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

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feature selection and classification - train and test on the sample?

I have a dataset of 93 records and 45 radiomics variables from various CT scans. I wanted to check if age and sex could be classified by the variables so I made a new variable with both sex and age. I ...
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1answer
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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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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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64 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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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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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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68 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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262 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
51 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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49 views

How to do and measure success of dimensionality reduction using ICA?

I have understood that PCA and ICA are two dimensionality reduction techniques similar to each other, with ICA being more powerful due to not limiting itself only to rotational transformations. PCA-...
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Why can we use time-ordered data to make estimates?

Let's say I'm trying to carry out independent component analysis (ICA). ICA operates by maximizing the statistical independence of the transformed variables. Another way to say this is that ICA ...
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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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225 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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501 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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97 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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1k 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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116 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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333 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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1answer
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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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379 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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1k 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
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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
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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
3k 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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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
36 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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148 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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119 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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155 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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357 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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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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149 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 ...
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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?
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Is it a good idea to use log scale on scree plots for PCA/ICA/FA?

I always found the concept of determining the "ideal" number of components/factors for an ICA/PCA/FA via a scree plot useful and quick, but also a bit shaky. In an effort to try to make the scree ...
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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 ...
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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, ...
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Extracting nonorthogonal sources in ICA/PCA/blind source seperation problem

My problem is essentially a 'blind source separation' problem. I have 3 non-orthogonal sources (or basis functions) and N random linear combinations (mixes) of said sources. My problem is to obtain ...
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Can I say independent components of ICA are also linear independent?

In other words, does the independent components form a vector basis? EDIT:Let'me try to clarify the question If I calculate $n$ independent components for a given set of $n$ dimensional ...
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ICA - How do I know the optimal number of components?

I'm trying to use the FastICA algorithm in MATLAB. My question is: How do I know, which is the optimal number of ICs? I have a matrix of 62 samples with 1009 signals and the FastICA algorithm returns ...
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1answer
65 views

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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PCA, ICA and Laplacian eigenmaps

I am very interested in the Laplacian eigenmaps method. Currently, I am using it to do dimension reduction for my medical data sets. However, I have run into a problem using the method. For example,...
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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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802 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 ...
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673 views

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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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 ...