A notion of stability for k-means clustering
arXiv:1801.09419v2
Originality Synthesis-oriented
AI Analysis
This work addresses theoretical stability issues in clustering for researchers, but appears incremental as it builds on existing concepts without demonstrating broad impact.
The paper tackles the problem of defining a stability notion for k-means clustering by linking it to quantization and a geometric condition called absolute margin, but does not report specific results or numbers.
In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the notion of quantization of a probability measure. We connect this notion of stability to a geometric feature of the underlying distribution of the data, named absolute margin condition, inspired by recent works on the subject.