Bank Customer Segmentation with K-means for Risk and Retention Profile

Adriano Martins Pereira; Edilson José Rodrigues

DOI: 10.22167/2675-6528-202602613

Article derived from a Course Conclusion Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

Customer segmentation based on financial and behavioral data proved relevant to support relationship, credit, and retention decisions, as heterogeneous bases made it difficult to define unique strategies for all profiles. The general objective of the study was to segment customers based on numerical variables of economic profile and product usage, identifying clusters with similar characteristics and analyzing their association with risk and behavior indicators, such as delays in the last 12 months, email openings, and churn. The research used an applied and quantitative approach, with structured and pre-processed data (handling inconsistencies and standardization by z-score), followed by the application of the K-means algorithm on numerical variables. The number of clusters was defined by complementary criteria (elbow method and silhouette score), and the clusters were visualized using PCA in two dimensions, in addition to being described by statistics and distributions. The results showed three groups with consistent visual separation and distinct sizes, as well as relevant empirical patterns: variables of economic and credit capacity showed positive associations with each other, while indebtedness was negatively related to the score and positively to delays, and churn showed more modest relationships with the evaluated indicators. It was concluded that clustering structured interpretable profiles consistent with risk and behavior signals, offering an objective basis for managerial analysis and group-based action targeting.

Keywords: Customer behavior; Data mining; Retention; Credit risk; Segmentation.

1. Introduction

Digital transformation has significantly boosted organizations’ ability to collect, store, and analyze large volumes of data about customers, transactions, and interactions over time. In highly competitive sectors, such as banking, retail, and services, this evolution has led to the increasing adoption of advanced analytical approaches. Such approaches aim to support strategic decisions related to market segmentation, customer relationship management (CRM), customer retention, and the mitigation of operational and financial risks.

In this scenario, customer segmentation transcends a merely descriptive marketing practice, consolidating itself as a fundamental strategic resource. It allows organizations to understand behavior patterns, identify groups with distinct needs and profiles, and consequently, guide more efficient interventions. Specialized literature emphasizes that the creation of value in CRM depends, to a large extent, on the ability to convert raw data into actionable knowledge about customer heterogeneity, their behavior, and relationship potential (Payne & Frow, 2005).

Despite the growing availability of data, a persistent challenge for organizations lies in the difficulty of synthesizing the vast diversity of customer profiles present in extensive and multivariate databases. Customers can exhibit distinct consumption patterns, debt levels, credit usage, investments, and payment behavior. These differences are not always easily discernible through univariate analyses or simple stratifications, which hinders the formulation of unique and effective strategies for all segments.

To address this complexity, unsupervised learning techniques become particularly useful, as they allow for the identification of latent structures in the data without the need for pre-defined labels. Cluster analysis, in this context, offers a set of methods that group observations into sets that are internally homogeneous and heterogeneous among themselves. This contributes to a deeper understanding of behavioral patterns and to the generation of hypotheses about customer profiles (Jain, 2010; Everitt et al., 2011).

Among clustering methods, the K-means algorithm stands out for its simplicity, scalability, and direct interpretation. Proposed by MacQueen (1967) and consolidated by Lloyd (1982) and Hartigan and Wong (1979), K-means seeks to partition data into k groups, minimizing the variance within each cluster. This ensures that observations in each group are close to a representative centroid.

The application of K-means, however, requires specific methodological care. It is essential to treat and standardize variables, for example, via z-score, to prevent attributes with different scales from dominating the clustering process (Hair et al., 2010). The definition of the adequate number of clusters (k) is also a critical decision, which can be supported by metrics such as the silhouette coefficient (Rousseeuw, 1987) and the Adjusted Rand Index (Hubert and Arabie, 1985), which evaluate the cohesion and separation between groups.

The practical relevance of clustering intensifies when connected to business decisions. Segmentation based on financial behavior, for example, can support customer retention and churn prevention actions, by indicating groups with a higher propensity to abandon services. Generalist policies tend to be less cost-effective than segmented interventions (Neslin et al., 2006; Verbeke et al., 2012). Additionally, the distinction between profiles contributes to the formulation of risk policies and credit limits more aligned with customers’ historical behavior and payment capacity (Hand & Henley, 1997; Thomas et al., 2002).

Thus, by grouping customers by patterns of income, spending, indebtedness, credit score, and delinquency history, it becomes possible to discuss, in a well-founded manner, the differences between profiles and their implications for relationship and risk management. In this context, this work aims to apply clustering techniques with an emphasis on K-means to segment customers based on quantitative financial variables, evaluating the quality and stability of the partitions (e.g., via silhouette and ARI) and interpreting the obtained clusters in terms of behavior and relevant indicators for CRM and risk decisions, such as default, delinquency, and possible propensity to churn.

2. Material and Methods

The research adopted a quantitative, exploratory, and applied approach, with the objective of segmenting customers based on numerical variables to generate useful knowledge for organizational practice. The exploratory character sought to identify latent patterns in data without pre-defined categories, while the applied nature focused on supporting managerial decisions (Gil, 2008; Vergara, 2016). The unit of analysis consisted of 1,500 individual customer records. The database, treated as secondary and originating from a CSV tabular file, gathered quantitative variables on financial behavior, including monthly income, card spending, investments, credit limit, account balance, indebtedness, credit score, number of products, monthly purchases, email opens, delays in the last 12 months, and churn. Principles of confidentiality and anonymization were observed.

The analyses were developed in a Python computational environment, using libraries such as pandas and numpy for data manipulation. Scikit-learn was employed for preprocessing and clustering modeling, including the K-means algorithm and evaluation metrics. Visualizations were generated with matplotlib. Parameters such as seeds (random_state) and tested intervals for k were controlled to ensure the reproducibility of the procedures.

The data preprocessing aimed to ensure consistency and comparability. A general inspection was performed to identify structure, variable types, missing values, duplicates, and inconsistencies. Missing values and inconsistent records were treated, and variables were converted to appropriate formats. Attribute selection for clustering considered only quantitative variables, aligned with K-means’ dependence on distance measures on comparable numerical scales (Vergara, 2016). Standardization was done by z-score (StandardScaler), ensuring balanced contribution from each attribute. Distribution and dispersion checks identified and treated outliers.

The clustering strategy adopted the K-means algorithm as the main method, seeking to partition observations into k groups, minimizing internal variability and maximizing separation between clusters (MacQueen, 1967; Lloyd, 1982; Hartigan & Wong, 1979). The definition of the number of clusters (k) was guided by the elbow method, which evaluates inertia, and by the silhouette coefficient (Rousseeuw, 1987), which measures cohesion and separation (Gil, 2008). After selecting k, the K-means model was trained with explicit parameter control to ensure consistency.

The evaluation and validation of the clustering verified the internal quality, separation between groups, and stability against initialization variations (Gil, 2008; Vergara, 2016). Robustness was assessed by stability analysis with multiple initializations, and the agreement between partitions was measured by the Adjusted Rand Index (ARI) (Hubert and Arabie, 1985). The Davies-Bouldin and Calinski-Harabasz indices complemented the validation. Principal Component Analysis (PCA) was employed for visualization and interpretive support, projecting the data into two or three dimensions for visual inspection of cluster separation (Jolliffe, 2002).

The interpretation of the clusters was performed after the definition of the final grouping, characterizing the profiles through descriptive statistics (mean, median, standard deviation, quartiles) for numerical variables and frequency distributions for categorical variables (Wedel & Kamakura, 2000). Cross-cluster analyses examined differences in prevalence and intensity of managerial indicators, such as delay and churn, supporting CRM and retention strategies (Payne & Frow, 2005). The analysis procedures were structured in a sequential pipeline, ensuring consistency and traceability (Fayyad, Piatetsky-Shapiro, & Smyth, 1996; Kelleher, Mac Namee, & D’Arcy, 2015). The results were organized into supporting tables, visualizations, and a final database with the cluster identification assigned to each record (Provost & Fawcett, 2013).

3. Results and Discussion

The data analysis revealed important patterns in the customer base, providing an in-depth understanding of financial behavior and service interaction. Initial results allowed for contextualizing the sample’s heterogeneity, while the application of the K-means algorithm generated a robust and interpretable segmentation. This approach aligns with the study’s objective of identifying clusters with similar characteristics, supporting strategic decisions for relationship management, credit, and retention, according to the literature on CRM and Data mining (Payne & Frow, 2005; Jain, 2010).

The final clustering, with three distinct groups, demonstrated that it is possible to structure customer profiles that reflect different economic capacities, risk levels, and engagement patterns. The detailed interpretation of each cluster, based on financial and behavioral variables, offers concrete subsidies for the formulation of targeted strategies, overcoming the limitations of generalist approaches. The validation of the grouping by multiple metrics and the proactive analysis of the profiles reinforce the managerial utility of the findings, connecting data analysis to practical business implications.

Initial characterization of variables and distribution of events

Initially, the analysis of the email open rate, an engagement indicator, revealed a majority concentration of clients with percentages between 20% and 45%. The presence of a portion of records with very low engagement, close to 0%, and a right tail extending to values above 60% was also observed. This behavior suggests the coexistence of customer groups with varying levels of interaction with communication campaigns, indicating the need for segmented communication strategies to optimize engagement.

The distribution of the number of delays in the last 12 months, an indicator of default risk, showed a concentration in low to moderate values, with the highest frequency observed between 2 and 6 delays. Although most records presented less than 8 delays, the presence of a right tail, with occurrences above 10 delays, evidenced significant heterogeneity in payment behavior. This pattern is crucial for differentiating risk profiles in the segmentation stage, allowing the identification of customers with a higher propensity for nonpayment.

The Churn variable, which represents the binary event of customer churn, showed a strong imbalance, with a predominance of records in class 0 (non-churn) and a smaller portion in class 1 (churn). Although the churn event is a minority in the dataset, which is common in churn problems, this imbalance does not prevent clustering. However, it requires that the differences between clusters regarding churn be compared in proportional terms (percentages) and not just by absolute counts, for a more precise interpretation of the profiles.

The distribution of customer categories, which included Regular, Intermediate, and Premium levels, revealed that the majority of the base falls into the Regular category, followed by Intermediate, and lastly, Premium. This composition suggests that the customer base is predominantly composed of lower value-added profiles, with a smaller fraction of high-value customers. This information is valuable for subsequent cross-referencing with clusters, allowing verification of whether the numerical segmentation aligns with existing value classifications and supporting the formulation of loyalty and retention strategies.

Linear relationships between numerical variables (Pearson correlation)

Pearson’s correlation matrix revealed a block of strong positive correlations among several financial variables. Monthly_Income, for example, showed a high correlation of approximately 0.96 with Credit_Limit, and relevant associations with Card_Spending and Investments. This pattern indicates that customers with higher income tend to have higher credit limits, spend more on their cards, and maintain larger investment volumes, which is consistent with the logic that economic capacity and credit availability are interconnected in the banking relationship.

In contrast, the Indebtedness variable demonstrated a strongly negative correlation of approximately -0.91 with the Credit_Score, as well as moderate negative correlations with other financial variables. This finding suggests that higher indebtedness is associated with a lower credit score and lower overall financial capacity. This relationship is fundamental for differentiating risk profiles, as indebtedness and credit score act as important contrast axes in customer segmentation.

On the events and behavior axis, the variable Delays_12m showed a positive correlation of approximately 0.51 with Indebtedness and a negative correlation of approximately -0.47 with Credit_Score. These patterns indicate that more delays are associated with higher indebtedness and a lower credit score, which aligns with the credit scoring literature (Hand & Henley, 1997; Thomas et al., 2002). Customers with greater financial pressure and a history of delays tend to exhibit worse scores, reinforcing the internal consistency of the data.

The Churn variable showed a moderate positive correlation of approximately 0.38 with Indebtedness and a moderate negative correlation of approximately -0.38 with Credit_Score. These results suggest that churn tends to occur more in profiles with higher indebtedness and less in profiles with a higher credit score. Although these associations do not establish causality, they indicate linear patterns in the sample that are consistent with findings on retention in financial services, where payment deterioration and increased risk raise the probability of evasion (Verbeke et al., 2012).

The Abertura_Email_Pct rate, in turn, showed weak correlations with the other variables. This result may indicate that e-mail engagement, in isolation, does not capture the entire dynamic of the Customer relationship. CRM literature suggests that contact indicators need to be integrated with usage, value, and risk variables to more fully explain customer retention (Payne & Frow, 2005). The correlation analysis, therefore, confirmed the interdependence of some financial variables and the relevance of risk indicators for segmentation.

Definition of the number of clusters (K) and K-means adjustment

The choice of the number of clusters (k) was a central analytical decision, evaluated through two complementary criteria: the elbow method and the silhouette index. The elbow method, which analyzes the behavior of inertia (sum of intra-cluster squared errors), showed a sharper decrease in inertia when moving from k=2 to k=3. From k=4 onwards, the reductions became progressively smaller, indicating that the compaction gains were becoming marginal. This pattern suggests that k=3 represents a balance point that adds detail without excessively increasing complexity.

The silhouette index, which simultaneously assesses internal cohesion and separation between clusters, showed its highest value at k=2, with a marked reduction at k=3 and a gradual drop for larger values. Although k=2 indicated the strongest average separation, the configuration with three groups remained viable and more informative for profile characterization. The adoption of k=3 was, therefore, an analytical compromise between clustering structure and profile granularity, seeking a segmentation that was both mathematically reasonable and managerially useful.

Complementary validation of the clustering solution

The complementary validation of the clustering solution reinforced the choice of k=3, considering multiple criteria. The Davies-Bouldin index, which measures the ratio between internal dispersion and separation between clusters (lower values are preferable), presented 0.7516 for k=2 and 0.9605 for k=3. On the other hand, the Calinski-Harabasz index, which compares the dispersion between clusters with internal dispersion (higher values are preferable), reached its highest value at k=3 (1,726.55), surpassing the value for k=2 (1,662.11). These results, together with silhouette and inertia, indicated that k=3, despite having lower average separation than k=2, preserves good internal quality and a favorable ratio between intergroup and intragroup dispersion.

For the final solution with k=3, the average distances of the observations to their respective centroids were 2.3075 in Cluster 0, 1.4738 in Cluster 1, and 1.7153 in Cluster 2. The distances between the centroids were 7.8268 between Clusters 0 and 1, 4.9294 between Clusters 0 and 2, and 3.0880 between Clusters 1 and 2. These values demonstrate that the distances between the group centers are greater than the average internal distances, confirming the intracluster homogeneity and intercluster heterogeneity of the solution. The stability analysis, performed through multiple initializations, resulted in an average Adjusted Rand Index (ARI) of 1.0, indicating high consistency of the obtained partitions and reinforcing the reliability of the segmentation.

Visualization of clusters via PCA (2D)

The projection of the clusters in two dimensions, using Principal Component Analysis (PCA), allowed for a visualization of the relative arrangement of the groups generated by K-means. Although PCA does not alter the cluster assignment, it facilitates visual inspection of the degree of separation and the identification of possible overlapping zones. A predominant separation was observed along the PC1 axis, with Cluster 2 concentrated in more negative values, Cluster 1 in more positive values, and Cluster 0 in an intermediate position. This visual distribution suggests that the clusters occupy distinct regions in the projected space, even with some partial overlap in the central regions, which is expected in real data with continuous profiles and correlated variables (Jolliffe, 2002).

Distribution of records by cluster

After adjusting K-means with k=3, the distribution of records per cluster indicated the formation of three groups with distinct sizes. Clusters 0 and 2 presented a larger volume of records, while Cluster 1 was the smallest. This pattern suggests the existence of two more frequent profiles in the database and one less common, but still relevant, profile for characterization. In operational terms, reading the relative size of the groups is useful for guiding the prioritization of complementary analyses, especially when comparing the distribution of churn, delays, and engagement among the profiles, allowing for more efficient resource allocation.

In summary, the initial results showed heterogeneity in email engagement, delay history, and churn presence. Furthermore, a set of strong correlations between financial variables supported consistent patterns of capacity and behavior. The definition of k=3 was supported by the elbow method and complemented by the silhouette index, and the PCA projection allowed visualization of the relative separation of groups. The detailed numerical characterization of each cluster, through means, medians, and percentiles per variable, as well as the distribution of churn, delays, and customer category within each group, was fundamental for the interpretation of the profiles.

The average customer profile by cluster, according to the analysis, revealed clear distinctions between the groups. Cluster 1 (n=272) stood out as the profile with the highest value and lowest risk, presenting the highest averages for Monthly Income (R$ 12,476.80), Card Spending (R$ 3,238.55), Investments (R$ 21,386.40), Credit Limit (R$ 19,745.22), Account Balance (R$ 8,964.19), Number of Products (5.42), and Monthly Purchases (16.27). Furthermore, this group registered the lowest Indebtedness (0.23), the highest Credit Score (817.65), the lowest average for Delays in the Last 12 Months (1.42), and the lowest churn percentage (6.9%). This profile represents customers with high economic capacity, intense financial usage, and low risk, being a priority for loyalty and relationship expansion strategies.

Cluster 0 (n=622) assumed an intermediate position, with moderate financial indicators and controlled risk. This group presented averages for Monthly Income (R$5,842.31), Card Spending (R$1,486.27), Investments (R$7,914.66), Credit Limit (R$8,621.58), Account Balance (R$3,118.75), Number of Products (3.18), and Monthly Purchases (9.64). Its Indebtedness was 0.46, Credit Score was 682.40, the average of Delays in the Last 12 Months was 3.78, and the Churn percentage was 15.8%. This group is relevant for relationship development and preventive retention actions, with potential for gradual growth and base maintenance.

Cluster 2 (n=606) was characterized as the profile with the highest vulnerability and risk. This group registered the lowest averages for Monthly Income (R$2,913.44), Card Spending (R$748.92), Investments (R$2,146.73), Credit Limit (R$3,911.36), Account Balance (R$1,204.51), Number of Products (2.11), and Monthly Purchases (5.83). In contrast, it presented the highest Indebtedness (0.72), the lowest Credit Score (528.17), the highest average for Delinquencies in the Last 12 Months (6.31), and the highest percentage of Churn (29.7%). This profile demands risk mitigation policies, renegotiation, and targeted communication, aiming for the recovery and regularization of the relationship.

The Email Open Rate also varied between the clusters. Cluster 1 demonstrated the highest engagement, with 47.91% open rate, followed by Cluster 0, with 34.82%, and Cluster 2, with the lowest engagement, registering 24.36%. This difference in communication engagement is an indicator that higher value and lower risk customers (Cluster 1) are more responsive to communications, while higher risk customers (Cluster 2) are less engaged, which may influence the effectiveness of marketing and relationship campaigns.

This detailed reading of the profiles reinforced that the segmentation not only separated customers by mathematical similarity but also produced groups with clear managerial meaning for credit, relationship, and retention decisions. The higher economic capacity and lower risk in Cluster 1, the intermediate position and controlled risk in Cluster 0, and the lower economic capacity and higher risk in Cluster 2, are pieces of information that allow for directing specific actions to each segment, optimizing customer portfolio management.

Propositive analysis of profiles

The propositive analysis of profiles, elaborated in the FOFA format (Strengths, Opportunities, Weaknesses, and Threats), translated the segmentation results into possibilities for managerial action. For Cluster 1, identified as the profile with the highest value and lowest risk, Strengths include higher income, high credit score, substantial investments, account balance, and expanded product usage, in addition to low churn and delinquency rates. The main Weakness is the concentration of value, which increases the relevance of retention. Opportunities lie in loyalty, premium relationship, investment expansion, and personalized offers, while Threats involve evasion to competitors and the loss of high-value clients. The Direction for this group is to prioritize retention, personalization, and responsible relationship expansion.

For Cluster 0, characterized as an intermediate profile, the Strengths are moderate financial capacity, controlled risk, and an already established relationship. Weaknesses include lower value and engagement indicators than Cluster 1, as well as intermediate churn. Opportunities focus on relationship development, increased engagement, and gradual product expansion. Threats for this group are migration to a higher-risk profile or loss of relationship due to low activation. The recommended Direction is to apply preventive retention, segmented communication, and offers compatible with the client’s capacity.

Finally, for Cluster 2, which represents the profile of greatest vulnerability and risk, the main Strength is the potential for recovery and the possibility of a relationship oriented towards regularization. The Weaknesses are lower income and credit score, higher indebtedness, high rates of delays and churn, and lower engagement. Opportunities include debt renegotiation, financial education, and review of credit conditions, in addition to preventive communication. Threats include nonpayment, evasion, further risk deterioration, and relationship reduction. The Direction for this group is to prioritize risk mitigation, monitoring, renegotiation, and early interventions, aiming at customer recovery and stabilization.

These action guidelines, derived from the propositional analysis, should be understood as decision support and not as automatic rules for credit granting or individual treatment. They allow the organization to adopt differentiated strategies: for Cluster 1, the priority is to preserve high-value, low-risk customers through loyalty and personalization (Payne & Frow, 2005). For Cluster 0, actions can focus on relationship development and preventive retention. For Cluster 2, the priority is to reduce vulnerabilities through monitoring, renegotiation, and targeted communication, aligning with risk management and retention.

The results obtained respond to the general objective of the study, which was to segment customers based on financial and behavioral variables, identifying clusters with similar characteristics and analyzing their association with risk and behavior indicators. The solution with three clusters produced a visually consistent segmentation in the PCA projection and with sufficiently distinct group sizes to support managerial reading, transforming multivariate data into interpretable profiles, a crucial aspect in segmentation studies (Wedel & Kamakura, 2000). The exploratory analysis of distributions and the correlation matrix confirmed consistent patterns of economic capacity, indebtedness, and risk, providing the empirical basis for interpreting the structure of financial behavior in the sample. The choice of three clusters, although the silhouette indicated greater separation in two, was supported by the inflection point in inertia and the PCA visualization, favoring a more informative and applicable segmentation. This approach allowed organizing the database into distinguishable and coherent groups with expected relationships between financial capacity, credit risk, and friction signals, offering an objective basis for describing profiles and directing subsequent analyses by cluster.

4. Conclusion

The study aimed to segment customers based on financial and behavioral variables, identifying clusters with similar characteristics and analyzing their association with risk and behavior indicators. The application of the K-means algorithm, after data preprocessing and standardization, structured the customer base into three distinct profiles. It was found that Cluster 1 represented higher value and lower risk customers, characterized by high income, substantial investments, and low debt, as well as lower rates of delays and churn. Cluster 0 was positioned as an intermediate profile, with moderate financial indicators and controlled risk. In turn, Cluster 2 was identified as the group with the highest vulnerability, presenting lower economic capacity, higher debt, and the highest percentages of delays and churn. Correlation analysis confirmed consistent patterns, such as the positive association between economic capacity and credit, and the negative relationship between indebtedness and credit score, which aligned with a higher number of delays and a greater propensity for churn. This segmentation provided an objective and interpretable basis for relationship and risk management, allowing for the formulation of differentiated strategies for each segment.

The choice of three clusters, although the silhouette index indicated greater separation into two groups, was supported by the elbow method and PCA visualization, favoring a more informative granularity for managerial application. However, the study acknowledges limitations inherent to the approach, such as the sensitivity of K-means to outliers and the influence of correlated variables in defining centroids. Additionally, a complete explanation of churn may require the inclusion of additional relationship variables or the application of supervised models in future studies. It is recommended that subsequent research explore the integration of qualitative data and the application of supervised machine learning techniques to enhance the predictive capability of events such as churn, as well as to deepen the analysis of the proposed action guidelines for each cluster.

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Article originating from the Final Course Project of the Specialization in Data Science and Analytics of the MBA USP/Esalq

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