# Questions tagged [ica]

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

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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 ...
29 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) ...
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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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### 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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### 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 ...
38 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 $p(x,y)=p(x)p(y)$. ...
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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 ...
36 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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### 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 Ã 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 ...
126 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: ...