There are many measures. Purity is one of them and its described below

http://nlp.stanford.edu/IR-book/html/htmledition/evaluation-of-clustering-1.html

purity 0 is bad and 1 is good.

The measures you mentioned has some ranges..

for silhouette its -1 to 1 explained below..

http://en.wikipedia.org/wiki/Silhouette_%28clustering%29

Similarly there are some range of values associated for each measure.

Hope this helps.

I mean how can you say that the particular clustering quality measure [CQM] is a good one.If I come up with a new CQM how can I make sure that it is a good one?

i think following post will be useful to you.

http://stats.stackexchange.com/questions/6252/clustering-quality-measure

Hello,

the thing is, we can't really say what clustering quality measure is good or not. The very notion of "good clustering" is relative, and is a question of point of view. The same applies for the quality measures. It depends on what you want to evaluate.

For instance, the Davies-Bouldin Index evaluates intra-cluster similarity and inter-cluster differences. If you consider these to be good criteria, go for the Davies-Bouldin. The Silhouette Index measure the distance between each data point, the centroid of the cluster it was assigned to and the closest centroid belonging to another cluster. If you consider that this is a good criterion, go for the silhouette index.

The same goes with all quality measures. You have to look what these quality indexes are measuring and check wether or not it seems relevant for the kind of clustering you are doing.

Other aspects that you may want to consider are wether or not these quality measures are normalized. For instance, the silhouette index is normalized and a value close to 1 is always good (for this index) whatever clustering you are trying to evaluate. However, the Davies-Bouldin for instance is not normalized and it's difficult to compare 2 values of Davies-Bouldin from different data sets. Another important aspect is to check that the quality measure that you want to apply uses the same metric than the clustering algorithm the results of which you are trying to evaluate. Otherwise, your quality measure will be biased.

Good luck !

I fully agree with Jermie. Meaning of "good clustering" is subjective and its interpretation varies with applications, time and even the analyst.  

You have to judge the need of your application and decide the best measure.

Good luck! 

You need a "ground truth" for a specific dataset. For example, the Iris dataset clustering result is well known.

You could also try the NMI (Normalized Mutual Information) measure and see how it correlates with each metric.

Or you could try a simple majority consensus vote on several (3 or 5) different metrics.

Regards, David N.

In principle I agree with Jeremie Sublime. In my book I approached the problem visually without making any model assumptions like the silhouette width (only good for spherical data structures). For details please read my book at no charge: http://www.springer.com/us/book/9783658205393

I take clustering as an approach to solve an optimisation problem , subject to constraints.

e.g. I once used K-means to cluster nodes in a communication network and realised that 70% of nodes in every cluster were (expectedly) not connected to their cluster heads. As my objective was to create clusters which are sub_networks in star topologies (each node needs to be connected to its cluster head), the disconnectedness was my metric to say that k-means was not a right scheme for my clustering.

Furthermore, one metric might not be enough in some cases. You might carefully combine them to calculate a related clustering score.

Say you have qualities A, B and a dis-quality C. The clustering score would be S=a*A+b*B - c*C or even S=a*A *b*B / c*C.

where a, b, and c are weighting coefficients related to situations.

The higher is S the better is your clustering.

One of the qualifications of well clusteredness measure is Perturbation Resilience which is discussed in Conference Paper Clustering under Perturbation Resilience

There are several performance indexes that evaluate the clustering quality. The idea is to assses the homogenity insede cluster and heterogenity among the clusters

Minimize the inter-similarities and maximize the intra similarities between the clusters by a quotient object function as a clustering quality measure.