# BiModalClust: Fused Data and Neighborhood Variation for Advanced K-Means Big Data Clustering
## 5 Experimental Evaluation
### Main Experiment Results  
A total of 7366 experiments were conducted in our study.  
Our analysis revealed no strong correlation between the choice of neighborhood change procedure and the results obtained. However, the cyclic neighborhood change procedure demonstrated a slight advantage over the sequential approach, yielding marginally better final accuracy.  
Additionally, we investigated two distinct strategies for centroid shaking within the algorithm: a uniformly random approach and reinitialization based on the K-means++ method. While the uniformly random strategy offered faster execution, it significantly compromised final accuracy, with accuracy deteriorating by as much as fivefold compared to K-means++ reinitialization. This performance gap can be attributed to the uniformly random method introducing excessive perturbation to the incumbent solution. Such drastic changes require substantially more iterations during the local search phase to reach an optimal solution, thereby reducing overall efficiency.  
For each algorithm, dataset (\(X\)), and cluster count (\(k\)), the minimum, median, and maximum values of relative error (\(\epsilon\)) and CPU time (\(t\)) were computed over \(n_{exec}\) runs. To determine the optimal maximum shaking power (\(p_{\text{max}}\)), additional experiments were performed by restarting the algorithm with varying \(p_{\text{max}}\) values according to the line search parameter optimization strategy.  
Line search optimization demonstrated that increasing the intensity of shaking generally leads to improved accuracy, albeit with a slight increase in the maximum convergence time. The optimal value of \(p_{\text{max}}\), based on median relative accuracy, was found to be 4. These findings suggest that more vigorous shaking enhances the algorithm's ability to escape local minima by effectively \"jumping out\" of their valleys. However, as expected, the subsequent descent from these perturbed positions via local search requires additional computational time.  
The overall performance of BiModalClust with the best-performing configuration (\(p_{\text{max}}=4\)) is summarized in Table 3 and 4.  
In Table 3, it can be observed that BiModalClust achieves average relative error results that are more than 3.3 and 6.5 times better than those of Big-means and K-means++, respectively. This performance gain is attributed to the enhanced fluidity of centroids, achieved by fusing random sample data streaming with systematic neighborhood exploration.  
As can be seen in Table 4, while BiModalClust demonstrates slightly longer processing times than Big-means, its computational efficiency remains competitive, with average runtime results under 3.0 s, outperforming advanced parallel HPClust variants from [25; 26]. The baseline K-means++ algorithm falls far behind in efficiency due to its inability to process big datasets.  
The observed efficiency of BiModalClust, coupled with its significant accuracy improvements, positions BiModalClust as a powerful and practical tool for solving industry-level big data clustering problems.