Review of the supervisor on the master's thesis: 
Aleksejs Lozkins«The stability based approach of cluster number determination»

The main goalof the dissertation work is to produce the cluster number validation criterionand to solve the data imprecision problem at the same time. The master's thesis propose the new algorithms of cluster number determination, which incertain sense improve the existing algorithm. 
In this work, the stability methodology is used as the basic approach for studying problems of clustering.Comparing to the mathematicalanalysis the stability concept in clustering analysis does not havea precise mathematical formulation.  We should understand that this concept depends on logical beliefs. However, it looks like good idea to think that stability should be the basic characteristic of the clustering.
The two different algorithms, which have different data inaccuracies interpretation, are proposed. These algorithmsaretested on artificial dataset. The algorithms parameters adjustment havebeen demonstratedand parameters interpretation is given. The stable clusteringunder proposed criterion of the European countries unemployment ratesfound and historical and geographical result interpretation are provided. The cluster analysis of European Union countries demographic indices are carried out.
The materials of this work are published in 7 printed works, 2 of them are thearticles in scientific journals and one paper is indexed in Scopus, 4 conference abstractsand 1 paper is under publication in the journal of geographical section applying the developed method to the real data. 
I think that given the extensive and systematic character of the work, the relevance of the objectives, evaluation of thesis work deserves the best score.  AleksejsLozkins  can be recommended to continue training in a graduate school. Results of master's thesis may be published in scientific journals.

 Research advisor, D.Sc.,professor Bure V. M.