## 4 Client Segmentation by Clustering  
For the segmentation of the customers, it was considered that the data obtained are described by numerical variables (for example, age) and categorical variables (for example, sex), and that they also have missing information (not all clients answered all the questions). Due to these elements, three clustering algorithms were applied, which are designed for handling mixed and incomplete data, such as those obtained from clients. The number of algorithms for mixed and incomplete data clustering is much smaller than their counterparts for numeric data. Among mixed and incomplete data clustering, there are a few with good behavior in practice, by finding a small number of clusters (less than 20). Previous research [49; 50] state that KMSF is very good for clustering, followed by k-Prototypes and AGKA. 1. The k-Prototypes algorithm [51]. Parameters: Number of clusters: \(k\). 2. The k-means with similarity functions (KMSF) algorithm [52]. Parameters: Number of clusters: \(k\), Similarity function: \(1/\)HEOM. 3. The genetic k-means clustering algorithm (AGKA) algorithm [53]. Parameters: Number of clusters: \(k\), Population number \(np=25\), crossover probability \(cp=1.0\), mutation probability \(mp=0.05\), number of iterations: \(it=100\). In the specialized literature, a large number of algorithms can be found to perform the clustering task. However, the vast majority of these algorithms only support patterns with numeric values in their features. In our research, the use of clustering algorithms is required to carry out customer segmentation. However, the patterns that describe the tourist clients in our dataset have a uniqueness the data obtained from the questionnaire are described by numerical variables (for example, age) and categorical variables (for exam-ple, sex), and that they also have missing information (not all clients answered all the questions). By considering these severe data constraints, the availability of clustering algorithms is dramatically reduced. There are VERY SCARCE clustering algorithms that support incomplete patterns with mixed traits, like the ones we discussed in our research. For these reasons, these three clustering algorithms were selected, which are one of the few that are designed for handling mixed and incomplete data, such as those obtained from clients. The advantages of adopting these three algorithms are clear: they allow handling mixed and incomplete data, such as those obtained from clients: this has a positive effect on the results, as shown in the tables and in the discussion section. For the application of these algorithms, the EEUC (Experimenter Environment for Unsupervised Classification) software was used, which allows the application and evaluation of data grouping algorithms [54]. The use of the EEUC software platform in our research is very relevant. The advantages of using EEUC are clear: this software platform is efficient, friendly, and allows the application and evaluation of data grouping algorithms, among which are the three algorithms selected for the segmentation of tourist clients. Consequently, the segmentation results are reliable and efficiently obtained. The number of groups to be obtained was defined from two to 10 groups. Subsequently, the groups obtained were evaluated to determine their quality. For this, the Dunn index was used, which is widely recommended to assess the quality of the clusters [55]. Clustering is a task of the unsupervised learning paradigm. The measures to measure the quality of the clusters thrown by the clustering algorithms fall broadly into three classes: internal validation is based on calculating properties of the resulting clusters; relative validation is based on comparisons of partitions generated by the same algorithm with different parameters or different subsets of the data; and external validation compares the partition generated by the clustering algorithm and a given partition of the data.