Hello Mustafa,

There is a lot of literature available on Cluster Analysis [1,2]. Based on your data and the specific task that you intend to achieve, you can use one of the existing cluster analysis techniques (Eg: Hierarchical clustering, Centroid-based clustering, Distribution-based, Density based etc.). 

Apart from using the right clustering technique, the distance measure is another point to ponder upon. There are several well-known distance measures (Euclidean, Chebyshev, Mahalanobis etc.) which you can use. Again, it depends upon prior-knowledge of your data and your ultimate task. These literature have information on Inter and Intra-cluster distances as well.

As a start, you can implement the K-Means clustering algorithm [3]. This is a well-known centroid-based clustering technique. You may use the Euclidean distance at first. The algorithm tries to minimize the intra-cluster variance (squared-Euclidean distance). Sometimes, the simplest of methods work well. 

As far as the further implementation is concerned, almost all of the well-known software tools have cluster analysis packages. If you are at an university, you could use MATLAB [4] or prefer an open-source platform, you could try Python [5].

Good luck with your research!

Best Regards,

Rijul Soans

References:

[1] Everitt et al., "Cluster Analysis", Wiley Publishers, 2011

[2] Fukunaga eta al., "Introduction to Statistical Pattern Recognition", Academic Press, 2012

[3] Duda et al., "Pattern Classification", Wiley Publishers, 2012

[4] http://in.mathworks.com/discovery/cluster-analysis.html

[5] https://datasciencelab.wordpress.com/2013/12/12/clustering-with-k-means-in-python/

Thank u very much.....

Hi Mustafa,

maybe you are looking for measures as "silhouette" (Rousseeuw ,1986), providing insight of distances intra- and inter-cluster. I attached the wiki link where the silhouette is explained. Most of the software include libraries and toolboxes with this measure already coded. In addition, I also enclosed a couple of papers where are handled different issues with intra- and inter-cluster distances (with mixed data).

Hope this helps.

Regards, Manuel

https://en.wikipedia.org/wiki/Silhouette_(clustering)

Article Identification of surgical practice patterns using evolution...

Conference Paper A Particle Swarm Optimization derivative applied to cluster analysis

Lots of thanks Mr. Manuel. Hope it will be continued..........

Hello mustafa

Linear discriminant analysis considers the fuzziness with in and between the cluster scatter matrices.