# Determining the Quality of a Dataset in Clustering Terms
## 3 Results  
### Results for Retail Customers  
AutoEmbedder did not generate any errors when coding the set. After using AutoEmbedder, the set contained 96 columns. Subsequently, after the application of the PCA, the number of columns decreased to 8. Similarities between customers were determined using the cosine similarity. The distribution of rescaled similarities is included in Figure 3.  
For a cut-off parameter of 0.75 by [PERSON]'s method, three groups were obtained. There were 565 customers in group 0, 929 customers in group number 1 and 746 customers in group number 2. The greedy modularity and label propagation methods divided the set of customers into two groups. There were 1285 customers in group 0 and 955 customers in group 1 for the greedy modularity and label propagation methods. The resulting divisions using the two methods were similar. The value of the Fowlkes-Mallows index comparing the two divisions was about 0.98, while the NMI parameter was about 0.94. After changing the cut-off parameter to 0.5, [PERSON]'s method also returned three communities, but the resulting groups were no longer as evenly distributed as with a cut-off parameter of 0.75. Using the greedy modularity method, two groups were obtained. The first group included 1200 customers, while the second group included 1040 customers. The label propagation method detected only one community in the graph consisting of all customers. With a cut-off parameter of 0.25, [PERSON]'s method divided the set of customers into two groups. There were 1048 customers in group number 0 and 1192 customers in group 1. Two groups were also formed using the greedy modularity method. There were 1131 customers in group 0 and 1109 customers in group number 1. The label propagation method gathered all customers into one community. For the graph methods, we compared the divisions using the modularity parameter. The highest value of the modularity parameter was characterized by the division obtained by [PERSON]'s method (0.566) with a cut-off parameter of 0.75. Using the DBSCAN method, we obtained three groups. There were 950 customers in group number 0, 831 customers in group 1 and 16 customers in group 2. Overall, 443 customers were not classified. We compared the graph methods and the DBSCAN method with ordinary clustering methods (\(k\)-means method). The \(k\)-means method divided customers into two groups. Figure 3: Histogram of scaled cosine similarity for the dataset of individual customers. Using the Calinski-Harabasz and Davies-Bouldin indices, we compared the quality of the obtained clusters in each method. The best values for the Calinski-Harabasz and Davies-Bouldin indices were obtained for the greedy modularity method with a cut-off parameter of 0.5. For the \(k\)-means method, we obtained similar index values. Using the NMI and Fowlkes-Mallows parameters, the similarity degree of the clusters obtained by the different methods was tested. The divisions obtained by different methods varied. The full results of the NMI and Fowlkes-Mallows indices are presented in Tables 2 and 3, respectively. The Calinski-Harabasz and Davies-Bouldin index values for various methods and various cut-off parameters are presented in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cut-Off Parameter** & **Method** & **CH Index** & **DB Index** \\ \hline
**0.25** & **Louvain** & **801.783** & **1.626** \\
0.25 & Greedy & 796.954 & 1.640 \\
0.25 & Label & - & - \\
0.5 & Louvain & 415.123 & 2.358 \\
0.5 & Greedy & 782.355 & 1.644 \\
0.5 & Label & - & - \\ - & DBSCAN & 314.034 & 2.484 \\ - & \(k\)-means & 249.258 & 2.873 \\
0.75 & Louvain & 542.745 & 2.080 \\
0.75 & Greedy & 773.752 & 1.624 \\
0.75 & Label & 781.243 & 1.625 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The Calinski–Harabasz (CH) and Davies–Bouldin (DB) index values for the different methods and different cut-off parameters (retail customers).