Independent Component Analysis separates the additive combination of multiple signals into their estimated components.
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26 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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0answers
11 views
Gaussianity and Whitening in ICA - The feeling and intuition behind it
I understand what ICA does at a high level but in the cocktail party problem context. All the examples, articles I have read take a similar problem to explain ICA where the aim is to derive the ...
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25 views
ICA vs EFA: scale ambiguity?
ICA (Independent Component Analysis) Model
$$s \sim \text{Non-Gaussian(parameters}_1)$$
$$x=As$$
EFA (Exploratory Factor Analysis) Model
$$z \sim \mathcal{N}(0,I)$$
$$\epsilon \sim \mathcal{N}(0,\...
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19 views
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
20 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 ...
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39 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 ...
2
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1answer
92 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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1answer
29 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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41 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 ...
5
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1answer
93 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....
2
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1answer
346 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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0answers
21 views
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 ...
7
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133 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 ...
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1answer
52 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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0answers
66 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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0answers
20 views
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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23 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 component analysis ...
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2answers
299 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 ...
6
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1answer
579 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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1answer
107 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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1answer
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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2answers
132 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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1answer
393 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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1answer
34 views
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 ...
2
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1answer
1k 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 ...
4
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1answer
399 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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2answers
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
80 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 ...
3
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1answer
4k 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 ...
2
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1answer
4k 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 ...
3
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2answers
811 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 ...
15
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2answers
3k views
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 ...
2
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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} $$
where $\mathbf A \in \mathcal{M}_{n,p}(\mathbb{R})$ and $\mathbf s \in \mathbb{R}^{p}$ such that the entries of $\mathbf s$ are i....
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1answer
154 views
ICA: plotting independent components
How do I find the directions of the independent components if I have already found the mixing matrix?
Let's say that I have this mixing matrix:
$$\mathcal W = \begin{bmatrix} 2 & -2 \\ 2 & 4 ...
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122 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 ...
2
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0answers
177 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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0answers
363 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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1answer
2k 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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1answer
160 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 ...
3
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2answers
2k views
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?
2
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1answer
421 views
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 ...
9
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3answers
4k views
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
...
3
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1answer
1k views
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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2answers
314 views
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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0answers
126 views
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 ...
3
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1answer
3k views
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 ...
1
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1answer
66 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 $...
9
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3answers
3k views
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,...
64
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2answers
31k 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 ...
4
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3answers
842 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 ...
