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

arXiv: https://arxiv.org/abs/2112.12549 · HTML: https://mlsanity.com/paper/2112.12549/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 17 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Built on by (most cited first, 9 of 9)

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- [Distance Functions and Normalization Under Stream Scenarios](https://mlsanity.com/paper/2307.00106/) (2023)
- [X-Ray cardiac angiographic vessel segmentation based on pixel classification using machine learning and region growing](https://mlsanity.com/paper/2605.20073/) (2026)
- [Local-sensitive connectivity filter (ls-cf): A post-processing unsupervised improvement of the frangi, hessian and vesselness filters for multimodal vessel segmentation](https://mlsanity.com/paper/2605.21251/) (2026)
- [Machine learning applied to emerald gemstone grading: framework proposal and creation of a public dataset](https://mlsanity.com/paper/2605.23777/) (2026)
- [Mathematical Morphology in Machine Learning](https://mlsanity.com/paper/2605.30700/) (2026)

## Abstract (arXiv)

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).