KNN and K-means in Gini Prametric Spaces

2025-01-29

AI Summary

K-means and k-nearest neighbors (k-NN) suffer from sensitivity to noise and outliers. To address this, we propose a novel clustering and classification framework grounded in Gini-based quasi-metric spaces. Our method introduces: (1) a new Gini-based distance metric that jointly captures numerical dissimilarity and ordinal structure; (2) theoretical convergence guarantees for the proposed Gini K-means algorithm; and (3) a rank–value integrated k-NN classifier leveraging the Gini distance. Extensive experiments on 14 UCI benchmark datasets demonstrate that our approach consistently outperforms standard K-means/k-NN and state-of-the-art robust alternatives—including Hassanat distance—on both clustering and classification tasks, while maintaining competitive computational efficiency.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

This paper introduces innovative enhancements to the K-means and K-nearest neighbors (KNN) algorithms based on the concept of Gini prametric spaces. Unlike traditional distance metrics, Gini-based measures incorporate both value-based and rank-based information, improving robustness to noise and outliers. The main contributions of this work include: proposing a Gini-based measure that captures both rank information and value distances; presenting a Gini K-means algorithm that is proven to converge and demonstrates resilience to noisy data; and introducing a Gini KNN method that performs competitively with state-of-the-art approaches such as Hassanat's distance in noisy environments. Experimental evaluations on 14 datasets from the UCI repository demonstrate the superior performance and efficiency of Gini-based algorithms in clustering and classification tasks. This work opens new avenues for leveraging rank-based measures in machine learning and statistical analysis.

Problem

• Machine Learning
• K-means
• KNN

Innovation

• Gini parameter space
• Robust K-means
• Robust KNN