Dear, Hooman Firoozi,

one way to estimate the number of cluster is to estimate a kind of cluster validity index. this index takes fundation on what is a good cluster (maximum variance beetween clusters and minimum intra clusters variance).

here a little article:

http://uni-obuda.hu/conferences/mtn2005/KovacsFerenc.pdf

here, this Cluster Validity Index in a image processing application:

https://www.researchgate.net/publication/224683111_Dimensionality_Reduction_Techniques_An_Operational_Comparison_On_Multispectral_Satellite_Images_Using_Unsupervised_Clustering

Best regards,

Ludovic

Conference Paper Dimensionality Reduction Techniques: An Operational Comparis...

Dear Firoozi,

There is no best cluster number in the unsupervised learning. Indeed, your problem definition can describe the number of clusters. Since your data set has 3 dimensions, you can use visualization techniques for understanding the statistical properties of your data set. For instance, you can use hierarchical methods (similarity/distance matrices) for depicting the Dendrogram of your data set. As another alternative, you can see the following paper:

P. Y. Mok, H. Q. Huang, Y. L. Kwok, J. S. Au: A robust adaptive clustering analysis method for automatic identification of clusters. Pattern Recognition, vol. 45, 2012.

Best regards,

Muhammad.

TLBO may be good alternative in this case. Please refer to the attached article.

http://link.springer.com/chapter/10.1007/978-81-322-2517-1_46