KNN and K-means in Gini Prametric Spaces

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.