introduction independent component analysis

... the components yi should be statistically independent This means that the value of any one of the components gives no information on the values of the other components In fact, in factor analysis ... the source separation problem, the original signals were the independent components” of the data set 1.3 INDEPENDENT COMPONENT ANALYSIS 1.3.1 Definition We have now seen that the problem of blind ... 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 least find components...

Ngày tải lên: 13/12/2013, 14:15

... by principal component analysis (PCA); see Sections 13.1.2 and 13.2.2 In noisy ICA, we also encounter a new problem: estimation of the noise-free realizations of the independent components (ICs) ... consider the ~ noisy independent components, given by si = si + ni , and rewrite the model as x = A~ s (15.3) We see that this is just the basic ICA model, with modified independent components What ... model This way we can estimate the mixing matrix and the noisy independent components The estimation of the original independent components from the noisy ones is an additional problem, though;...

Ngày tải lên: 17/10/2013, 19:15

... ESTIMATION OF THE INDEPENDENT COMPONENTS Maximum likelihood estimation Many methods for estimating the mixing matrix use as subroutines methods that estimate the independent components for a known ... methods for reconstructing the independent components, assuming that we know the mixing matrix Let us denote by m the number of mixtures and by n the number of independent components Thus, the mixing ... small, the (t) are the realizations of the independent components, and C is an irrelevant constant The functions fi are the log-densities of the independent components Maximization of (16.7) with...

Ngày tải lên: 20/10/2013, 10:15

... unknown realvalued m -component mixing function, and is an n-vector whose elements are the n unknown independent components Assume now for simplicity that the number of independent components n equals ... : : : xn into n independent components y1 : : : yn , giving a solution for the nonlinear ICA problem This construction also clearly shows that the decomposition in independent components is by ... 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 of hidden neurons...

Ngày tải lên: 20/10/2013, 10:15

... means that simply finding a matrix so that the components of the vector C A V z(t) = Vx(t) (18.3) are white, is not enough to estimate the independent components This is because there is an infinity ... infinity of different matrices that give decorrelated components This is why in basic ICA, we have to use the nongaussian structure of the independent components, for example, by minimizing the higher-order ... time-lagged covariances only This is in contrast to ICA using higher-order information, where the independent components are allowed to have identical distributions Further work on using autocovariances...

Ngày tải lên: 24/10/2013, 08:15

... the signal x(t) to be deconvolved Estimating just one independent component , we obtain the original deconvolved signal s(t) If several components are estimated, they correspond to translated ... one independent component, which x x 364 CONVOLUTIVE MIXTURES AND BLIND DECONVOLUTION is easier than estimating all of them In convolutive BSS, however, we often need to estimate all the independent ... assumed to be time -independent constants, and the number of terms over which the convolution index k runs is finite Again, we observe only the mixtures xi (t), and both the independent source...

Ngày tải lên: 24/10/2013, 08:15

... 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 dependencies between the components ... methods of independent subspaces or topographic ICA, on the other hand, we assume that we cannot really find independent components; instead we can find groups of independent components, or components ... that the components si are independent However, ICA is often applied on data sets, for example, on image data, in which the obtained estimates of the independent components are not very independent, ...

Ngày tải lên: 28/10/2013, 15:15

... into independent components One can always obtain uncorrelated components, and this is what we obtain with FastICA In image feature extraction, however, one can clearly see that the ICA components ... processing the signals, for example, to compress or denoise them Naturally, we shall use independent component analysis (ICA) as the principal model for natural images We shall also consider the extensions ... must note that ICA applied to image data usually gives one component representing the local mean image intensity, or the DC component This component normally has a distribution that is not sparse;...

Ngày tải lên: 28/10/2013, 15:15

... the existence of statistically independent source signals, their instantaneous linear mixing at the sensors, and the stationarity of the mixing and the independent components (ICs) The independence ... concomitant sound Principal component analysis (PCA) has often been used to decompose signals of this kind, but as we have seen in Chapter 7, it cannot really separate independent signals In fact, ... response components For each component presented in Fig 22.4 a and Fig 22.4 b, left, top and, right side views of the corresponding field pattern are shown Note that the first principal component...

Ngày tải lên: 07/11/2013, 09:15

... user’s subsequent transmitted symbols are assumed to be independent, these products are also independent for a given user i Denote the independent sources a1 m b1 m : : : aLm bKm by yi (m) i ... cost function can be separated, and the different independent components can be found one by one, by taking into account the previously estimated components, contained in the subspace spanned by ... minimization task becomes much simpler [344] Complexity minimization then reduces to principal component analysis of temporal correlation matrices This method is actually just another example of blind...

Ngày tải lên: 07/11/2013, 09:15

... time-varying underlying factor or independent component sj (t) on the measured time series is approximately linear The assumption of having some underlying independent components in this specific application ... mean and unit variance), the independent components 444 OTHER APPLICATIONS 20 40 28 48 16 20 40 28 48 16 20 40 28 48 16 20 40 28 48 16 Fig 24.2 Four independent components or fundamental factors ... different orders in the classic AR prediction method for each independent component In reality, especially in real world time series analysis, the data are distorted by delays, noise, and nonlinearities...

Ngày tải lên: 07/11/2013, 09:15

... (Hardback); 0-471-22131-7 (Electronic) What is Independent Component Analysis? In this chapter, the basic concepts of independent component analysis (ICA) are defined We start by discussing a couple ... distribution Now let us mix these two independent components Let us take the following mixing matrix: A0 = 10 10 (7.13) 156 WHAT IS INDEPENDENT COMPONENT ANALYSIS? Fig 7.6 The joint distribution ... vertical axis: s2 158 WHAT IS INDEPENDENT COMPONENT ANALYSIS? Fig 7.9 The joint distribution of the observed mixtures x1 and x2 , obtained from supergaussian independent components Horizontal axis:...

Ngày tải lên: 23/12/2013, 07:19

... (especially maximum nongaussianity) are able to estimate single independent components, whereas others need to estimate all the components at the same time Some objective functions use nonpolynomial ... covariance matrix) can be utilized, and therefore, the independent components can be actually separated, which is not possible by PCA and classic factor analysis Often, the data is preprocessed by whitening ... showing how to estimate the independent components oneby-one This is possible by a deflationary orthogonalization of the estimates of the individual independent components With every estimation method,...

Ngày tải lên: 23/12/2013, 07:19

... ESTIMATION OF THE INDEPENDENT COMPONENTS Maximum likelihood estimation Many methods for estimating the mixing matrix use as subroutines methods that estimate the independent components for a known ... methods for reconstructing the independent components, assuming that we know the mixing matrix Let us denote by m the number of mixtures and by n the number of independent components Thus, the mixing ... small, the (t) are the realizations of the independent components, and C is an irrelevant constant The functions fi are the log-densities of the independent components Maximization of (16.7) with...

Ngày tải lên: 20/01/2014, 11:20

... unknown realvalued m -component mixing function, and is an n-vector whose elements are the n unknown independent components Assume now for simplicity that the number of independent components n equals ... : : : xn into n independent components y1 : : : yn , giving a solution for the nonlinear ICA problem This construction also clearly shows that the decomposition in independent components is by ... 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 of hidden neurons...

Ngày tải lên: 20/01/2014, 11:20

... means that simply finding a matrix so that the components of the vector C A V z(t) = Vx(t) (18.3) are white, is not enough to estimate the independent components This is because there is an infinity ... infinity of different matrices that give decorrelated components This is why in basic ICA, we have to use the nongaussian structure of the independent components, for example, by minimizing the higher-order ... time-lagged covariances only This is in contrast to ICA using higher-order information, where the independent components are allowed to have identical distributions Further work on using autocovariances...

Ngày tải lên: 20/01/2014, 11:20

... the signal x(t) to be deconvolved Estimating just one independent component , we obtain the original deconvolved signal s(t) If several components are estimated, they correspond to translated ... one independent component, which x x 364 CONVOLUTIVE MIXTURES AND BLIND DECONVOLUTION is easier than estimating all of them In convolutive BSS, however, we often need to estimate all the independent ... assumed to be time -independent constants, and the number of terms over which the convolution index k runs is finite Again, we observe only the mixtures xi (t), and both the independent source...

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 dependencies between the components ... methods of independent subspaces or topographic ICA, on the other hand, we assume that we cannot really find independent components; instead we can find groups of independent components, or components ... that the components si are independent However, ICA is often applied on data sets, for example, on image data, in which the obtained estimates of the independent components are not very independent, ...

Ngày tải lên: 20/01/2014, 11:20

... the existence of statistically independent source signals, their instantaneous linear mixing at the sensors, and the stationarity of the mixing and the independent components (ICs) The independence ... concomitant sound Principal component analysis (PCA) has often been used to decompose signals of this kind, but as we have seen in Chapter 7, it cannot really separate independent signals In fact, ... response components For each component presented in Fig 22.4 a and Fig 22.4 b, left, top and, right side views of the corresponding field pattern are shown Note that the first principal component...

Ngày tải lên: 20/01/2014, 11:20