A principled approach to cluster evaluation is to measure how well the
cluster membership captures the structure of unseen data. A natural measure
for this is to measure how much of the entropy of the data is captured by
cluster membership. For kmeans and its natural L_2 metric, the natural
cluster quality metric is the squared distance from the nearest centroid
adjusted by the log_2 of the number of clusters. This can be compared to
the squared magnitude of the original data or the squared deviation from the
centroid for all of the data. The idea is that you are changing the
representation of the data by allocating some of the bits in your original
representation to represent which cluster each point is in. If those bits
aren't made up by the residue being small then your clustering is making a
bad tradeoff.
In the past, I have used other more heuristic measures as well. One of the
key characteristics that I would like to see out of a clustering is a degree
of stability. Thus, I look at the fractions of points that are assigned to
each cluster or the distribution of distances from the cluster centroid.
These values should be relatively stable when applied to heldout data.
For text, you can actually compute perplexity which measures how well
cluster membership predicts what words are used. This is nice because you
don't have to worry about the entropy of real valued numbers.
Manual inspection and the socalled laugh test is also important. The idea
is that the results should not be so ludicrous as to make you laugh.
Unfortunately, it is pretty easy to kid yourself into thinking your system
is working using this kind of inspection. The problem is that we are too
good at seeing (making up) patterns.
On Tue, Jun 16, 2009 at 2:35 PM, Grant Ingersoll <gsingers@apache.org>wrote:
> What tools/approaches are people using to validate their clustering output?
> Are there utilities that we should be implementing that would make this
> easier for users?
>
>
