# KNN and K-means in Gini Prametric Spaces

arXiv: https://arxiv.org/abs/2501.18028 · HTML: https://mlsanity.com/paper/2501.18028/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 29 Jan 2025.

## Builds on (most cited first, 6 of 6)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Distance and Similarity Measures Effect on the Performance of K-Nearest Neighbor Classifier -- A Review](https://mlsanity.com/paper/1708.04321/) (2017)
- [A Scalable Algorithm for Individually Fair K-means Clustering](https://mlsanity.com/paper/2402.06730/) (2024)
- [Dimensionality Invariant Similarity Measure](https://mlsanity.com/paper/1409.0923/) (2014)
- [Principal Component Analysis: A Generalized Gini Approach](https://mlsanity.com/paper/1910.10133/) (2019)
- [Gini Covariance Matrix and its Affine Equivariant Version](https://mlsanity.com/paper/1610.07925/) (2016)

## Built on by (most cited first, 2 of 2)

- [Scalable anomaly detection via a univariate Christoffel function](https://mlsanity.com/paper/2606.12483/) (2026)
- [Optimizing Multidimensional Scaling in Gini Metric Spaces](https://mlsanity.com/paper/2605.25124/) (2026)

## Abstract (arXiv)

This paper introduces enhancements to the K-means and K-nearest neighbors (KNN) algorithms based on the concept of Gini prametric spaces, instead of traditional metric spaces. Unlike standard distance metrics, Gini prametrics incorporate both value-based and rank-based measures, offering robustness to noise and outliers. The main contributions include: (1) a Gini prametric that captures rank information alongside value distances; (2) a Gini K-means algorithm that is provably convergent and resilient to noisy data; and (3) a Gini KNN method that performs competitively with state-of-the-art approaches like Hassanat's distance in noisy environments. Experimental evaluations on 16 UCI datasets demonstrate the superior performance and efficiency of the Gini-based algorithms in clustering and classification tasks. This work opens new directions for rank-based prametrics in machine learning and statistical analysis.