Greedy Algorithms for Approximating the Diameter of Machine Learning Datasets in Multidimensional Euclidean Space

TL;DR

This paper introduces four greedy algorithms for approximating the diameter of high-dimensional datasets efficiently, overcoming the scalability issues of traditional methods, and demonstrates their effectiveness on machine learning datasets.

Contribution

The paper presents four scalable greedy algorithms for dataset diameter approximation, suitable for large, high-dimensional data in machine learning applications.

Findings

Algorithms scale near-linearly with data size and dimensions.

Experimental results confirm efficiency on various datasets.

Recommended for practical use in machine learning tasks.

Abstract

Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension, so the time complexity grows exponentially in most cases, which makes these algorithms impractical. Therefore, we implemented 4 simple greedy algorithms to be used for approximating the diameter of a multidimensional dataset; these are based on minimum/maximum l2 norms, hill climbing search, Tabu search and Beam search approaches, respectively. The time complexity of the implemented algorithms is near-linear, as they scale near-linearly with data size and its dimensions. The results of the experiments (conducted on different machine learning data sets) prove the efficiency of the implemented algorithms and can therefore be recommended for finding the diameter to be used by different machine learning applications when needed.