Cluster Optimization for Exponential, Right-Triangular, and Uniformly Distributed Data

Cluster analysis aims to categorize data objects into cohesive groups based on their intrinsic characteristics, often modeled by probability distributions. This paper presents a novel Mathematical Programming-Dynamic Programming (MP-DP) clustering method developed by the authors, applied to datasets characterized by exponential, right-triangular, and uniform distributions. The MP-DP technique optimizes cluster partitions by leveraging the probability distributions inherent in the data. We conducted a comparative evaluation to assess the performance of MP-DP against four established clustering methodologies: K-Means, Fuzzy C-Means, expectation-maximization, and Genie++ hierarchical clustering. Results from extensive simulations and real-world datasets consistently demonstrate the superior efficacy of MP-DP in achieving optimal clustering outcomes. Specifically, MP-DP excels in handling diverse data distributions and effectively mitigating the effects of noise and uncertainty, thereby enhancing clustering accuracy and reliability. This study highlights the significant advancement offered by MP-DP in clustering research. It underscores the method’s potential for applications across various domains, such as healthcare, environmental monitoring, and manufacturing, where robust and efficient data clustering is essential for insightful data analysis and decision-making.