# 0.2 Independent component analysis (ica)

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A brief discussion of ICA (Independent Component Analysis).

## Independent component analysis

Imagine the data we have is a linear mixture of unknown latent factors and the factors are mutually independent and non-Gaussian, our goal is to find the underlying structure and identify these components. As shown before, PCA assumes Gaussianity. The condition ${U}^{T}U=I$ and ${V}^{T}V=I$ imply independence only when the data is Gaussian. ICA corrects this by looking for maximally independent components (rather than uncorrelated) ones. We know that uncorrlation is characterized by: while independence is given by $E\left[f\left(x\right)g\left(y\right)\right]=E\left[f\left(x\right)\right]E\left[g\left(y\right)\right]$ The independence is stronger than uncorrelation because it measures the existence of any relationship. On the other hand, uncorrlation only measures linear relationship. Model for ICA looks like this:

$\begin{array}{l}X=AS\\ \stackrel{^}{S}=W\stackrel{^}{X}\end{array}$

where A is the mixing matrix and S is the source signals (rows of S independent) and we recover the signal using the “whitening” matrix W, where: $W={A}^{-1}$ Popular algorithms do this by maximizing its distance from Gaussian using either entropy or neg-entropy (Gaussian has maximal entropy) – they are solved using quasi-Newton scheme. In addition to this, some often used contrast functions to Gaussian include 3rd moment skewness, 4th moment kurtosis (kurtosis is zero for a Gaussian random variable) and sigmoidal. We used FastICA. It’s efficient and converges quickly. (Figure Credit: http://zone.ni.com/reference/en-XX/help/372656B-01/lvasptconcepts/tsa_multivariate_stat_analysis/)

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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