Optimizing Euclidean Distance Computation
Mussabayev R.
December 2024Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2024#12Issue 23
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.
approximate methods , block vector approximations , computational optimization , Euclidean distance , K-means clustering , K-nearest neighbors (KNNs) , parallelization , spatial data structures , triangle inequality , vectorization
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Laboratory for Analysis and Modeling of Information Processes, Institute of Information and Computational Technologies, Almaty, 050010, Kazakhstan
AI Research Lab, Satbayev University, Almaty, 050013, Kazakhstan
Laboratory for Analysis and Modeling of Information Processes
AI Research Lab
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