07 Февраль 2019
# MODEL OF HIERARCHICAL FUNCTIONAL SYSTEM FOR CLUSTER ANALYSIS

## Collection of Scientific Papers of KhNUPS 2(56). Kharkiv, 2018, p. 82 - 88.

The model of the hierarchical functional system of the subject area for cluster analysis is considered, based on the concept of stratification of the knowledge base. The mechanism of interpretation of the hierarchical functional system model for fuzzy classification of heterogeneous data based on the method of dynamic condensations is investigated. A graphical view of the hierarchical functional system for cluster analysis is given.

Keywords: hierarchical functional system, cluster analysis, knowledge base, expert system.

A model of a hierarchical functional system for cluster analysis

The article considers the model of the hierarchical functional system of the subject area for cluster analysis, based on the concept of layering of the knowledge base. The mechanism of interpretation of the model of the hierarchical functional system for fuzzy classification of heterogeneous data based on the dynamic condensed method is investigated. The mathematical model of cluster analysis is studied. The dynamic condensed method is adapted for fuzzy classification of heterogeneous data. The strategy for clustering in the "KARKAS" system is outlined. Examples of rules and frames of the knowledge base of the expert system of cluster analysis are considered. A graphical view of the hierarchical functional system is shown before the consultation for choosing the cluster analysis algorithm.

Keywords: hierarchical functional system, cluster analysis, knowledge base, expert system.

Model of the hierarchical functional system for cluster analysis

The article considers the model of the hierarchical functional system of the subject area for cluster analysis is considered, based on the concept of the knowledge base bundle. The mechanism of interpretation of the hierarchical functional system model for the fuzzy classification of heterogeneous data based on the dynamic condensation method is investigated. The mathematical model of cluster analysis is studied. The method of dynamic condensations for the blurred classification of heterogeneous data has been adapted. The strategy of clustering in the "KARKAS" system is outlined. Examples of rules and frames of the knowledge base of the expert system of cluster analysis are considered. A graphical view of the hierarchical functional system is shown before consulting for the choice of the cluster analysis algorithm.

The model ontology subject domain in system "KARKAS", consists of hierarchy of classes of subject domain, communications between them (conclusion rules) which operate within the limits of this model. In system the interpretation mechanism ontology in the conditions of dynamic change of its parameters (a base class, communications between classes and interactions of objects of classes) is offered. The system is constructed by a modular principle and for this reason has the possibility of connecting other additional modules. In the architecture of the system it is possible to allocate the following basic modules: the loader; the module for working out knowledge base; the consultation module; the module cluster analysis the data.

The subject domain model is considered as a functional system in which the result makes an organizing impact on all stages of ontology formation. Classes and communications between them can be considered as a logical design of a functional system.

In system "KARKAS" the hierarchical functional system is the formalized reflexion of subject domain in the form of hierarchical structure of a set of managing directors a component which cooperate among themselves for overall objective achievement.

Keywords: hierarchical functional system, cluster analysis, knowledge base, expert system.

Introduction. An important point in cluster analysis is the selection of metrics (measures of proximity of objects), which decisively depends on the final version of dividing objects into groups with a given algorithm of partitioning [1].

Another important value in cluster analysis is the distance between clusters of objects. The choice of one or another measure of the distance between clusters depends on the geometric shapes that form the objects in the feature space. For example, using the "nearest neighbor" distance has good clustering results when objects in the feature space form a chain structure. The "distant neighbor" distance is used when objects form spherical clouds. If the objects form ellipsoids, it is recommended to use the distances between their centers of gravity.

Algorithms of cluster analysis differ in great variety. These can be, for example, algorithms that implement a complete enumeration of objects or carry out random division of a set of objects. At the same time, most of such algorithms consist of two stages. At the first stage, the initial (random) division of the set of objects into clusters is specified and the quality function of the division is determined. At the second stage, objects are transferred from cluster to cluster until the value of the partition quality functional stops improving.

The problem of clustering is that for each specific type of data, the structure of the location of objects in the space of features, it is necessary to either correctly choose a well-known algorithm, or adapt it or develop a new one. To solve this problem, the knowledge of experts is widely used.

The purpose of this work is to study the model of a hierarchical functional system based on the concept of stratification of the knowledge base of the subject area for cluster analysis. This work is a development of research [2 ‒ 7].

Formulation of the problem. Develop an effective mathematical model of cluster analysis for heterogeneous data.