Min-Max-Jump distance and its applications

TL;DR

This paper introduces Min-Max-Jump distance (MMJ) and demonstrates its effectiveness across clustering, evaluation, and prediction tasks, with new algorithms for distance computation.

Contribution

It proposes the MMJ distance and integrates it into K-means, Silhouette coefficient, and label prediction, offering novel applications and algorithms.

Findings

MMJ-based K-means improves clustering quality.

MMJ-based Silhouette coefficient enhances cluster evaluation.

MMJ distance achieves good performance in label prediction.

Abstract

We explore three applications of Min-Max-Jump distance (MMJ distance). MMJ-based K-means revises K-means with MMJ distance. MMJ-based Silhouette coefficient revises Silhouette coefficient with MMJ distance. We also tested the Clustering with Neural Network and Index (CNNI) model with MMJ-based Silhouette coefficient. In the last application, we tested using Min-Max-Jump distance for predicting labels of new points, after a clustering analysis of data. Result shows Min-Max-Jump distance achieves good performances in all the three proposed applications. In addition, we devise several algorithms for calculating or estimating the distance.