Developments and Applications of Nonlinear Principal Component Analysis
The algorithm of the basic components of a linear analysis. Work on nonlinear PCA, or NLPCA, autoassociative's neural networks, principal curves and manifolds, kernel the combination's of these approaches. The problem areas that require research.
Подобные документы
- 1. Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit
Auto-associative models as a new tool for building nonlinear principal component analysis methods. The successive approximations of a dataset by manifolds of increasing dimensions. The theoretical comparison between PCA and auto-associative models.
статья, добавлен 08.02.2013 Linear Principal Components. A linear model formulation. The Principal Curve and Surface models. Theory for principal curves and surfaces. Algorithmic details. Estimation of curves and surfaces. Gold assay pairs. Generalized linear principal components.
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учебное пособие, добавлен 25.11.2013Normed linear spaces. Contraction mapping theorem. Applications to differential and integral equations. Linear transformations. Product spaces and Fubini's theorem. Projection and self-adjoint operators. Gram-Schmidt orthonormalization. Fourier analysis.
курс лекций, добавлен 03.07.2013Approximations in Scientic Computation, сomputer Arithmetic, mathematical Software. Linear Systems, solving Linear Systems, Iterative Methods for Linear Systems. Linear Least Squares, eigenvalues and Singular Values, Nonlinear Equations, optimization.
учебное пособие, добавлен 25.11.2013Practical methods for solving nonlinear equations. Metrological support of iterative methods for solving nonlinear equations with inaccurate initial data. Modeling the behavior of iterative methods for different values of initial data and their errors.
статья, добавлен 11.09.2022The study of optimal control problems for linear parabolic equations with unbounded coefficients in the main part of elliptic operator. The peculiarities of this type of equations. Setting of the optimal control problem and its preliminary analysis.
статья, добавлен 23.06.2016The unsupervised methods required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis is a promising approach for the analysis of genome-wide transcriptomic data.
статья, добавлен 08.02.2013Comparative analysis for the algorithm for solving two-parameter game models. Comparison of the values of the game price and the probabilities of strategies. The accuracy and reliability of the results are analyzed with the help of a numeric example.
статья, добавлен 11.07.2018- 12. Improving the mathematical model of the dynamics for underwater vehicles with asymmetrical hulls
Model of motion, which takes into account the asymmetry of hulls, infiltration processes and surface waves in the form of a system of nonlinear differential equations. Estimation of the error as a function of the magnitude of the initial velocities.
статья, добавлен 25.10.2016 Proving of the theorem on a normal limit distribution of the normalized number of false solutions of a beforehand consistent system of nonlinear random equations over the field GF(2) with additional condition on the number of nonzero components.
статья, добавлен 25.03.2016- 14. Algorithms to determine solvability of linear integro-differential equations with analytic functions
Further, we found sufficient conditions on linear Volterra integro-differential equations of the third kind to be correct in analytical functions which generalize the well-known fact of correctness of a Volterra integral equation of the second kind.
статья, добавлен 12.08.2020 - 15. Elliptic curves
Affine plane curves. A brief introduction to the p-adic numbers. Regular functions on projective curves. Plane projective cubic curves with a rational inflection point. Reduction of an elliptic curve. Cohomology of finite, infinite Galois groups.
учебное пособие, добавлен 03.07.2013 Consideration the results of simulation definition spectral analysis of signals, which consist of harmonic signals with noninteger periods. Studied the change of spectral components by changing width of Fourier transformation by discarding samples.
статья, добавлен 29.01.2016Finding common solutions of linear differential equations of the fourth order, the coefficients of which satisfy the system of three differential equations of the first order. The problem of conformal mapping of polygons, whose sides are arcs of circles.
статья, добавлен 04.02.2017Assessment of convergence result for the sequential procedure in the form of alternating maximization to the maximum likelihood estimation for a family of models - Generalized linear models. Variable Linear Regression procedure. Using techniques ALS.
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статья, добавлен 25.03.2016Combinatorial description. Teichmuller curves. Recurrence relation. Asymptotics of numbers of branched coverings of a torus, volumes of moduli spaces of holomorphic differentials. The character of the infinite wedge representation. Cylinder decomposition.
контрольная работа, добавлен 26.08.2016Rules for binary addition, multiplication, subtraction and division. Time complexity of extended Euclidean algorithm. Existence of multiplicative inverse. Cancellation law of congruence. Introduction to finite field theory. Corollary of Euler’s theorem.
статья, добавлен 08.03.2014Provides the analysis of the connection existing between constituent components of a binomial expression. The need to study this connection is predetermined by the lack of a clear distinction between binomials and other types of formulaic language.
статья, добавлен 09.08.2022An optimal boundary control problem associated to the linear parabolic equation. The characteristic feature of this equation, skew-symmetric. A unique solution to the original optimal boundary control problem, singular character of the original matrix.
статья, добавлен 30.10.2016Yangian for gln is the associative algebra historically first example of the quantum group. Bethe subalgebras in Yangians, theories and concepts used in this problem. Analysis and proof of lemmas. The Cartan subalgebra of the regular diagonal matrices.
тезисы, добавлен 17.11.2015