Questions tagged [independent-component-analysis]

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

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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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What is the difference in the “solutions” of FastICA and Infomax?

So, I feel like I can understand the basic difference between FastICA and Infomax: Infomax tries to minimize the mutual information between variable. FastICA tries to maximize the non-gaussianity of ...
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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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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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When will PCA be equivalent to ICA?

$X = AS$ where $A$ is my mixing matrix and each column of $S$ represents my sources. $X$ is the data I observe. If the columns of $S$ are independent and Gaussian, will the components of PCA be ...
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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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PCA vs FA vs ICA for dimensionality reduction in questionaire data

I am trying to identify personality traits underlying the multidimensional data from a questionnaire. In more abstract terms this means reducing the dimensionality of my data from N-dimensional (where ...
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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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520 views

Blind source separation of convex mixture?

Suppose I have $n$ independent sources, $X_1, X_2, ..., X_n$ and I observe $m$ convex mixtures: \begin{align} Y_1 &= a_{11}X_1 + a_{12}X_2 + \cdots + a_{1n}X_n\\ ...&\\ Y_m &= a_{m1}X_1 + ...
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Independent Component Analysis (ICA): fewer sources than features (fastICA)

I am trying to understand how the ICA by A. Hyvärinen, J. Karhunen, E. Oja (2001) works in practice. In particular, I have problems trying to understand its application to factor-analysis-kind of ...
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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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Proof that the mutual information I(X;Y) between two random variables X and Y is 0 if and only if X and Y are independent

On the Wikipedia of 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 $p(x,y)=p(x)p(y)$. ...
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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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135 views

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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Conduct ICA on a subset of the dataset and using rest of the data to extract timeseries for prediction (CV-classifier)?

I have an issue regarding cross-validation and dimensionality reduction, specifically in the realms of neuroimaging. What I found out so far is that: if I wanted to conduct ICA on a dataset in order ...
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PCA, ICA and Laplacian eigenmaps

Question I am very interested in the Laplacian Eigenmaps method. Currently, I am using it to do dimension reduction on my medical data sets. However, I have run into a problem using the method. For ...
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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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ICA for Noise Reduction over a Dataset

Suppose my dataset consists of $N$ example vectors $\mathbf{x}_{1}, \ldots, \mathbf{x}_{N}$ where $\mathbf{x}_{n} \in \mathbb{R}^{p}$ $\forall n$. I assume that each vector $\mathbf{x}_{n}$ is ...
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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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1answer
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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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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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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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Evaluate output of different dimensionality reduction methods

I used PCA, ICA, and FA to perform dimensionality reduction on my data. How can I measure which method performed best? If I reduce my data to 3 dimensions and plot it, what type of trends would ...
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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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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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1answer
630 views

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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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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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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What is the relationship between independent component analysis and factor analysis?

I am new to Independent Component Analysis (ICA) and have just a rudimentary understanding of the the method. It seems to me that ICA is similar to Factor Analysis (FA) with one exception: ICA assumes ...
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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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What is mean by the non-gaussianity in the independent component analysis(ICA)?

What is mean 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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434 views

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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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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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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Significance of a source phase in a complex ICA

I am using complex-valued ICA to extract sources for complex-valued sensor data. One of the three ambiguities for complex ICA is phase ambiguity, i.e., phase rotation $\exp(i\theta_k)$ of the sources $...
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1answer
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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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Using kurtosis to assess significance of components from independent component analysis

In PCA eigenvalues determine the order of components. In ICA I am using kurtosis to obtain the ordering. What are some accepted methods to assess the number, (given I have the order) of components ...
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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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Making sense of independent component analysis

I have seen and enjoyed the question Making sense of principal component analysis, and now I have the same question for independent component analysis. I mean I want to make a comprehensive question ...
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1answer
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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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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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296 views

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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Project new data using independent components analysis

I’m trying to project new data into a space I created with icafast. The R package ica does not come with it's own predict function. Here is my attempt to do so. This is in vein of what I can do with ...
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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 ...