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Questions tagged [independent-component-analysis]

Independent Component Analysis separates the additive combination of multiple signals into their estimated components.

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What is meant by the assumption of statistical independence among sources in Independent Component Analysis?

One of the underlying assumptions of independent component analysis (ICA) that I consistently see written is "statistical independence across the source signals". In the context of the ...
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Differences Between Independent Components from ICA Directly on Samples vs. Mixing Matrix from ICA on Features After PCA Dimensionality Reduction

My understanding is that for Independent Component Analysis (ICA), it is recommended to have more samples than features to avoid underdetermination which might cause convergence or stability issues. ...
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Independent Component Analysis (ICA): Why rotate whitened data by principal components instead of right singular vectors?

I have a data matrix $ X $ that is $n \times m$, where $n$ is the number of features and $m$ is the number of samples and $ n < m$. Let the Singular Value Decomposition (SVD) of $X$ be $$ X = U \...
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Do we need to scale our features before applying ICA, like in PCA?

I am reasonably certain that we don't need to scale data before applying ICA, like we do for the PCA. In PCA we do this because it assumes normal distribution of the features, and in ICA we don't ...
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Geometric Intuition Behind Whitening for ICA

I know there are a couple posts asking about why we whiten the data for ICA. I understand why we whiten to fix scaling invariants between the sources and to increase the computationally efficiency. ...
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Why is non-negative matrix factorization better than ICA in neuronal analysis

I've recently joined a neuroscience lab and am currently reading up on their pipeline to analyze 2-photon calcium imaging with single neuron resolution. The data consist of a movie where the pixel ...
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What does ICA using only one component return?

I understand that with multiple components, the result will be coefficients that lead to maximally independent series. When requesting only one component I'm unclear if it actually does optimization ...
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Is it possible to turn PCA into ICA by rotating the eigenvectors?

Assume that you have made a PCA analysis and you got your eigenvectors inside the projection matrix $W$. If you project your data $X$ with $W$, then you get the desired projected dimension. But PCA ...
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ICA and Gaussian: a misleading example

A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is ...
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Is the first independent component of independent component analysis always important?

I was looking at a neuroscience paper that used ICA to reduce dimensionality of calcium signaling profiles in 20 randomly selected neurons of a zebrafish brain. I presume that in Figure 2, ICA was ...
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Does blind source separation (ICA) work if channels of mixture are observed asynchronously?

Does Independent Component Analysis (ICA - fastICA, SOBI, etc.) work reliably when applied to a multidimensional mixture (observation) $X = (X^1, \cdots, X^d)$ if the different channels $X^i$ of the ...
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Why PCA is not considered in the taxonomy of blind source separation approaches?

Blind source separation (BSS) approaches are divided in the literature into four methods, including independent component analysis (ICA), sparse component analysis (SCA), and non-negative matrix ...
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How many sources can be detected in ICA?

Is there an upper (or even lower?) limit for the number of sources which can be identified in ICA?
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How to use ICA as a specific factor rotation in orthogonal factor model

I am trying to understand the way ICA is used as factor rotation in the traditional orthogonal factor model. The idea of using ICA as a specific factor rotation is often mentioned in the literature (...
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Why ICA doesn't work on Gaussian data

Examples I found explain this using standard Gaussian data, i.e. $\mathcal{N}(0, I)$ (e.g. in Andrew Ng CS229 lecture page 3), saying that if so, mixing matrix with arbitrary rotations can not be ...
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independence in independent component analysis

ICA is quite popular for analyzing brain images (e.g. group ICA). One common assumption/constraint is that the signals in the brain come from "independent spatial sources". I'm confused ...
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ICA: a question about the non-gaussian requirement

I'm new in the ICA processing and I'm trying to understand the non-gaussian requirement. I read that the problem is that, if the composed data is $\mathbf{x}=\mathbf{As}$ with $\mathbf{A}$ (unknown) ...
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Blind source separation using FastICA

Reading the example by scikit-learn on how to use the FastICA function, I couldn't understand the following plot: In the third plot ("ICA recovered signal") - why is the magnitude different ...
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Relationship between minimizing mutual information and maximizing non-Gaussianity in Independent Component Analysis (ICA)

In independent component analysis (ICA), we assume that the observe data $\bf{x}$ from $n$ channels come from linear mixing of $n$ independent sources $\bf{s}$: $$ \bf{x}=\bf{As} $$ And we try to find ...
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How can I show that two random variables are independent if their mutual information is 0?

On the Wikipedia page for mutual information, it says that $I(X;Y)=0$ if and only if $X$ and $Y$ are independent. I can proof that if $X$ and $Y$ are independent, then $I(X;Y)=0$, because $p(x,y)=p(x)...
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GO-GARCH using Fast-ICA rmgarch package with MVNORM distribution

R package rmgarch by Ghalanos estimates the GO-GARCH model using fast-ICA. I have read that ICA aims to separate a multivariate signal into additive sub-...
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Why signals can be assumed non-Gaussian in ICA?

I understand why assumption of non-gaussianity is needed in ICA-model. I just can't find any source for why some signals e.g sound signals can be assumed to be non-gaussian. Doesn't everything in ...
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whiteness vs Uncorrelatedness

While studying ICA in the book by Aapo Hyvarinen I found the following scentence: "A slightly stronger property than uncorrelatedness is whiteness. Whiteness of a zero-mean random vector, say y, ...
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ICA and orthogonality of Independent Components

In the book by Aapo Hyvärinen, it is shown that: Where z is the white vector of a data matrix x, s are the IC's and à is the mixing matrix of the whitened data matrix z. My question is: If the matrix ...
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Can I combine independent components from different models using PCA?

I have a set of independent components for each subject in my dataset (i.e. an ica model was generated for each subject). The samples used to generate each set of ICs are aligned across subjects, and ...
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FastICA results not exactly consistent on repetition

I have asked this on stack overflow but couldn't get an answer. I am using the fastICA implementation in R. Example code: ...
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Estimation of NegEntropy

I am trying to evaluate the different ICA algorithms. To do that, one of the measure which I use, is to estimate the non-gaussianity using NegEntropy. I am trying to find a formula/function which can ...
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Principal component analysis in two dimensions

During my studies, I stumbled upon the following exercise: We have the following joint probability distribution: $$p(x,y) = p(x) p(y|x)$$ $$p(x) = \mathcal{N}(0,1), p(y \mid x) = \frac{1}{2} \delta(y ...
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Blind source seperation on space data [closed]

in a uni project we gathered spectrum data from the ISS (time x frequency). The challenge is now to analyse this data and especially try to seperate the signals. As far as I understood it the common ...
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Making vectors independent of each other

Assume that I have three vectors $A, B, C$ containing information about a set of variables. There may be common information shared between these vectors, that is $A, B, C$ are not independent. What ...
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Testing statistical independence before using ICA

First a little bit of background. I'm interested in exploring the performance of Independent Component Analysis (ICA) in the context of disentangling intracranial EEG signals. These signals are ...
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What does ICA return?

I am confused with ICA. With PCA I understood that it always gives the components with maximum variance. What does ICA return? Does it return components with maximum independence? How to find best ...
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FastICA of orthonormal inputs

In Wikipedia page of FastICA it says FastICA seeks an orthogonal rotation of prewhitened data Which means if the input is orthonormal, so would be the output. This can be examined numerically but ...
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ICA for noise reduction of covariance matrix

Trying to understand ICA in the context of noise reduction of covariance matrices (of dimensionality M). I understand in PCA, you can reconstruct the covariance matrix by squaring the first N ...
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Doesn't the non-Gaussian source assumption of ICA render it practically useless?

Gaussian distributions appear everywhere in nature, indeed this was largely the justification for most classical methods' reliance on assumption of normality. ICA assumes non-Gaussian sources, indeed ...
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The lack of correlation determines the second-degree cross-moments (covariances) of a multivariate distribution?

It is given in the following image that lack of correlation determines the second-degree cross-moments (covariances) of a multivariate distribution,while in general statistical independence ...
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Why does the Independent Component Analysis require non-gaussian?

This I found on google while I was going through the Independent Component Analysis in unsupervised learning. Let x = As where A is the Mixing Matrix. So, Lets assume that s here is Gaussian ...
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What is meant by the non-gaussianity in the independent component analysis (ICA)?

What is meant by non-gaussianity in ICA? Why do we use in ICA? How is Non-Gaussianity is an important and essential principle in ICA estimation? Following is the statement I found in a research paper....
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Numerical Example of Independent Component Analysis

Can somebody explain ICA(Independently Component Analysis) with a small practical example over here. I have seen lot of programs and libraries written and you can just apply that to your data to find ...
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Connecting PCA singular values to generating parameters

I have a non-linear function of the following form $y_i = f(x_i,\theta)$ where $x_i$ is known and $\theta$ is a vector of parameters. I have generated $n$ realizations of $y_i$ by sampling from a ...
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Why are Gaussian distributions the only "forbidden" source distribution for ICA?

I know it's commonly asked why Gaussians are forbidden from use in independent components analysis. This is because a gaussian source distribution will result in the same observed distribution no ...
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Why is infinite data required to verify statistical independence

I've been reading about Independent Component Analysis and the FastICA algorithm. The wiki page for FastICA states: FastICA is an efficient and popular algorithm for independent component ...
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Understanding Natural gradient learning Independent component analysis

I am quite a novice to statistics and am currently fighting my way through the "Neural Networks and Machine Learning" Book by Haykin. (p.516-518) In the discussion about independent ...
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ICA, how to check for Gaussian components?

Independent Component Analysis (ICA) requires that at most one of the additive subcomponents of a multivariate signal is Gaussian. If I do not know the distributions of the subcomponents, how do I ...
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PCA is to CCA as ICA is to?

PCA looks for factors in data that maximize explained variance. Canonical correlation analysis (CCA), as far as I understand, is like an PCA but looks for a factors that maximize cross covariance ...
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ICA - independence of coefficients and maximizing independence

Hopefully this isn't too silly a question but I'm wondering how in independent component analysis when we've got independent coefficients then we identify parts of a face such as eyes, mouth, nose, ...
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Using only one mic in Cocktail Party Algorithm

So I came across this piece of code that separates 2 audio sources from 2 mixed audio sources has shown here: ...
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Why are gradient-based methods better for nonstationary environments?

In the book Independent Component Analysis (Hyvärinen et al. 2001), it is mentioned on page 178: The advantage of such gradient methods, closely connected to learning in neural networks, is that ...
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What is the advantage of FastICA over other ICA algorithms?

I have seen that FastICA is the only ICA algorithm implemented in many packages. What are the advantages of FastICA compared to other algorithms? What are its disadvantages?
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ICA - extract one non-Gaussian source among many Gaussian sources with a-priori information

I have $N$ mixtures consisting of one non-Gaussian source (I know the distribution) and many (more than $N$) Gaussian sources. I also know how my non-Gaussian source is mixed into the signal (I know ...
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