Recurrent approximation as the tool for expansion of functions and modes of operation of neural network

Abstract

Розглянуто роль рекурентної штучної нейронної мере-жі (РШНМ) для розв'язку характерних задач координаці-йного управління. Сформовано структуру РШНМ обробки інформації на базі векторів -індикаторів та рекурентної апроксимації. Продемонстровано, що корекція нуля, калі-брування, вимірювання, визначення похибки апроксимації, дозволяє розв'язувати задачі мінімізації, розширити функці-ональні можливості та реалізувати нові режими її роботи. Представлено алгоритми аналітичного навчання нейрону з декількома входами та приклад формування продуктивних правил при розв'язуванні задачі мінімізації Ключові слова: рекурентна мережа, режими роботи, продуктивні правила, аналітичне навчання нейрону, оцінка похибки, координаційне управління Рассмотрена роль рекуррентной искусственной ней-ронной сети (РИНС) для решения задач координационно-го управления. Сформирована структура РИНС обработки информации на основе векторов -индикаторов и рекур-рентной аппроксимации. Продемонстрировано, что кор-рекция нуля, калибровка, измерение, определение ошиб-ки аппроксимации позволяет решать задачи минимизации, расширить функциональные возможности и реализовывать новые режимы ее работы. Представлены алгоритмы анали-тического обучения нейрона с несколькими входами и при-мер формирования продуктивных правил при решении зада-чи минимизации Ключевые слова: рекуррентная сеть, режимы работы, порождающие правила, аналитическое обучение, оценка ошибки аппроксимации, координационное управление

Synthesis of a trend’s integral estimate based on a totality of indicators for a time series data

“…It is especially true for the conditions of limited gold-currency and energy resources, time limits and military aggression. Under such conditions, the solution of mutually related organizational, technical and economic problems requires modeling and mapping the results using the modern means [15][16][17][18][19][20][21].…”

“…At present, there is an experience on the basis of which the common representation of nonlinear objects by the description paradigm was replaced with a super modern paradigm [16]. Their representation by the recurrent network, which extended the boundaries of its capabilities due to the application of the recurrent approximation method is not less effective [17]. The introduction of the comparative theory of the scalar multifactor evaluation including identification [19], together with the introduced three-level comparator [20], forms the basis to evaluate the errors of the model [20] and to control its construction based on the multifactor relevance criterion [21].…”

“…Thus, the experience of implementation of papers [29][30][31][32] demonstrated that construction of the method that will ensure the formation of the expression of the integral criterion of the quantitative estimate and the illustration of the course of socio-economic processes for the determined list of indica-tors is decisive [29][30][31]. In this regard, to unite the benefits of the prescription control paradigm [16], representation of the integral criterion with the unified expression [17] is a reasonable and logically grounded problem. The development of the specified direction of mathematical substantiation of the cybernetic approach to the construction of the system of estimation of public administration effectiveness to combat corruption in the society, the control and information effectiveness will be ensured only due to the use of a special method for the formation of the integral indicator.…”

“…The development of the specified direction of mathematical substantiation of the cybernetic approach to the construction of the system of estimation of public administration effectiveness to combat corruption in the society, the control and information effectiveness will be ensured only due to the use of a special method for the formation of the integral indicator. Its implementation, together with the use of network technologies and analytical leaning [17], recurrent calibration [33] or graphical representation and presentation through the operation of matrix algebra opens up new opportunities and stimulates the search for new forms of representation of time series [34].…”

“…There exist some examples of the successful construction of nonlinear models for integral estimation by the system of four or five types of indicators. For example, the deflection of functionals from quadratic forms, which are minimized [16] or represented by artificial and recurrent networks [17], or assess the integral indicator of adequacy [21], was constructed based on the known physical relation. Even though they do not apply directly to the solution of the problem of generalization of four time series, they are an example of solving the problem of integral estimate.…”