Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [independent-component-analysis]

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

When a signal is additively composed of S independent sources and M >= S independent measurements of the signal are available, then the signal may be separated into estimated sources. The standard example is the "cocktail party problem," where recordings from M microphones are used to separate the speech signals of S party-goers talking simultaneously.

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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 that the observed random variables are a linear…
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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 + a_{m2}X_2 + \cdots + a_{mn}X_n \end{align} with $\sum_j…
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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 about the intuitive ways to understand ICA? I…
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How do I select the number of components for independent components analysis?

In the absence of good a priori guesses about the number of components to request in Independent Components Analysis, I'm looking to automate a selection process. I think that a reasonable criterion might be the number that minimizes the global…
Mike Lawrence
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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 example, I have some data (spectra signals), and 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 between two data sets. So find pca like factors,…
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Does ICA require to run PCA first?

I reviewed an application-based paper saying that applying PCA before applying ICA (using fastICA package). My question is, does ICA (fastICA) require PCA to be run first? This paper mentioned that ... it is also argued that pre-applying PCA…
Samo Jerom
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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 matter what the mixing matrix $A$ is. Hence, it is…
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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 that are singificant apart from prior knowledge…
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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, but the PCs are orthogonal, are they not? I am a bit…
January
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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. But I am not able to understand it. Please…
ironman
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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 extremely similar to that of ICA? Is this the only…
Swiss Army Man
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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 N is the number of questions) to a more…
TheChymera
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Why do we whiten the data before running ICA?

Why do we usually pre-whiten the data before doing independent components analysis (ICA), like making all eigenvalues equal? Doesn't that take away some information regarding the data?
user3684606
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SVD & ICA -- or why doesn't the other rotation matrix in SVD solve for independent components?

When data are a linear mixture of non-gaussian sources, it can be shown that with a rotation, an independent rescaling of each of the rotated axes, and a second rotation you can recover the original, independent axes. Singular value decomposition…
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