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...

Ngày tải lên: 21/01/2014, 06:20

... 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...

Ngày tải lên: 21/01/2014, 06:20

... 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...

Ngày tải lên: 26/01/2014, 07:20

... 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...

Ngày tải lên: 26/01/2014, 07:20

... 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...

Ngày tải lên: 23/12/2013, 07:19

... 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...

Ngày tải lên: 20/01/2014, 11:20

... 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...

Ngày tải lên: 20/01/2014, 11:20

... 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...

Ngày tải lên: 20/01/2014, 11:20

... 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...

Ngày tải lên: 20/01/2014, 11:20

... 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...

Ngày tải lên: 20/01/2014, 11:20