A Note On k-Means Probabilistic Poverty

TL;DR

This paper demonstrates through examples that the commonly used random initialization in k-means clustering does not guarantee probabilistic k-richness, challenging assumptions about its theoretical properties.

Contribution

It provides a proof and example showing that the standard k-means algorithm with random start lacks the probabilistic k-richness property.

Findings

Standard k-means with random initialization does not have probabilistic k-richness.

The paper offers a specific example illustrating this limitation.

Abstract

It is proven, by example, that the version of $k$-means with random initialization does not have the property probabilistic k-richness.