# Determining the Quality of a Dataset in Clustering Terms
## 3 Results
### Results for Resellers  
The clustering algorithms on a data set of resellers were tested using AutoEmbedder. AutoEmbedder did not generate any errors when coding the set. After using AutoEmbedder, the set consisted of 132 columns. Then, the number of columns was reduced to 43 following the application of the PCA. The similarities between customers were determined using cosine similarity. The distribution of rescaled similarities is included in Figure 4.  
The first cut-off point tested was 0.75. For this value, the obtained graph was inconsistent, and therefore no clustering was performed on it (the number of groups would be more than 400, with all observations being 701). For a cut-off parameter of 0.5, [PERSON]'s method returned three groups. There were 151 resellers in group 0, 215 resellers in group 1 and 335 resellers in group 2. Using the greedy modularity method, we obtained two groups with the following numbers: group 0--351 resellers, group 1--350 resellers. The label propagation method also detected two communities in the graph; 350 customers were \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Cut-Off** & \multirow{2}{*}{**Group 0**} & \multirow{2}{*}{**Group 1**} & \multirow{2}{*}{**Group 2**} & **Total** \\  & **Parameter** & & & & **Number of** \\  & & & & & **Groups** \\ \hline Louvain & 0.75 & 565 & 929 & 746 & 3 \\ Greedy & 0.75 & 1285 & 955 & - & 2 \\ Label & 0.75 & 1285 & 955 & - & 2 \\ Louvain & 0.5 & 40 & 1185 & 1015 & 3 \\ Greedy & 0.5 & 1200 & 1040 & - & 2 \\ Label & 0.5 & 2240 & - & - & 1 \\ Louvain & 0.25 & 1048 & 1192 & - & 2 \\ Greedy & 0.25 & 1131 & 1109 & - & 2 \\ Label & 0.25 & 2240 & - & - & 1 \\ \(k\)-means & - & 1039 & 1201 & - & 2 \\ DBSCAN & - & 950 & 831 & 16 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Total number of groups and group sizes for each method (retail customers). \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Cut-Off Parameter**} & **Method** & **Modularity** \\ \hline
**0.75** & **Louvain** & **0.566** \\
0.75 & Greedy & 0.463 \\
0.75 & Label & 0.409 \\
0.5 & Louvain & 0.309 \\
0.5 & Greedy & 0.309 \\
0.25 & Louvain & 0.205 \\
0.25 & Greedy & 0.202 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Modularity values for different graph methods and different cut-off parameters (retail customers). clustered in group 0 and 351 customers in group 1. According to the Fowlkes-Mallows index value, it could be deduced that the clustering obtained by the greedy modularity and label propagation methods were identical, and the Louvain community clustering was similar to them (the index was 0.83). The NMI values confirmed that the greedy modularity and label propagation methods gave the same clusters. According to the NMI parameter, the similarity between the two clusterings and that obtained from the Louvain community method was slightly lower compared to those seen with the Fowlkes-Mallows parameter but still quite significant. For the greedy modularity and label propagation methods, we obtained a slightly higher value for the modularity parameter than for the Louvain method (around 0.3). Subsequently, a test was conducted for a cut-off point of 0.25. With a cut-off parameter of 0.25, [PERSON]'s method divided the set of customers into two groups. There were 356 resellers in group 0 and 345 resellers in group 1. Two groups were likewise created using the greedy modularity method. There were 382 resellers in group 0 and 319 resellers in group number 1. The label propagation method yielded a single group bringing together all resellers. According to the Fowlkes-Mallows parameter, the groups obtained by the label propagation method were roughly similar to the groups from the other graph methods (the index value was around 0.71). The least similar groups were those obtained by the Louvain community and greedy modularity methods (value around 0.5). According to the NMI parameter, the clustering had no similarities at all.