# BiModalClust: Fused Data and Neighborhood Variation for Advanced K-Means Big Data Clustering
## 2 Related Work  
To address the high non-convexity challenge of MSSC, a variety of optimization strategies have been developed, each with unique strengths and limitations:  
* Gradient-based methods excel in quickly locating local minimizers, but their reliance on smooth gradients often leads to entrapment in suboptimal solutions due to the non-convexity of the objective function [5].
* Stochastic optimization algorithms leverage randomness to escape local minima, enabling broader exploration of the solution space and increasing the likelihood of discovering global optima [6,7].
* Heuristic and metaheuristic search strategies strike a balance between exploration and exploitation, systematically refining solutions while avoiding premature convergence [2,3,8].
* Hybrid approaches, which integrate elements of gradient-based methods, stochastic algorithms, and metaheuristics, harness the complementary strengths of these techniques [9]. By synergizing their capabilities, hybrid methods often uncover superior solutions that standalone strategies might overlook.  
These diverse methodologies highlight the intricate interplay of exploration and exploitation in MSSC, underscoring the need for innovative approaches to achieve effective and scalable clustering in big data environments.  
The existing clustering algorithms for the MSSC problem can also be divided into two broad categories: traditional and alternative approaches.  
Traditional algorithms are well-known for their simplicity and effectiveness and have been the subject of extensive research. Among these, the K-means algorithm stands out as the most widely used for solving the MSSC problem (1), along with its numerous extensions, such as Forgy [10], K-means++ [11], and multi-start K-means [12]. Another notable traditional method is [PERSON]'s method [13], which delivers solution quality comparable to more advanced heuristics. However, a significant drawback of [PERSON]'s method is its reliance on computing a squared distance matrix, making it impractical for large datasets due to its high computational demands.  
On the other hand, alternative algorithms have been developed to overcome the limitations of traditional approaches, primarily focusing on enhancing solution quality and computational performance for the MSSC problem. Prominent examples of advanced alternative algorithms include MDEClust [9], HG-means [3], LMBM-Clust [5], I-k-means-+ [14], BWKM [15], BDCSM [16], and Coresets [17]. These methods are often characterized by their complexity and hybrid nature, incorporating meta-heuristic principles or combining simpler algorithms to enhance performance. Despite achieving the quality of a state-of-the-art solution, these alternative algorithms frequently fall short in terms of computational efficiency. In many cases, their runtime exceeds that of K-means by several orders of magnitude, making them less suitable for applications requiring rapid processing of large datasets.  
Despite the significant advancements, the existing clustering methods face two fundamental challenges. First, they struggle to process big data effectively, as most algorithms require at least one complete pass through the entire dataset, which becomes infeasible when the dataset size approaches infinity. Second, they fail to ensure a thorough exploration of the intricate solution landscape, often falling into local optima traps and thereby compromising the global optimization convergence.  
To address these critical issues, we propose the BiModalClust algorithm, an innovative integral clustering approach that achieves a significant leap in performance. By fusing optimization along the input data stream and the solution landscape structure modalities, our algorithm introduces qualitatively new global convergence properties while having the capacity to process big data. This dual-modal strategy not only resolves the limitations of traditional and alternative methods but also sets a new standard for robust and scalable clustering solutions.