#### Name

Lutsenko Yevgeniy Veniaminovich

#### Scholastic degree

•

#### Academic rank

professor

#### Honorary rank

â€”

#### Organization, job position

Kuban State Agrarian University

#### Web site url

## Articles count: 244

In this article, on a small and evident numerical example, methodological aspects of a process engineering of detection of knowledge from the trial-and-error data explicitly are considered, representation of knowledge and its usage for problem solving of forecasting, decision making and data domain examination in system-cognitive analysis (SC-analysis) and its programmatic toolkit - intellectual "Eidos" system are shown

One of the "points of growth" of applied statistics is
methods of reducing the dimension of statistical
data. They are increasingly used in the analysis of
data in specific applied research, such as sociology.
We investigate the most promising methods to
reduce the dimensionality. The principal
components are one of the most commonly used
methods to reduce the dimensionality. For visual
analysis of data are often used the projections of
original vectors on the plane of the first two
principal components. Usually the data structure is
clearly visible, highlighted compact clusters of
objects and separately allocated vectors. The
principal components are one method of factor
analysis. The new idea of factor analysis in
comparison with the method of principal
components is that, based on loads, the factors
breaks up into groups. In one group of factors, new
factor is combined with a similar impact on the
elements of the new basis. Then each group is
recommended to leave one representative.
Sometimes, instead of the choice of representative
by calculation, a new factor that is central to the
group in question. Reduced dimension occurs during
the transition to the system factors, which are
representatives of groups. Other factors are
discarded. On the use of distance (proximity
measures, indicators of differences) between
features and extensive class are based methods of
multidimensional scaling. The basic idea of this
class of methods is to present each object as point of
the geometric space (usually of dimension 1, 2, or 3)
whose coordinates are the values of the hidden
(latent) factors which combine to adequately
describe the object. As an example of the
application of probabilistic and statistical modeling
and the results of statistics of non-numeric data, we
justify the consistency of estimators of the dimension of the data in multidimensional scaling,
which are proposed previously by Kruskal from
heuristic considerations. We have considered a
number of consistent estimations of dimension of
models (in regression analysis and in theory of
classification). We also give some information about
the algorithms for reduce the dimensionality in the
automated system-cognitive analysis

The article considers measuring scales as a tool for creating formal models of real objects and a tool for increasing the degree of formalization of these models to a level sufficient to implement them on computers.
It also describes the different types of measuring scales, allowing to create models of varying degrees of formalization; lists the types of transformation valid during the processing of empirical data obtained with scales of different types; develops the task of metriza-tion of the scales, i.e. conversion to the most formalized mind; it proposes 7 ways of metrization of all the types of scales, providing a joint comparable quantitative processing of heterogeneous factors measured in different units of measure due to the conversion of all scales to one universal unit of measurement in which the measurement number of information is selected. All of these methods of metrization have been implemented in the system-cognitive analysis and in the Eidos intellectual system

In the article, we have considered the application of a system-cognitive analysis and the Eidos-X++ intellec-tual system to create complex multifactor models of nonlinear control objects on the basis of noisy frag-mented empirical data of large dimension and for the use of these models to solve problems of forecasting, executive decision making and research of the model objects. We have formulated the systematic generalization of the principle of Ashby (for nonlinear systems). The numerical example of a study of an abstract nonlinear system (Lissajous figures), in which the combined effect of multiple factors is the sum of the influences of each of these factors separately, that says about non-compliance of these factors, the principle of superposition and nonlinear effects in the system under consideration. It is shown, that the proposed device and software tools allow us to model such systems. We note, that the proposed device and instrumentation allow to interpret some classification scale, as projected geographical coordinates of the event, and others, like the foreseeable events and their severity, which allows you to get cartographic visualization of recognition of the place and time of events

The method of ordinary least squares (OLS) is widely known and deservedly popular. However, some attempts to improve this method. The result of one of such attempts is the weighted least squares (WMNC), the essence of which is to give the observation a weight which is inversely proportional to the errors of their approximation. Thereby, in fact, monitoring is ignored the more the difficult to approximate it. The result of this approach, formally, is the approximation error decreasing, but in fact, this occurs by partial refusal to consider the "problem" of observations, making a big mistake. If the idea underlying WMNC to bring to the extreme (and absurd), then in the limit, this approach will lead to the fact that from the entire set of observations there will be only those that lie almost exactly on the trend obtained by the method of least squares, and the rest will simply be ignored. However, according to the author, it's not a problem, and the failure of its decision, though it might look like a solution. In the work we have proposed a solution, based on the theory of information: to consider the weight of observations, the number of the argument of the value function. This approach was validated in the framework of a new innovative method of artificial intelligence: methods for automated system-cognitive analysis (ASA-analysis) and implemented 30 years ago in its software toolkit, which is "Eidos" intelligent system in the form of so-called "cognitive functions". This article presents an algorithm and software implementation of this approach, illustrated in detailed numerical example. In the future it is planned to give a detailed mathematical basis of the method of weighted least squares, which is modified by the application of information theory to calculate the weights of the observations, and investigate its properties

This article briefly discusses the mathematical nature of the author's proposed modification of the weighted least squares, in which the amount of the data is used as the weights of observations. There are two variants of this modification. In the first one, the weighting of the observations was made by replacing one observation with a certain amount of the information in it by the corresponding number of observations for unit weight, and then we applied the standard method of least squares. In the second method, the weighting of the observations was performed for each value of the argument by replacing all observations with a certain amount of information in one observation of unit weight which had been obtained as a weighted average of them, and then we applied the standard method of least squares. We have described in detail the technique of numerical calculations of the amount of information in the observations, based on the theory of automated system-cognitive analysis (ASC-analysis) and implemented it with a help of software tools - intelligent system called "Eidos". The article provides an illustration of the proposed approach on a simple numerical example. In the future, we are planning to give more detailed mathematical basis of the method of weighted least squares, which is modified by using the amount of information as weights, but also to explore its properties

In this article, the problem of short-range forecasting of the trends of economical indexes of diversified corporation is stated, on the basis of application of systemic-cognitive analysis and its tooling (intellectual system "Eidos") the formal problem definition and data domain formalization, i.e. development of classification and descriptive dials and graduations and shaping of training sample is performed

In this article, the routine of synthesis of four models of the corporation, different by frequent measure of correlation between past indexes of the factories entering into corporation and the future statuses of corporation as a whole is featured, verification of all private models with utilization of two integral measure is fabricated, forecasting of the future statuses of corporation on their system of determination is performed

In this article, the problem of short-range forecasting of value and dynamics of economical indexes of diversified corporation is stated, on the basis of application of systemic-cognitive analysis and its tooling (intellectual system "Eidos") the formal problem definition and data domain formalization, i.e. development of classification and descriptive dials and graduations and shaping of training sample is performed