Optimizing Euclidean Distance Computation

Rustam Mussabayev ()
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Rustam Mussabayev: Laboratory for Analysis and Modeling of Information Processes, Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan

Mathematics, 2024, vol. 12, issue 23, 1-36

Abstract: This paper presents a comparative analysis of seventeen different approaches to optimizing Euclidean distance computations, which is a core mathematical operation that plays a critical role in a wide range of algorithms, particularly in machine learning and data analysis. The Euclidean distance, being a computational bottleneck in large-scale optimization problems, requires efficient computation techniques to improve the performance of various distance-dependent algorithms. To address this, several optimization strategies can be employed to accelerate distance computations. From spatial data structures and approximate nearest neighbor algorithms to dimensionality reduction, vectorization, and parallel computing, various approaches exist to accelerate Euclidean distance computation in different contexts. Such approaches are particularly important for speeding up key machine learning algorithms like K-means and K-nearest neighbors (KNNs). By understanding the trade-offs and assessing the effectiveness, complexity, and scalability of various optimization techniques, our findings help practitioners choose the most appropriate methods for improving Euclidean distance computations in specific contexts. These optimizations enable scalable and efficient processing for modern data-driven tasks, directly leading to reduced energy consumption and a minimized environmental impact.

Keywords: Euclidean distance; computational optimization; K-means clustering; K-nearest neighbors (KNNs); vectorization; parallelization; triangle inequality; spatial data structures; block vector approximations; approximate methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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