Questions tagged [ica]

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

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What kind of a matrix factorization is appropriate for my problem?

I have the following problem: I measure mass concentrations of a pollutant 'p' in n stations (same pollutant in all stations). And I have many observations. Theoretically, I believe that if I assume ...
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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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32 views

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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43 views

How are the signs of the loadings in ICA interpreted?

In my novice understanding of ICA, we generate two matrices: a source matrix, which describes the contribution of variables to the independent components (analogous to loadings in PCA..?) and the ...
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15 views

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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58 views

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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33 views

ICA with a Laplace distribution

It's pretty common to set up ICA with a logistic distribution, but how would you find the loss and gradient with a Laplace distribution?
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105 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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152 views

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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51 views

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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39 views

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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49 views

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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521 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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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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126 views

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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1answer
394 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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2answers
59 views

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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533 views

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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869 views

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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907 views

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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1answer
62 views

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 component analysis ...
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588 views

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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1k views

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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242 views

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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2k views

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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270 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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803 views

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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3k views

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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1answer
588 views

What does the number of independent components produced by ICA depend on?

I'm a student working on my bachelor thesis performing independent component analysis (ICA) on some fMRI data using MELODIC FSL. I would like to ask some questions regarding the results of ICA. ...
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2k views

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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1answer
97 views

Is it possible to apply PCA to the reconstructed data of ICA?

I have read that it is not possible to verify the variance and order of independent component extracted from ICA. So, I reconstructed the spectra from matrix A and ST(independent component) then ...
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1answer
5k views

Why are we using ICA? [duplicate]

I am new to Independent Component Analysis (ICA) and have a rudimentary understanding of the method. I understand that PCA finds vectors on which the projected data has maximum variance. ICA, on ...
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1answer
6k views

The Independence in Independent Component Analysis - Intuitive Explanation

I could use a little bit of help in understanding a concept with regards to ICA: ICA decomposes a multivariate signal into 'independent' components through 1. orthogonal rotation and 2. maximizing ...
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3answers
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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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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
38 views

Identifiability of a particular Independent Component Analysis model

I am considering the model : $$ \mathbf{x} = \mathbf{A}\mathbf{s} $$ where $\mathbf A \in \mathcal{M}_{n,p}(\mathbb{R})$ and $\mathbf s \in \mathbb{R}^{p}$ such that the entries of $\mathbf s$ are i....
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207 views

ICA: plotting independent components

How do I find the directions of the independent components if I have already found the mixing matrix? Let's say that I have this mixing matrix: $$\mathcal W = \begin{bmatrix} 2 & -2 \\ 2 & 4 ...
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156 views

Reducing number of variables for Independent Component Analysis

Say I have a dataset with $n$ observations of $p$ random variables. Since $p$ is "large" (mine is 72), I would like to perform a fastICA only on a subset of $k$ variables, maintaining the same number ...
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251 views

What is the difference between independent subspace analysis and independent component analysis?

What is the difference between independent subspace analysis (ISA) and independent component analysis (ICA)?
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507 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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3k views

Linear independence vs statistical independence (PCA and ICA)

I'm reading this interesting paper on application of ICA to gene expression data. The authors write: [T]here is no requirement for PCA components to be statistically independent. That is true, ...
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275 views

Independent component analysis with nonnegative mixing matrix

In independent component(s?) analysis, I have the observed signal, $O$, the mixing matrix, $A$, and the source matrix, $S$, with $O ≈ AS$ I've found some literature on ICA with the sources assumed to ...