# Is Marina Meila's work “The Uniqueness of a Good Optimum for K-Means” a general result applicable to other clustering algorithms as well?

In this paper, a bound on the “error subspace” projection is established, which is then used to show that any two clusterings with small distortion are close. Which immediately follows that, if a good clustering, $C$, is discovered for a given dataset (say manually, or by whatever ssuitable means), then another clustering, $C_1$, is going to be close to the optimal clustering if it minimizes the distortion between the two clusterings.

The paper was presented as optimality for k-means. But I could not find any specific detail that stops it from being applicable to general clustering algorithms. That's why I want to confirm here by asking whether this method of determining existence of an optimal algorithmic clustering applicable to other algorithms beyond k-means.

Meilă, Marina. "The uniqueness of a good optimum for k-means." In Proceedings of the 23rd international conference on Machine learning, pp. 625-632. ACM, 2006.

• Please give a complete reference (the title is a good start, but a little more information would be helpful). If for some reason the site you linked to goes down for a period of time the paper should still be easy to find. – Glen_b Jun 30 '17 at 9:56
• The answer is yes. Look at her new paper papers.nips.cc/paper/… Maybe she read your question :) – Amir Jan 9 at 18:09