# BiModalClust: Fused Data and Neighborhood Variation for Advanced K-Means Big Data Clustering
## 1 Introduction
Furthermore, integrating the Variable Neighborhood Search (VNS) metaheuristic [4] facilitates an in-depth exploration of each consecutive solution landscape. This enables the algorithm to address local challenges such as degenerate clusters and the fragmentation of a single true cluster into multiple centroids. A key limitation of existing initialization-sensitive iterative methods, such as Forgy K-means and K-means++, is their inability to effectively handle scenarios where multiple initial centroids are positioned within a single well-separated cluster. This issue arises because centroids struggle to traverse the empty margins separating clusters, especially in sparsified datasets obtained through random sampling. In such cases, the centroids remain trapped, failing to converge toward an optimal solution. Section 5.3 empirically demonstrates this phenomenon and its adverse effects on clustering accuracy. By leveraging its bimodal optimization strategy, BiModalClust addresses these challenges, providing a robust and scalable solution for K-means clustering in big data contexts. The algorithm processes the input data in a streaming fashion. During each iteration, a random sample \(S\) is drawn from the dataset \(X\). The degenerate clusters and \(p\) randomly selected centroids from the current solution \(C\) are reinitialized using the K-means++ algorithm on the sample \(S\). This reinitialization step acts as a \"shaking\" mechanism to perturb the incumbent solution and explore alternative configurations. The variable \(p\), referred to as the shaking power, is cyclically incremented across iterations, with its upper bound defined by the hyperparameter \(p_{max}\). Following this step, a local search phase using the K-means algorithm is conducted on \(S\), starting from the perturbed incumbent solution to identify potentially improved solutions within the current neighborhood. The iterative process continues until a predefined time limit \(T\) is reached. Overall, this study examines the synergy between big data clustering and advanced optimization metaheuristics, particularly focusing on hybridization to enhance clustering performance. We propose a novel clustering heuristic named BiModalClust, designed to extend the global optimization capabilities of traditional clustering methods by fusing data streaming with global optimization approaches. By embedding the Variable Neighborhood Search (VNS) framework [4], a powerful metaheuristic approach, BiModalClust achieves a refined clustering methodology. Comprehensive experimental analyses conducted on a wide array of real-world datasets reveal that BiModalClust outperforms existing methods, establishing itself as the new state-of-the-art within the MSSC clustering algorithm family. Remarkably, it surpasses the current state of the art, Big-means [2], showcasing its robustness and innovative advancements in big data clustering. The structure of this paper is as follows. Section 2 reviews related work, including existing clustering methods. Section 3 introduces the foundational concepts of the VNS metaheuristic. Section 4 presents a detailed pseudocode of BiModalClust, elaborates on its core properties, and provides an analysis of its time complexity. Section 5 outlines the experimental setup and describes the conducted experiments. Finally, Section 6 discusses the experimental results, concluding the paper with final reflections and insights.