An overview of data mining concepts based on neural networks
Erofeeva V. A. (SPbSU)



Using of stochastic approximation type algorithm for selection of optimal step-size of local voting protocol for differentiated consensuses achievement in a multi-agent network with topology cost constraints
Ivanskiy Y. V. (SPbSU)



Metrics for heuristic algorithms for solving the problem of automata minimization
Melnikova E. A. (SSU, Samara), Trenina M. A. (TSU, Togliatti)



Heuristic algorithms for generating binary relation matrices on the states of canonical automata
Sofonova N. V.(TSU, Togliatti), Dudnikov V. A.(DLNU, Lugansk)



Evaluation of possible ranges for the output of linear systems subjected to exogenous disturbances
Shcherbakov P. S. (ICS RAS, Moscow)




An Overview of Data Mining Concepts Based on Neural Networks

V. A. Erofeeva

St. Petersburg State University



Key words: neural networks, pattern recognition, supervised learning, chaotic neural networks, recurrent neural networks, oscillatory neural networks, deep learning.


At present, the development of aspects of human’s activity is associated with generation and accumulation of large amounts of data, which may contain important practical information. In recent years, methods of data mining automation based on intellectual data analysis have been developing. Artificial neural networks, inspired by biological neural networks, are used in many areas of information technology, including computer vision, voice recognition, natural language processing. In this paper we provide an analysis of existing neural network concepts, their classification and consider their application to the problem of pattern recognition.


Bibliogr.: 50 refs.


Using of Stochastic Approximation Type Algorithm for Selection of Optimal Step-size of Local Voting Protocol for Differentiated Consensuses Achievement in a Multi-agent Network with Topology Cost Constraints

Y. V. Ivanskiy

St. Petersburg State University



Key words: differentiated consensuses, multi-agent systems, randomized algorithms, stochastic approximation, SPSA.


In this paper, a new consensus problem, differentiated consensuses, is studied. This consensus problem is that, in a system with multiple classes, consensus is desired for every class, and the values themselves may be different for different classes. Specifically, we investigate differentiated consensuses in a distributed stochastic network system of nodes (agents), where tasks, classified with different priorities, are serviced. The network system is assumed to have a switched topology, noise, and delays in measurements, and the cost on the topology.

The goal is to reach/maintain balanced (equal) load, i.e., consensus, across the network and, at the same time, to satisfy the topology cost constraint, both for every priority class. A control protocol is proposed. With this protocol, network resources are allocated in a randomized way with probabilities corresponding to each priority class. Step-size of proposed protocol is selected using stochastic approximation type algorithm. We prove that the proposed control protocol is able to meet the topology cost constraint and achieve approximate consensus for each of the priority classes in the network.


Bibliogr.: 54 refs.


Metrics for Heuristic Algorithms for Solving the Problem of Automata Minimization1

E. A. Melnikova, M. A. Trenina

Samara State University, Togliatti State University

ya.e.melnikova@yandex.ru, trenina.m.a@yandex.ru


Key words: discrete optimization; heuristic algorithms; clustering situations; minimization of nondeterministic finite automata; metrics.


To minimize nondeterministic finite automata, clustering algorithms are applied for the subtasks in a special multi-heuristics approach to discrete optimization. Over the resulting set of subproblems, various discrete metrics are considered and their properties are investigated.


Bibliogr.: 7 refs.


Heuristic Algorithms for Generating Binary Relation Matrices on the States of Canonical Automata

N. V. Sofonova

Togliatti State Universit


V. A. Dudnikov

Dahl Lugansk National University



Key words: nondeterministic finite automata, graphs, adjacency table, isomorphism, heuristic algorithms, stochastic discrete optimization.


This article is devoted to the invariance binary relation matrices defined on the states of canonical automata which characterize a given regular language. We give a special definition of equivalence of such matrices and present algorithms, including heuristic ones, for computing the amount of non-equivalent matrices. We present the results of computational experiments on finding the number of possible matrices of binary relations on the states of canonical automata for dimensions up to 4×5, which show the ways of getting similar results for higher dimensions when using better computing devices.


Bibliogr.: 14 refs.


Evaluation of Possible Ranges for the Output of Linear Systems Subjected to Exogenous Disturbances

P. S. Shcherbakov

Institute of Control Sciences RAS, Moscow



Key words: Linear systems, exogenous disturbances, rechability sets.


We consider linear systems with nonzero initial conditions and subjected to bounded persistent exogenous disturbances. A transparent and computationally simple method is proposed for the component-wise evaluation of the output vector.


Bibliogr.: 14 refs.