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everyone. I am puzzled, when without having truth labels, is there exist an absolute measure for clustering, like correctness for classification, to evaluate the quality of a clustering result? That is, when I have a clustering result, how to evaluate its quality without other results to compare?

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There are many such quality criterions.

Pretty much every algorithm has its own. For example k-means minimizes the SSQ for the given k (if you do not constrain k, the optimum is 0, every point its own cluster).

However, does an absolute criterion make sense?

I doubt so. You never can blindly rely on a clustering result. There is too much that can go wrong, including failure to preprocess the data well.

Being an explorative method, clustering was successful if and only if you as the user learned something new about your data. Do not take the user out of the loop. Clustering is a subjective technique, there is no objective quality to it.

Suggested reading:

Estivill-Castro, Vladimir (20 June 2002). "Why so many clustering algorithms — A Position Paper". ACM SIGKDD Explorations Newsletter 4 (1): 65-75.

who noted that clustering is in the eye of the beholder

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  • $\begingroup$ Since I have no labels, the external criterion are not useable. And those popular internal criterion, such as Partition (SC) index, Xie-beni (XB), Davies-bouldin (DB), are absolute values, and only when there are several clustering results are compared, one can know the minimum/maximum index value represents a optimal partition. So I still wonder, does there exist an index, whose value means probability, i.e., the value of "1" indicates a perfect result ? Is there an absolute standard for clustering, like correctness for classification, to evaluate the quality of a clustering result? $\endgroup$ – yang May 1 '15 at 12:55
  • $\begingroup$ Again, there is no such thing as a perfect result. You really should read that reference. Internal criterions are useless IMHO. $\endgroup$ – Has QUIT--Anony-Mousse May 1 '15 at 13:01

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