Stochastic optimization for unsupervised feature learning
Boiarov A. A. (SPbSU)



Some auxiliary algorithms for the problem of state-minimization of nondeterministic finit automata
Zubova M. A. (TSU), Melnikov B. F. (SSU)



A note on the Fiedler number and convergence rate of Laplacian systems
Malkovsky N. V. (SPbSU)



Use of randomized algorithms in the identification of the model parameters of dynamic plant
Ponyatskiy V. M. (KBP, Tula)




Stochastic Optimization for Unsupervised Feature Learning

A. A. Boiarov

Saint Petersburg State University



Key words: stochastic optimization, machine learning, unsupervised learning, clustering, object character recognition, convolutional neural network.


One of the most important tasks of machine learning is learning of deep hierarchy of features for another problems. It helps to describe internal data structure and improves the classification results. Recently, algorithms of unsupervised feature learning are actively used for this purpose. However, not all of these algorithms can be easily tuned. In this paper, we consider a stochastic optimization

modification of the feature learning method based on the K-means algorithm. This new algorithm represents an idea of online-learning; it allows to achieve a significant boost in speed and happen to be stable against noise. The paper discusses a successful example of application of the modified method in the handwritten character recognition system. This system has a close relationship with a convolutional neural networks.


Bibliogr.: 16 refs.


Some Auxiliary Algorithms for the Problem of State-minimization of Nondeterministic Finite Automata

M. A. Zubova, post-graduate student

Togliatti State University


B. F. Melnikov, proifessor

Samara State University



Key words: Nondeterministic finite automata; universal automaton; basic automaton; state-minimization.


In the minimization of nondeterministic finite automata, it is often the case that the covering set of blocks defines the automaton which is not equal to the initial one (Waterloo automaton, etc.). However, despite the presence of such constructions in certain regular languages, a very important subproblem of the state-minimization problem of nondeterministic finite automata is the one of choosing the covering set of grids of minimum possible cardinality. In this paper, we describe some auxiliary algorithms for the solution of this problem (including the ones for constructing heuristic algorithms). We also consider in details an example, where the greedy heuristic does not lead to the stateminimum automaton.


Bibliogr.: 20 refs.


A Note on the Fiedler Number and Convergence Rate of Laplacian Systems

N. V. Malkovsky

Saint Petersburg State University


Key words: Linear dynamical systems, Laplacian systems, consensus protocols, asymptotic analysis.


This paper concentrates on the analysis of the asymptotic rate of convergence of Laplacian dynamical systems, based on the well-known results from algebra and algebraic graph theory. Typically, the works that consider applications of Laplacian dynamical systems, present standard estimates of the rate of convergence exploiting the so called Fiedler number, the smallest in absolute value nonzero eigenvalue of the corresponding Laplacian matrix. It happens that improved bounds can be obtained by expanding the Fiedler number and extractind an additional factor of n2, with n being the size of the system.


Bibliogr.: 13 refs.


Use of Randomized Algorithm in the Identification of the Model Parameters of Dynamic Plants

V. M. Ponyatskiy

KBP, Tula

kbkedr@tula.net, pwmru@rambler.ru


Key words: Dynamic plant, model, signal, noise, estimate, gain coefficient.


We consider the problem of performance evaluation of control system elements from the measured data signals in the laboratory or field tests. These signals have a number of features (presence of signal noise, time-variance, etc.). Conventionally, in the presence of Gaussian noise, signal processing is based on Kalman filtering. In the works by O.N. Granichin, randomized algorithms are used for the identification of linear models of dynamic plants when measuring offset. The paper offers continuous and discrete-time algorithms for processing the measured signals obtained in the framework of Kalman filtering techniques and allows for estimating the coefficients of nonlinear models with almost arbitrary noise. Experiments performed in Matlab and further analysis of the results show that the estimates of the model parameters of the dynamic plant using the designed randomized identification algorithms are insensitive to almost arbitrary interference, unlike conventional algorithms based on Kalman filtering which do not provide estimates of the model parameters in these conditions.


Bibliogr.: 7 refs.