Optimizing the Mean Shift Algorithm for Efficient Clustering

Mean Shift is a flexible, non-parametric clustering algorithm that identifies dense regions in data through gradient ascent on a kernel density estimate. Its ability to detect arbitrarily shaped clusters without requiring prior knowledge of the number of clusters makes it widely applicable across diverse domains. However, its quadratic computational complexity restricts its use on large or high-dimensional datasets. Numerous acceleration techniques, collectively referred to as Fast Mean Shift strategies, have been developed to address this limitation while preserving clustering quality. This paper presents a systematic theoretical analysis of these strategies, focusing on their computational impact, pairwise combinability, and mapping onto distinct stages of the Mean Shift pipeline. Acceleration methods are categorized into seed reduction, neighborhood search acceleration, adaptive bandwidth selection, kernel approximation, and parallelization, with their algorithmic roles examined in detail. A pairwise compatibility matrix is proposed to characterize synergistic and conflicting interactions among strategies. Building on this analysis, we introduce a decision framework for selecting suitable acceleration strategies based on dataset characteristics and computational constraints. This framework, together with the taxonomy, combinability analysis, and scenario-based recommendations, establishes a rigorous foundation for understanding and systematically applying Fast Mean Shift methods.