Questions tagged [independent-component-analysis]
Independent Component Analysis separates the additive combination of multiple signals into their estimated components.
77
questions
0
votes
0
answers
11
views
Do we need to scale our features before applying ICA, like in PCA?
I am reasonably certain that we don't need to scale data before applying ICA, like we do for the PCA. In PCA we do this because it assumes normal distribution of the features, and in ICA we don't ...
1
vote
1
answer
73
views
Geometric Intuition Behind Whitening for ICA
I know there are a couple posts asking about why we whiten the data for ICA. I understand why we whiten to fix scaling invariants between the sources and to increase the computationally efficiency.
...
- 11
0
votes
0
answers
22
views
Why is non-negative matrix factorization better than ICA in neuronal analysis
I've recently joined a neuroscience lab and am currently reading up on their pipeline to analyze 2-photon calcium imaging with single neuron resolution. The data consist of a movie where the pixel ...
- 1
1
vote
0
answers
18
views
What does ICA using only one component return?
I understand that with multiple components, the result will be coefficients that lead to maximally independent series.
When requesting only one component I'm unclear if it actually does optimization ...
- 11
8
votes
1
answer
744
views
Is it possible to turn PCA into ICA by rotating the eigenvectors?
Assume that you have made a PCA analysis and you got your eigenvectors inside the projection matrix $W$. If you project your data $X$ with $W$, then you get the desired projected dimension.
But PCA ...
- 349
0
votes
0
answers
14
views
Can I use Independent component Analysis on features extracted from a single timeseries?
Consider this simplified situation: I have a single time series and from that I compute a set of parameters (e.g. mean and variance). These parameters are however not independent from one another (e.g....
- 43
0
votes
0
answers
17
views
BSS/ICA "blind" performance evaluation
I'm currently working with ICA and currently using SIR (Signal-to-Interference Ratio) to mesure performance evaluation of the method. I'm working with another technic to run after ICA to estimate the ...
1
vote
1
answer
53
views
ICA and Gaussian: a misleading example
A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is ...
- 747
1
vote
1
answer
41
views
Is the first independent component of independent component analysis always important?
I was looking at a neuroscience paper that used ICA to reduce dimensionality of calcium signaling profiles in 20 randomly selected neurons of a zebrafish brain.
I presume that in Figure 2, ICA was ...
- 11
1
vote
0
answers
26
views
Does blind source separation (ICA) work if channels of mixture are observed asynchronously?
Does Independent Component Analysis (ICA - fastICA, SOBI, etc.) work reliably when applied to a multidimensional mixture (observation) $X = (X^1, \cdots, X^d)$ if the different channels $X^i$ of the ...
- 155
2
votes
0
answers
184
views
Why PCA is not considered in the taxonomy of blind source separation approaches?
Blind source separation (BSS) approaches are divided in the literature into four methods, including independent component analysis (ICA), sparse component analysis (SCA), and non-negative matrix ...
- 186
0
votes
0
answers
87
views
How many sources can be detected in ICA?
Is there an upper (or even lower?) limit for the number of sources which can be identified in ICA?
- 3,123
1
vote
0
answers
91
views
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 (...
- 11
4
votes
1
answer
997
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 ...
- 231
1
vote
2
answers
142
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 ...
- 231
3
votes
0
answers
127
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) ...
- 747
1
vote
0
answers
99
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 ...
- 127
1
vote
0
answers
328
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 ...
- 221
6
votes
1
answer
2k
views
How can I show that two random variables are independent if their mutual information is 0?
On the Wikipedia page for 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)...
- 221
0
votes
0
answers
94
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-...
0
votes
0
answers
125
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 ...
- 1
0
votes
0
answers
30
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, ...
- 71
1
vote
2
answers
662
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 à is the mixing matrix of the whitened data matrix z. My question is: If the matrix ...
- 71
1
vote
0
answers
147
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 ...
- 11
1
vote
1
answer
612
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:
...
- 33
1
vote
0
answers
364
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 ...
- 21
2
votes
2
answers
439
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 ...
- 21
1
vote
0
answers
14
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 ...
- 11
0
votes
0
answers
72
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 ...
- 13
2
votes
1
answer
94
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 ...
- 21
3
votes
1
answer
2k
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 ...
- 159
1
vote
1
answer
66
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 ...
- 109
2
votes
0
answers
273
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 ...
- 2,391
2
votes
1
answer
787
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 ...
- 313
2
votes
2
answers
115
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 ...
- 692
1
vote
0
answers
1k
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 ...
- 692
9
votes
1
answer
3k
views
What is meant by the non-gaussianity in the independent component analysis (ICA)?
What is meant 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....
- 692
2
votes
1
answer
2k
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 ...
- 395
1
vote
0
answers
73
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 ...
- 31
10
votes
1
answer
965
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 ...
- 283
2
votes
1
answer
83
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 ...
- 733
1
vote
0
answers
68
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 ...
- 45
2
votes
2
answers
741
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 ...
- 340
11
votes
1
answer
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 ...
- 7,341
1
vote
1
answer
445
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, ...
- 539
2
votes
1
answer
2k
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:
...
- 123
0
votes
2
answers
464
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 ...
- 327
0
votes
1
answer
2k
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?
- 327
2
votes
1
answer
100
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 ...
- 141
7
votes
1
answer
4k
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 ...
- 964