## 4 Results
### Cluster Analysis  
Based on the regression analysis, we further conducted a clustering analysis of the significant variables to identify representative group interaction patterns. These patterns, with their concentrated trends in specific interaction features, provide key insights into the causes of coordination difficulties across different scenarios. In this study, we used the K-means clustering method. To determine the optimal number of clusters, we experimented with configurations ranging from 2 to 10 clusters and evaluated them using the elbow method and silhouette coefficient. Ultimately, we selected five clusters as the optimal solution. Figure 6 provides a detailed view of the distribution of each feature across the different categories. \begin{table}
\begin{tabular}{c l c c c c c} \hline \hline
**Dimensions** & **Features** & **coef (\(\beta\))** & **std err** & z & \(p\)-Value** & **VIF** \\ \hline IS & Neg Log Speaking Interval & 0.2710 * & 0.110 & 2.470 & 0.014 & 1.076 \\ \hline SR & Group Area & \(-\)0.0852 & 0.108 & \(-\)0.790 & 0.429 & 1.020 \\ \hline IP & Speaking Duration Ratio & \(-\)0.9142 ** & 0.160 & \(-\)5.721 & 0.000 & 2.250 \\  & Utterance Count & \(-\)0.5211 ** & 0.191 & \(-\)2.733 & 0.006 & 2.992 \\  & Speaking Intention Count & \(-\)0.5344 ** & 0.117 & \(-\)4.577 & 0.000 & 1.095 \\ \hline CQ & Max Speaker Duration Ratio & 0.3258 & 0.167 & 1.948 & 0.051 & 2.078 \\  & Speaking Overlap Ratio & 0.3875 ** & 0.148 & 2.614 & 0.009 & 1.711 \\ \hline  & Constant & 0.4707 ** & 0.108 & 4.364 & 0.000 & 1.000 \\ \hline \hline \end{tabular}  
* \(p<0.05\), *
* \(p<0.01\)_. **IS**: Individual Status, **SR**: Spatial Relationships, **IP**: Interaction Proactivity, **CQ**: Communication Quality.  
\end{table} 
Table 3: Results of the logistic regression analysis and variance inflation factor (VIF). Based on the feature distribution across clusters, we summarized the main characteristics of each cluster:  
* **C1--Prolonged Single-turn Scenario**: This cluster is characterized by the highest proportion of speaking duration but a low number of speaking turns and almost no speech overlap. Participants wishing to speak hold a relatively low status in the current interaction. This suggests that the interactions in this cluster are primarily dominated by long monologues from a few participants, with limited group interaction, leaning toward a unidirectional information-sharing pattern. * **C2--High-status Role Scenario**: This cluster exhibits moderate levels of speaking duration and speaking turns, with a low proportion of speech overlap. A notable feature is that participants wishing to speak have a relatively high status. This reflects interactions where participants expressing speaking intentions are closely tied to the ongoing exchange and hold a relatively dominant role. * **C3--Intense Interaction Scenario**: This cluster features the highest rate of speech overlap and speaking turns, with a speaking duration proportion close to the highest. Participants wishing to speak have high status, and the speaking intentions of other participants are also strong. This type of interaction demonstrates a highly intense interactive state, where group members frequently speak, indicating high engagement and interaction density. * **C4--Low-activity Scenario**: This cluster is characterized by long periods without speech activity, with participants speaking infrequently, resulting in an overall silent state. This indicates a \"cold\" interaction phase where group members exhibit low willingness to participate, lacking active speaking and engagement. * **C5--High-competition Scenario**: This cluster shows the highest number of speaking intentions, moderate levels of speaking duration and speaking turns, and a low proportion of speech overlap. Such interactions likely occur when a topic of broad interest prompts participants to express speaking intentions collectively, resulting in turn-taking competition and reflecting a high level of interaction demand.