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Оглавление |
Страницы |
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Stochastic
optimization for unsupervised feature learning |
3-16 |
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2 |
Some
auxiliary algorithms for the problem of state-minimization of
nondeterministic finit automata |
17-29 |
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3 |
A note on
the Fiedler number and convergence rate of Laplacian
systems |
30-35 |
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4 |
Use of
randomized algorithms in the identification of the model parameters of dynamic
plant |
36-44 |
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
ma.zubova@gmail.com
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
malkovskynv@gmail.com
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.