## 4 Results and Discussion
### Cluster Description  
From the analysis of segmentation variables, it becomes feasible to implement promotional campaigns, incentive actions, and even methods to rescue lost customers. However, the analysis is not necessarily finished; one of the important steps after obtaining the cluster profiles is the description process. Cluster description consists of the individual analysis of the clusters from variables external to the clustering process, called descriptive variables [40]. These variables can contain information from questionnaires, and other characteristics pertinent to the scope of the company. As the database has a large amount of eligible information, five were chosen for the cluster description process: age, sex, time of contact with the store, number of purchases per season, and rate of returns. After extracting the descriptive data, mosaic charts were used for display. This type of chart is similar to a bar chart but displays the information in cells that have their size relative to the amount of information observed and may vary in width according to the number of customers/purchases in a cluster, and in height according to the percentage of the variable observed compared to the percentage of other variables. Another concept pertinent to the mosaic chart is the statistical model applied, called bimodal distribution, which displays abnormal variations in the distribution of values based on an assumption of independence of variables. In this way, higher-than-expected values (above two standard deviations, or outside the 95% value limit) are displayed in red shades of greater intensity, lower-than-expected values are displayed in blue shades of greater intensity, and normal values take on green. With this view, it is possible to observe unique characteristics of clusters that have abnormal variations. Regarding the descriptive information used, the age variable was transformed into an ordinal variable. This variable starts from 18 to 24 years old, considering age intervals of six years onwards for each category, with the penultimate one being for customers over 40 years old and the last one for a category representing a lack of information in the register. The gender variable available in the database consists of the categories \"male\" and \"female\". The result of the graphs applied to these variables can be seen in Figure 10, which presents the age graph on the left side and the sex graph on the right side; each graph displays on the vertical axis the categories of the descriptive variables analyzed and on the horizontal axis the clusters. Since the distribution of the cells occurs according to the observed variable and the number of observations in the cluster, the size of each varies in width and height. Taking cluster 6 (C6) as an example, its width is thin due to the low number of customers it has, and the height of each cell belonging to it depends on the percentage that each category represents in relation to the other categories in the same cluster; if a category has 99% of customers, it will occupy 100% of the cell, as in cluster 6 (C6) in the graph on the right side. By analyzing Figure 10, it is possible to have the following interpretations:  
1. Regarding age (left graph), the cluster of recent customers (C1) has a lower-than-expected number (cells in blue) of adult and elderly customers and higher concentrations of young adults and customers with no information, indicating that there may be a flow of young people being attracted by the store. The cluster of lost customers (C2) has a higher-than-expected number of customers who did not inform their age, indicating a certain resistance to filling out registrations. The cluster of customers being lost (C5) has a higher-than-expected number of customers over 30 years old, indicating a possible dissatisfaction with the products offered to this age group, information that is corroborated by the fact that the flow of recent customers (C1) has more young people than expected. 2.