On The Sharp Threshold Interval Length of Partially Connected Random Geometric Graphs During K-Means Classification

TL;DR

This paper analyzes the sharp threshold interval length in partially connected random geometric graphs during K-means classification, estimating the number of classes formed based on data point distribution and connection thresholds.

Contribution

It introduces a probabilistic framework to determine the threshold interval length affecting cluster formation in random geometric graphs during K-means.

Findings

Derived estimates for the mean number of classes formed

Identified conditions for high-probability cluster formation

Analyzed the impact of connection thresholds on clustering outcomes

Abstract

In $K$-means classification, a set of data will form clusters, i.e. classes, if the measured distances between data points (or some common point in each class) are below a certain threshold. With the assumption that the data points are randomly generated throughout some bounded region according to a certain probability distribution, we estimate the mean number of classes to form with high probability.