## Electronic Journal of Statistics

### A notion of stability for k-means clustering

#### Abstract

In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the field of quantization of a probability measure. We connect this definition of stability to a geometric feature of the underlying distribution of the data, named absolute margin condition, inspired by recent works on the subject.

#### Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 4239-4263.

Dates
First available in Project Euclid: 15 December 2018

https://projecteuclid.org/euclid.ejs/1544842901

Digital Object Identifier
doi:10.1214/18-EJS1500

Mathematical Reviews number (MathSciNet)
MR3892141

Zentralblatt MATH identifier
07003242

Keywords
Clustering k-means stability

#### Citation

Le Gouic, T.; Paris, Q. A notion of stability for k-means clustering. Electron. J. Statist. 12 (2018), no. 2, 4239--4263. doi:10.1214/18-EJS1500. https://projecteuclid.org/euclid.ejs/1544842901

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