The paper presents a general approach to solving the problem 
of building of adaptive recognition systems for weighed samples of w-objects. 
The features of these systems were investigated and new problems 
of construction of the adaptive recognition systems were determined. 
Algorithms for a building and optimization of weighted samples 
of w-objects was presented and analyzed.
The metrics for distance determination between the objects of weighted training samples is proposed. 
Expansion of effective algorithms of recognition on the weighed samples 
of w-objects with distance calculation on the basis of the proposed metrics is done. 
Experimental results were confirmed the efficiency of the offered approach.