I need the ways to statistically measure the quality of clusters formed after performing clustering technique from data mining like kmeans, etc.
below measures can be used for cluster quality
SSE(sum of the square error from the items of each cluster),Inter cluster distance,Intra cluster distance for each cluster,Maximum Radius,Average Radius
http://www.amazon.com/dp/0387781889/?tag=stackoverfl08-20
You can use the clustering validity index, such as WB index, DB index or BIC.
There are a number of metrics used to quantify the quality of clustering, but you need to determine which is more suitable for your application. Read the answers to the question in the link, they have good suggestions and explanation.
http://stats.stackexchange.com/questions/6252/clustering-quality-measure
Yes of course, all the clustering validity indices are based on these two measures.
set up a confusion matrix then calculate the purity measure
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I think that the confusion matrix is used only in the case of classification (not in clustering).
Confusion matrix is not limited to its use. It is simply a tabular way of organizing our clustering or classification results in order to aid its evaluation; hence the confusion in the term.
https://en.wikipedia.org/wiki/Cluster_analysis
It really depends whether you know the ground truth clusters or not.
In the first case, you could proceed with "external clustering quality metrics". A widely used metric in this case is Purity. But you can proceed with others, like Homogeneity, Completeness, V-Measure, Precision, Recall, Normalized Mutual Information and CMM (for streaming environments).
In the second case, it is, no ground-truth is known, you could proceed with metrics that account for the distribution of data, and nothing besides it. These metrics are called "internal clustering quality metrics". Examples include: Silhouette coefficient and Sum of Squared Distances (SSQ).
My master's dissertation covers these subjects at least partially, but it is in portuguese. I will leave a link here in case someone else needs it too.
https://www.ppgia.pucpr.br/pt/arquivos/mestrado/dissertacoes/2015/dissertacao_jean_barddal.pdf
Usually clustering algorithms are non-supervised which often means that the correct partition into classes is not know and the number of classes is also unknown. In these cases there are measures of cluster validity based in maximizing inter-cluster distances and minimizing intra-cluster distances. There is a vast scientific literature on cluster validity. If in your case you know the correct partition then you can use a distance measure between partitions to measure how similar to the correct clustering is the clustering obtained by the algorithm. For that matter I proposed in 1991 a distance between partitions based on information theory. You can find the paper describing it in: R. López de Mántaras; A Distance-based Attribute Selection Measure for Decision Tree Induction. Machine Learning Journal, 1991, Vol. 6,nº 1, pp. 81-92. If you have problems finding this paper let me know ([email protected]) and I will send you a PDF of that paper.
There are several clustering validity measures:
Partition Coeffcient (PC)
Classiffcation Entropy (CE)
Partition Index (SC)
Separation Index (S)
Xie and Beni's Index (XB)
Dunn's Index (DI)
Alternative Dunn Index (ADI).
You should try one of them.
Looking for an answer in the same question, I found useful this article http://www.sciencedirect.com/science/article/pii/S003132031200338X and the "clValid" package in R https://cran.r-project.org/web/packages/clValid/clValid.pdf . Maybe it is also useful to you.
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