## 4 Results
### Clustering Parameter Selection and Result of Cluster  
Subsequently, selection of parameters for the clustering process was necessary. Using customer- and product-oriented RFMCEIP results, correlation analysis was conducted to determine the appropriate model. The objective was to identify variable relationships within the range of 0.2 to 0.8 and eliminate variables that exhibit the highest and lowest correlations to minimize the risk of multicollinearity. Table 4 presents the correlation matrix for the RFMCEIP customer-oriented group. It reveals strong positive correlations between \"frequency\" and \"monetary\" variables (0.89), indicating that customers who make more frequent purchases tend to spend higher amounts. The customer engagement index (CEI) refers to customer participation and interactions with the business. It consists of two main aspects: the time between one purchase and the next and the frequency of purchases. The correlation test results showed that the _CEI_ index exhibits strong negative correlations with the _frequency_ (\(-1.00\)) and _monetary_ (\(-0.88\)) variables. Such can be observed in cases where a customer was more active in the past than they are currently and has made almost no repurchases recently. Such purchasing behavior could be an indication that the customer needs to be more fully engaged and consistently active with the business. Conversely, a _CEI_ index greater than 0 indicates that this customer has been quite active recently and shows more proactive repurchasing behavior compared to the past. The analysis also shows several weak correlations. The \"_recency_\" variable has a weak positive correlation with the _CEI_ index (0.20), indicating a slight connection between recent interactions and higher customer involvement. Conversely, the correlation between _recency_ and _monetary_ is weaker (<0.2), suggesting a less robust relationship, while the _periodicity_ also shows weak correlations with other variables, suggesting limited relationships with _recency_, _frequency_, and _monetary_ variables and _CEI_ index. Thus, at least one variable from each combination was selected for the model, including the RFM, MCEIP, and FMP models. Table 5 presents the correlation matrix for the RFMCEIP (RFM with customer engagement index and periodicity) in a product-oriented context. Notably, recency variables were \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Customer** & **Recency** & **Frequency** & **Monetary** & **CEI** & **Periodicity** \\ \hline Recency & 1.00 & \(-0.22\) & \(-0.17\) & 0.20 & \(-0.30\) \\ Frequency & \(-0.22\) & 1.00 & 0.89 & \(-1.00\) & 0.01 \\ Monetary & \(-0.17\) & 0.89 & 1.00 & \(-0.88\) & 0.01 \\ CEI & 0.20 & \(-1.00\) & \(-0.88\) & 1.00 & \(-0.01\) \\ Periodicity & \(-0.30\) & 0.01 & 0.01 & \(-0.01\) & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation Matrix for RFMCEIP Customer-Oriented Group. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Description** & **Recency** & **Frequency** & **Monetary** & **CEI** & **Periodicity** \\  & **(Days)** & **(Times)** & **(USD)** & **CEI** & **(Days)** \\ \hline
15 cm Christmas Glass Ball 20 Lights & 76 & 437 & 3387.15 & 0.926 & 8.36 \\ Pink Cherry Lights & 76 & 230 & 1478.00 & 0.926 & 12.53 \\ White Cherry Lights & 76 & 216 & 1378.70 & 0.928 & 1.62 \\ Record Frame 7” Single Size & 76 & 323 & 792.95 & 0.942 & 3.02 \\ Strawberry Ceramic Trinket Box & 76 & 1859 & 2297.12 & 0.608 & 0.92 \\... &... &... &... &... &... \\ Gin and Tonic Diet Metal Sign & 76 & 37 & 92.94 & 0.991 & 0.45 \\ Set of 6 Ribbons Party & 76 & 13 & 37.17 & 0.997 & 0.96 \\ Silver and Black Orbit Necklace & 76 & 1 & 2.95 & 1.000 & 0.00 \\ Cream Hanging Heart T-light Holder & 76 & 7 & 20.25 & 0.998 & 0.32 \\ Paper Craft, Little Birdie & 76 & 1 & 2.08 & 1.000 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RFMCEIP Product-Oriented Value Result. not included due to constant recency values for all products. Several interesting correlations were found.