What's a good metric to analyze the quality of the output of a clustering algorithm?

Question

I've been trying out the kmeans clustering algorithm implementation in scipy. Are there any standard, well-defined metrics that could be used to measure the quality of the clusters generated?

ie, I have the expected labels for the data points that are clustered by kmeans. Now, once I get the clusters that have been generated, how do I evaluate the quality of these clusters with respect to the expected labels?

Answer 1

_{I am doing this very thing at that time with Spark's KMeans.}

I am using:

• The sum of squared distances of points to their nearest center (implemented in computeCost()).

• The Unbalanced factor (see Unbalanced factor of KMeans? for an implementation and Understanding the quality of the KMeans algorithm for an explanation).

Both quantities promise a better cluster, when the are small (the less, the better).