K$ Clustering

K-means clustering is a fundamental machine learning technique aiming to partition data points into k clusters, minimizing the within-cluster variance. Current research emphasizes developing faster and more robust algorithms, including those addressing fairness concerns (e.g., ensuring equitable representation across groups) and incorporating semi-supervised learning with pairwise constraints. These advancements improve scalability and accuracy, impacting diverse applications from data analysis and resource allocation to personalized medicine and anomaly detection. Furthermore, research explores theoretical guarantees for approximation algorithms and the development of quantum algorithms to accelerate computation.