I want to do clustering and evaluating the clusters.I have mixture of nominal and discrete numerical data. I did clustering and now i want to use some useful indices to choose the best number of clusters. which of the internal indices i should use? I mention again that the data are mixture of nominal and discrete numerical data. Thanks
Dear Ghazaleh,
I think the optimization of cluster number depends on the type of classification you used.
I already used this article which provides some example of indexes (for tree classification):
Guidi et al. 2009 : A new procedure to optimize the selection of groups in a classification tree: Applications for ecological data, Ecological Modelling.
Hope this help
One of the way, but time consuming, is to try different amount of clusters. For each set of n clusters evaluate the inter-classes variance, and between -class variance. Then plot these variances as a function of n (amount of clusters). There should be some optimum in the way minimal intra class variance and maximum of inter class variance.
You can try to apply a Latent Class model, and chose the best number of cluster by BIC index or other statistical indices. in LC models a discrete latent variable not directly observable, whose categories are usually called latent class, is assumed to affect the responses of subjects to a number of manifest variables whose scores are directly observable. This feature allows to classify observational units into a preferably small set of latent classes, representing the underlying sub-populations, that is sufficient to explain away the associations observed among the manifest variables. The latent classes are mutually exclusive and exhaustive because every subject belongs to one and only one latent class. At the beginning, you can try a package for R, called poLCA.
In my eyes "to choose the best number of clusters" is a double wrong, since it is doubtful if a best cluster can be defined, and any partial data classification runs the risk of irrelevancy (any arbitrary correlation can be supported partially).
It is a problem of automatic clustering that can detect automatically number of clusters. Commonly it uses variance within clusters
You could look into using Bayesian Information Criterion or a Penalized Sum of Squared Errors to have a metric on the quality of your clustering based on the density of the clusters, the variance, and etc ... So, I agree with Jan and Roberta!
Thank you all, but can anyone explain me the poLCA and the Latent Class model?
is it just for clustering mixed data? or it is used for clustering categorical data?
I suggest you read the article: http://www.researchgate.net/publication/278403191_Numerical_Coding_of_Nominal_Data
Perhaps there you will find the answer.
Article Numerical Coding of Nominal Data