Review on the master’s thesis  “The stability based approach of  cluster number determination” by Aleksejs Lozkins  The cluster number validation is one of basic and important problems in cluster analysis which is not solved in general case. There are lots of local-optimality criteria of finding the appropriate cluster number adapted for the data specificity but the uniform criterion does not exist. The work presents a new way of stable cluster number estimation which is different from existing stability concepts.  The work presents an approach for appropriate cluster number estimation using the stability concept in cluster analysis. The master’s thesis proposes new algorithms for cluster number validation and considers data inaccuracies at the same time. This idea can be interpreted as an upgrade in certain way of existing approaches. The simulation uses two variants of data perturbation: artificial data perturbation and augmented data as union of perturbed and initial data. This idea is relatively new and paves way for obtaining new cluster number validation criteria.  The literature review and main methods of cluster analysis are mentioned in the master’s dissertation. The notation for proposed method is developed and introduced. The rough distance between clusterings is proved under developed notation and is adapted to proposed algorithms. The algorithm’s application on artificial data led to the expected results. The two applications on real data and the stable clusterings interpretation are carried out.  The work has clear structure, consistent presentation and mathematical notation. The precise statement of the problem is listed and clear results are obtained. In general, the results of this work are significant from academic view and can be used in different applications. I recommend to continue the research in frame of PhD thesis. Surely, I think the master's thesis goals are reached and the work deserves the “excellent” mark.   PhD in Physics, Head of Mathematical Models Department, BIA – Technologies 								Krasilnikov M.B.