## 2 Study Background
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Related/Characteristics** & **[PERSON], [PERSON], and [PERSON] [43]** & **[PERSON], [PERSON], and [PERSON] [44]** & **[PERSON] et al. [45]** \\ \hline Clustering target & Products & Customers & Customers \\ Model used & RFM & LRFMP & R + FM \\  & & Customer & Customer \\ Targeting objective & Inventory management & relationship & relationship \\  & & management & management \\ Clustering algorithm used & K-means & K-means & K-means \\ Methodological focus & Optimization of k & Formulation of a & Formulation of \\  & with different metrics & new model and & a new model and \\ Number of data & & analysis of results & offer campaign \\ (customers/products) & 2043 & 16,024 & 3,000,000 \\  & 8 (Elbow Method, & \\  & Silhouette Index, & \\  & Calinski–Harabasz Index, & \\  & Davies–Bouldin Index, & \\  & Ratkowski Index, & \\  & Hubert Index, & \\  & Ball–Hall Index, and & \\  & Krzanowski–Lai Index) & & \\ Number of generated clusters & 3 & 5 & 10 \\  & Inferences about the data & Not applicable & Yes & Yes \\ Using external indexes & No & No & No \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between related works. customer segment, primarily aiming to increase the company's profits, also using a control group and comparison of income before and after the campaign. [PERSON], [PERSON], and [PERSON] [43] demonstrated the possibility of applying RFM outside the conventional use of customer segmentation and acquired clusters with an average variance of 0.19113. In addition, the authors suggested other forms of data comparison, such as particle swarm optimization, medioids, or even maximizing expectancy. [PERSON], [PERSON], and [PERSON] [44] segmented customers from a market network in Turkey into \"high contribution loyal customers\", \"low contribution loyal customers\", \"uncertain customers\", \"high spending lost customers\" and \"lost customers\". low cost\". In this way, the authors provided visions and strategies (promotions, offers, perks) to increase income on customer behavior, but limited themselves to applying it to a specific market segment. [PERSON] et al. [45] grouped customers of an e-commerce company based on their recency, resulting in \"Active\", \"Expiring\" and \"Expiring\" customers, and from these segments, they successively separated them into groups of \"High\", \"Medium\" and \"Low\" values, subsequently validating the segmentation through an offer campaign for customers in the \"Active\" group. [PERSON] et al. [46] introduced pioneering techniques such as text mining for assortment optimization, effectively identifying identical products in competitor portfolios, and successfully matching items with incomplete and inconsistent descriptions. Related works presented by other authors implemented the RFM model in the context of clustering by K-means, using either internal indexes or no index to assert the quality of the clusters. In addition to using internal indexes, this work applied three external index techniques, bringing a new approach compared to the others. Considering this, the research question that comes up is as follows: Is it possible to use RFM values with clustering techniques, internal indices, and external indices for customer segmentation? The external indices were used in this work due to the uncertainty generated by the internal validation indices in contrast to real data (variability in the results indicative of the number of suggested clusters), making it necessary to acquire other views on the dataset, so that it could be possible to ensure the ideal number of clusters (meaningful, coherent, and stable). For this, we used (i) a global stability measure based on the adjusted Rand index (ARI), (ii) a cluster stability measure based on the Jaccard index, and (iii) segment level stability across method solutions (SLSa) from the entropy measure, which are the differentials of this work in relation to its correlates.