Optimizing Euclidean Distance Computation

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, bei...

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Published in:	Mathematics (Basel) Vol. 12; no. 23; p. 3787
Main Author:	Mussabayev, Rustam
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.12.2024
Subjects:	Algorithms Bioinformatics Clustering Comparative analysis Computational linguistics computational optimization Data analysis Data mining Data structures Datasets Efficiency Energy conservation Energy consumption Euclidean distance Euclidean geometry Euclidean space Geospatial data Germany Information management K-means clustering K-nearest neighbors (KNNs) Language processing Linear algebra Machine learning Mathematical optimization Methods Natural language interfaces Optimization parallelization Spatial data Task complexity vectorization Germany
ISSN:	2227-7390, 2227-7390
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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.
AbstractList	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.
Audience	Academic
Author	Mussabayev, Rustam
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SubjectTerms	Algorithms Bioinformatics Clustering Comparative analysis Computational linguistics computational optimization Data analysis Data mining Data structures Datasets Efficiency Energy conservation Energy consumption Euclidean distance Euclidean geometry Euclidean space Geospatial data Germany Information management K-means clustering K-nearest neighbors (KNNs) Language processing Linear algebra Machine learning Mathematical optimization Methods Natural language interfaces Optimization parallelization Spatial data Task complexity vectorization
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Title	Optimizing Euclidean Distance Computation
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