Tài liệu Independent component analysis P8 pdf
Tài liệu Independent component analysis P8 pdf
... of independent components. For pedagogical purposes, let us
assume in this motivating section that all the independent components have identi-
cal distributions. Estimating the independent components ... supergaussian independent components and
then take this, or its sign, as the value of . For example, if is the tanh function,
then works for supergaussian independent components.
St...
Tài liệu Independent component analysis P1 pdf
... of independent components:
.
.
.
.
.
.
(1.6)
where is some unknown matrix. Independent component analysis now consists of
estimating both the matrix and the , when we only observe the .Note
INDEPENDENT ... which the components are statistically independent. In
practical situations, we cannot in general find a representation where the components
are really independent, but we can at...
Tài liệu Independent component analysis P3 pdf
... Optimization
Methods
The main task in the independent component analysis (ICA) problem, formulated in
Chapter 1, is to estimate a separating matrix that will give us the independent
components. It also became ... MATRIX GRADIENTS
3.1.1 Vector gradient
Consider a scalar valued function of variables
57
Independent Component Analysis. Aapo Hyv
¨
arinen, Juha Karhunen, Erkki Oja
Copy...
Tài liệu Independent component analysis P12 pdf
... principal component analysis (PCA). These methods give
components that are uncorrelated linear combinations of input variables, as explained
in Chapter 6. We will show that independent components ... independent of
the orientation. Whether the criterion results in independent components, depends
strongly on the nonlinearities . A more detailed analysis of the criterion (12.25)
and...
Tài liệu Independent Component Analysis - Chapter 14: Overview and Comparison of Basic ICA Methods pptx
... showing how to estimate the independent components one-
by-one. This is possible by a deflationary orthogonalization of the estimates of the
individual independent components.
With every estimation ... the
classic optimization methods, for example, (stochastic) gradient methods and Newton
273
Independent Component Analysis. Aapo Hyv
¨
arinen, Juha Karhunen, Erkki Oja
Copyright
2001...
Tài liệu Independent Component Analysis - Chapter 16: ICA with Overcomplete Bases ppt
... Overcomplete
Bases
A difficult problem in independent component analysis (ICA) is encountered if the
number of mixtures is smaller than the number of independent components .This
means that the mixing ... obtain the independent
components (ICs) by simply inverting the mixing matrix . Therefore, even if
we knew the mixing matrix exactly, we could not recover the exact values of the
i...
Tài liệu Independent Component Analysis - Chapter 17: Nonlinear ICA ppt
... unknown real-
valued -component mixing function, and is an -vector whose elements are the
unknown independent components.
Assume now for simplicity that the number of independent components equals
the ... quite nonlinear,
because nonlinear factor analysis is able to explain the data with 10 components
equally well as linear factor analysis (PCA) with 21 components.
Different numbers...
Tài liệu Independent Component Analysis - Chapter 18: Methods using Time Structure ppt
... minimization.
18
Methods using Time
Structure
The model of independent component analysis (ICA) that we have considered so
far consists of mixing independent random variables, usually linearly. In many
applications, ... that the components
of the vector
(18.3)
are white, is not enough to estimate the independent components. This is because
there is an infinity of different matrices
t...
Tài liệu Independent Component Analysis - Chapter 19: Convolutive Mixtures and Blind Deconvolution pptx
... convolutive
mixtures.
Blind deconvolution is a signal processing problem that is closely related to basic
independent component analysis (ICA) and blind source separation (BSS). In com-
munications and related areas, ... and
after that separation of convolutive mixtures. Many techniques for convolutive mix-
355
Independent Component Analysis. Aapo Hyv
¨
arinen, Juha Karhunen, Erkki...
Tài liệu Independent Component Analysis - Chapter 20: Other Extensions pptx
... by independent subspaces
analysis, to be explained next.
20.2.2 Independent subspace analysis
Independent subspace analysis [204] is a simple model that models some dependen-
cies between the components. ... independence of the components. In the model
called independent subspace analysis, the components are divided into subspaces that
are independent, but the components inside...
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