Interval Prediction Based on Experts’ Statements

In the work [1] we proposed an approach of forming a consensus of experts’ statements in pattern recognition. In this paper, we present a method of aggregating sets of individual statements into a collective one for the case of forecasting of quantitative variable.

A Statistical Convergence Aplication for the Hopfield Networks

When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ξ^1,ξ^2,...,ξ^p as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented

Constructing of a Consensus of Several Experts Statements

∗ The work was supported by the RFBR under Grant N04-01-00858.

Generalizing of Neural Nets: Functional Nets of Special Type

Special generalizing for the artificial neural nets: so called RFT – FN – is under discussion in the report. Such refinement touch upon the constituent elements for the conception of artificial neural network, namely, the choice of main primary functional elements in the net, the way to connect them(topology) and the structure of the net as a whole. As to the last, the structure of the functional net proposed is determined dynamically just in the constructing the net by itself by the special recurrent procedure. The number of newly joining primary functional elements, the topology of its connecting and tuning of the primary elements is the content of the each recurrent step. The procedure is terminated under fulfilling “natural” criteria relating residuals for example. The functional proposed can be used in solving the approximation problem for the functions, represented by its observations, for classifying and clustering, pattern recognition, etc. Recurrent procedure provide for the versatile optimizing possibilities: as on the each step of the procedure and wholly: by the choice of the newly joining elements, topology, by the affine transformations if input and intermediate coordinate as well as by its nonlinear coordinate wise transformations. All considerations are essentially based, constructively and evidently represented by the means of the Generalized Inverse.

Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

Evaluating Misclassification Probability Using Empirical Risk

* The work is supported by RFBR, grant 04-01-00858-a

A New Approach for Eliminating the Spurious States in Recurrent Neural Networks

As is well known, the Convergence Theorem for the Recurrent Neural Networks, is based in Lyapunov ́s second method, which states that associated to any one given net state, there always exist a real number, in other words an element of the one dimensional Euclidean Space R, in such a way that when the state of the net changes then its associated real number decreases. In this paper we will introduce the two dimensional Euclidean space R2, as the space associated to the net, and we will define a pair of real numbers ( x, y ) , associated to any one given state of the net. We will prove that when the net change its state, then the product x ⋅ y will decrease. All the states whose projection over the energy field are placed on the same hyperbolic surface, will be considered as points with the same energy level. On the other hand we will prove that if the states are classified attended to their distances to the zero vector, only one pattern in each one of the different classes may be at the same energy level. The retrieving procedure is analyzed trough the projection of the states on that plane. The geometrical properties of the synaptic matrix W may be used for classifying the n-dimensional state- vector space in n classes. A pattern to be recognized is seen as a point belonging to one of these classes, and depending on the class the pattern to be retrieved belongs, different weight parameters are used. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented.

Learning Technology in Scheduling Based on the Mixed Graphs

We propose the adaptive algorithm for solving a set of similar scheduling problems using learning technology. It is devised to combine the merits of an exact algorithm based on the mixed graph model and heuristics oriented on the real-world scheduling problems. The former may ensure high quality of the solution by means of an implicit exhausting enumeration of the feasible schedules. The latter may be developed for certain type of problems using their peculiarities. The main idea of the learning technology is to produce effective (in performance measure) and efficient (in computational time) heuristics by adapting local decisions for the scheduling problems under consideration. Adaptation is realized at the stage of learning while solving a set of sample scheduling problems using a branch-and-bound algorithm and structuring knowledge using pattern recognition apparatus.

One Approach for the Optimization of Estimates Calculating Algorithms

In this article the new approach for optimization of estimations calculating algorithms is suggested. It can be used for finding the correct algorithm of minimal complexity in the context of algebraic approach for pattern recognition.

Automatic ECG Analysis for Preliminary and Detailed Diagnostics Based on Scale-space Representation

A novel approach of automatic ECG analysis based on scale-scale signal representation is proposed. The approach uses curvature scale-space representation to locate main ECG waveform limits and peaks and may be used to correct results of other ECG analysis techniques or independently. Moreover dynamic matching of ECG CSS representations provides robust preliminary recognition of ECG abnormalities which has been proven by experimental results.

Basic Principles of Organization of the Medium and Thinking Process of the Human in its Conceptual Presentation

Given in the report conceptual presentation of the main principles of fractal-complexity Ration of the media and thinking processes of the human was formulated on the bases of the cybernetic interpretation of scientific information (basically from neurophysiology and neuropsychology, containing the interpretation giving the best fit to the authors point of view) and plausible hypothesis's, filling the lack of knowledge.

Оптимизация Оценки Вероятности Ошибочной Классификации в Дискретном Случае

* Работа выполнена при поддержке РФФИ, гранты 07-01-00331-a и 08-01-00944-a

Построение Логико-Вероятностных Моделей Временных Рядов с Использованием Цепей Маркова

The method of logic and probabilistic models constructing for multivariate heterogeneous time series is offered. There are some important properties of these models, e.g. universality. In this paper also discussed the logic and probabilistic models distinctive features in comparison with hidden Markov processes. The early proposed time series forecasting algorithm is tested on applied task.

Использование FRiS-Функций для Решения Задачи SDX

Рассматривается задача структуризации избыточного набора информации, выявления основных закономерностей, содержащихся в нем с помощью аппарата FRiS-функций. В результате решения этой задачи (задачи SDX) на основе исходного множества объектов строится его сокращенное описание в терминах классов и существенных признаков. Данное описание снабжено системой правил, позволяющих восстанавливать значения всех признаков на основе существенных и находить место новым объектам в системе построенных классов.

Выявление Фракталоподобных Структур в ДНК-Последовательностях

Разработан и реализован алгоритм выявления фракталоподобных структур в ДНК- последовательностях. Фрактальность трактуется как самоподобие, основанное на свойстве симметрии или комплементарной симметрии. Локальные фракталы интересны своей способностью аккумулировать множественные палиндромно-шпилечные структуры с потенциально возможными регуляторными функциями. Выявлены реальные случаи проявления фрактальности в различных геномах: от вирусов до человека. Рассмотрена возможность использования фракталоподобных структур в качестве маркеров, различающих близкие классы последовательностей.