If there are more than one similarity function in these methods, you can compare between them to show the differences between the algorithms with various similarity functions.

You can also tryout several topic modelling technique such as pLSA, LDA etc.

Thank you all.

Will I be able to use the Rand index to compare two user data (with the same variables)?

Dear Eiman

Actually, I am agree with Bahadorreza, you may use cluster aggregation techniques for making good cluster or consensus clustering.

for comparing clusterings you may use Rand, Adjust Rand, Jaccard, or the other similarity measurments. In one of my work I used the combination of them for 5 clustering algorithms;

https://www.researchgate.net/profile/Reza_Mahini/publication/310282544_Cluster_Aggregation_for_Analyzing_Event-Related_Potentials/links/5949db99aca272a30c6cc1ea/Cluster-Aggregation-for-Analyzing-Event-Related-Potentials.pdf

Hope it would be helpful!

Best,

Reza

Conference Paper Cluster Aggregation for Analyzing Event-Related Potentials

This also is the available clustering methods in distributed system

https://spark.apache.org/

Clustering: K-means, Gaussian mixtures (GMMs),...

https://spark.apache.org/mllib/

In my opinion, there are two questions inside: how to model a user and what mathematical methods to use to calculate users' clusters. Of course, the answer on the best clustering algorithm depends on answers of the above questions. 

User modeling: To model a user, you can use numerical emotion models (HMMs), personality models (Big-Five), and culture models (synthetic cultures). To calculate clusters, you can use statistical toolkit WEKA containing many useful clustering algorithms (more than 10) that can be tested using your data.

I attach a chapter about user modeling (you might find it in your university library), downloading WEKA and clustering.

http://weka.sourceforge.net/doc.dev/weka/clusterers/EM.html

http://www.cs.waikato.ac.nz/ml/weka/downloading.html

Chapter Acquisition of Intercultural Data

Thank you all.

We usually use Python or R for clustering which makes it convenient to alter the code and add other metrics and various visualisation functions.

Of course, it is a matter of taste: R or WEKA. I am more familiar with WEKA. FYI: WEKA was originally developed in Java, but it has a Python interface that relies on the Java implementation. WEKA implements hierarchical clustering algorithms such as Cobweb but doesn't implement BIRCH (s. link).

https://en.wikipedia.org/wiki/BIRCH