Questions tagged [independent-component-analysis]

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

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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 (...
526 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 + ...
54 views

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 ...
33 views

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 ...
53 views

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 ...
56 views

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 ...
1k views

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 ...
35 views

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) ...
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 ...
16 views

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 ...
26 views

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 ...
26 views

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 ...
104 views

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 $p(x,y)=p(x)p(y)$. ...
53 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 ...
147 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: ...
35 views

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 ...
3k views

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 ...
42 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-...
42 views

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 ...
17 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, ...
120 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 Ã is the mixing matrix of the whitened data matrix z. My question is: If the matrix ...
34 views

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 ...
68 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 ...
204 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 ...
74 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 ...
2k views

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 ...
11 views

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 ...
44 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 ...
559 views

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 ...
758 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 ...
2k 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 ...
32 views

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 ...
36k views

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 ...
140 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 ...
1k 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....
450 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 ...
706 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 ...
1k 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 ...
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 ...