arXiv subjects

Vladislav Gennadievich Malyshkin

Publications and source records attributed to Vladislav Gennadievich Malyshkin.

23 records · Page 2Linked to original sources

arXiv2015

Features in Energy Accumulation in Double Layer on the surface of Graphene Material

An application of quantum size carbon structures--graphenes as electrodes of supercapacitors is studied. A fundamental limit of energy and power density arising from quantum nature of objects due to singularity in graphene density of states near Dirac point is determined and technical solutions to partially offset the negative factors are considered. The maximum possible specific capacitance of nanostructured electrode materials is determined.

physics.chem-ph↗

arXiv2015

Radon-Nikodym approximation in application to image analysis

For an image pixel information can be converted to the moments of some basis $Q_k$, e.g. Fourier-Mellin, Zernike, monomials, etc. Given sufficient number of moments pixel information can be completely recovered, for insufficient number of moments only partial information can be recovered and the image reconstruction is, at best, of interpolatory type. Standard approach is to present interpolated value as a linear combination of basis functions, what is equivalent to least squares expansion. However, recent progress in numerical stability of moments estimation allows image information to be recovered from moments in a completely different manner, applying Radon-Nikodym type of expansion, what gives the result as a ratio of two quadratic forms of basis functions. In contrast with least squares the Radon-Nikodym approach has oscillation near the boundaries very much suppressed and does not diverge outside of basis support. While least squares theory operate with vectors $ $, Radon-Nikodym theory operates with matrices $ $, what make the approach much more suitable to image transforms and statistical property estimation.

cs.CV↗

arXiv2015

Norm-Free Radon-Nikodym Approach to Machine Learning

For Machine Learning (ML) classification problem, where a vector of $\mathbf{x}$--observations (values of attributes) is mapped to a single $y$ value (class label), a generalized Radon--Nikodym type of solution is proposed. Quantum--mechanics --like probability states $ψ^2(\mathbf{x})$ are considered and "Cluster Centers", corresponding to the extremums of $ /<ψ^2(\mathbf{x})>$, are found from generalized eigenvalues problem. The eigenvalues give possible $y^{[i]}$ outcomes and corresponding to them eigenvectors $ψ^{[i]}(\mathbf{x})$ define "Cluster Centers". The projection of a $ψ$ state, localized at given $\mathbf{x}$ to classify, on these eigenvectors define the probability of $y^{[i]}$ outcome, thus avoiding using a norm ($L^2$ or other types), required for "quality criteria" in a typical Machine Learning technique. A coverage of each `Cluster Center" is calculated, what potentially allows to separate system properties (described by $y^{[i]}$ outcomes) and system testing conditions (described by $C^{[i]}$ coverage). As an example of such application $y$ distribution estimator is proposed in a form of pairs $(y^{[i]},C^{[i]})$, that can be considered as Gauss quadratures generalization. This estimator allows to perform $y$ probability distribution estimation in a strongly non--Gaussian case.

cs.LG↗

arXiv2015

Multiple-Instance Learning: Radon-Nikodym Approach to Distribution Regression Problem

For distribution regression problem, where a bag of $x$--observations is mapped to a single $y$ value, a one--step solution is proposed. The problem of random distribution to random value is transformed to random vector to random value by taking distribution moments of $x$ observations in a bag as random vector. Then Radon--Nikodym or least squares theory can be applied, what give $y(x)$ estimator. The probability distribution of $y$ is also obtained, what requires solving generalized eigenvalues problem, matrix spectrum (not depending on $x$) give possible $y$ outcomes and depending on $x$ probabilities of outcomes can be obtained by projecting the distribution with fixed $x$ value (delta--function) to corresponding eigenvector. A library providing numerically stable polynomial basis for these calculations is available, what make the proposed approach practical.

cs.LG↗

arXiv2015

Multiple--Instance Learning: Christoffel Function Approach to Distribution Regression Problem

A two--step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the second step, build outcome variable Christoffel function, but use the bag's Christoffel function value at given point as the weight for the bag's outcome. The approach allows the result to be obtained in closed form and then to be evaluated numerically. While most of existing approaches minimize some kind an error between outcome and prediction, the proposed approach is conceptually different, because it uses Christoffel function for knowledge representation, what is conceptually equivalent working with probabilities only. To receive possible outcomes and their probabilities Gauss quadrature for second--step measure can be built, then the nodes give possible outcomes and normalized weights -- outcome probabilities. A library providing numerically stable polynomial basis for these calculations is available, what make the proposed approach practical.

cs.LG↗