)

This paper contains 11 sections, 2 theorems, 5 equations, 1 figure, 7 tables.

Table of Contents

  1. Introduction
  2. Customer segmentation: a graph-based approach
  3. The max-k-cut problem
  4. Reduction of graph G: an auxiliary problem
  5. Retrieving an optimal solution to the original problem
  6. Methodology
  7. Results and discussion
  8. Computational experiments
  9. Business analysis
  10. Conclusion
  11. Data availability

Key Result

Theorem 1

Consider the graph $G$, built as described in Section 2.1, given as input to bqo_formulation. Then, there is at least one optimal segmentation solution for bqo_formulation.

Figures (1)

  • Figure 1: Example of a graph $G^{\prime}$ in (ii) obtained from $G$ in (i).

Theorems & Definitions (6)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof : Proof
  • Theorem 2
  • proof : Proof