Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier

TL;DR

This paper introduces a new distance metric combining Minkowski and Chebyshev distances, demonstrating improved computational efficiency and competitive accuracy with k-NN across multiple datasets.

Contribution

The paper proposes a novel intermediary distance metric that enhances speed and accuracy in k-NN classification, supported by extensive empirical evaluation.

Findings

Proposed distance is 1.3 times faster than Manhattan distance.

Achieves 329.5 times faster neighborhood iteration than Euclidean distance.

Outperforms average accuracy in 26 of 33 datasets.

Abstract

This work proposes a distance that combines Minkowski and Chebyshev distances and can be seen as an intermediary distance. This combination not only achieves efficient run times in neighbourhood iteration tasks in Z^2, but also obtains good accuracies when coupled with the k-Nearest Neighbours (k-NN) classifier. The proposed distance is approximately 1.3 times faster than Manhattan distance and 329.5 times faster than Euclidean distance in discrete neighbourhood iterations. An accuracy analysis of the k-NN classifier using a total of 33 datasets from the UCI repository, 15 distances and values assigned to k that vary from 1 to 200 is presented. In this experiment, the proposed distance obtained accuracies that were better than the average more often than its counterparts (in 26 cases out of 33), and also obtained the best accuracy more frequently (in 9 out of 33 cases).