Domains identification by the parameter values in multidimensional space

Abstract

Abstract As a result of cluster and discriminant data analysis, the objects are distributed among different classes represented in the multidimensional space of parameter values. At the next stage, it is relevant to use the results obtained in various applications. The most frequently solved task is the diagnostics of a newly received object when the class of the object is determined through parameter values. In terms of a data view model, the problem can be reduced to determining a domain in parameter space, the new object belonging to this domain. The solution to this problem depends on the way the data analysis results are described and presented. Previously the graphic data model was considered to describe the domains separated by surfaces in the multidimensional space. Moreover, a constructive approach was proposed to describe an error in the representation of the boundaries, making it possible to take into account the experimental data errors. The mathematical model proposed in the given article is used to develop a domain identification algorithm by the parameter values in the multidimensional space. The proof of correctness and the estimation of computational complexity are provided for the algorithm. The results obtained make it possible to use the algorithm to calculate various characteristics of objects: state, intervals of existence, etc.