Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Principal component analysis
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
== Similar techniques == === Independent component analysis === [[Independent component analysis]] (ICA) is directed to similar problems as principal component analysis, but finds additively separable components rather than successive approximations. === Network component analysis === Given a matrix <math>E</math>, it tries to decompose it into two matrices such that <math>E=AP </math>. A key difference from techniques such as PCA and ICA is that some of the entries of <math>A</math> are constrained to be 0. Here <math>P</math> is termed the regulatory layer. While in general such a decomposition can have multiple solutions, they prove that if the following conditions are satisfied : # <math>A</math> has full column rank # Each column of <math>A</math> must have at least <math>L-1</math> zeroes where <math>L</math> is the number of columns of <math>A</math> (or alternatively the number of rows of <math>P</math>). The justification for this criterion is that if a node is removed from the regulatory layer along with all the output nodes connected to it, the result must still be characterized by a connectivity matrix with full column rank. # <math>P</math> must have full row rank. then the decomposition is unique up to multiplication by a scalar.<ref>{{Cite journal|title = Network component analysis: Reconstruction of regulatory signals in biological systems|last1=Liao|first1=J. C.|last2=Boscolo|first2=R.|last3=Yang|first3=Y.-L.|last4=Tran|first4=L. M.|last5=Sabatti|first5=C.|author5-link=Chiara Sabatti|last6=Roychowdhury|first6=V. P.|journal=Proceedings of the National Academy of Sciences|volume=100|issue=26|date=2003|pages=15522β15527|doi=10.1073/pnas.2136632100|pmid = 14673099|pmc = 307600|bibcode = 2003PNAS..10015522L|doi-access=free}}</ref> === Discriminant analysis of principal components === Discriminant analysis of principal components (DAPC) is a multivariate method used to identify and describe clusters of genetically related individuals. Genetic variation is partitioned into two components: variation between groups and within groups, and it maximizes the former. Linear discriminants are linear combinations of alleles which best separate the clusters. Alleles that most contribute to this discrimination are therefore those that are the most markedly different across groups. The contributions of alleles to the groupings identified by DAPC can allow identifying regions of the genome driving the genetic divergence among groups<ref>{{Cite journal|title = Discriminant analysis of principal components: a new method for the analysis of genetically structured populations.|last1=Liao|first1=T.|last2=Jombart|first2=S.|last3=Devillard|first3=F.|last4=Balloux|journal=BMC Genetics|date=2010|volume=11|pages=11:94|doi=10.1186/1471-2156-11-94|pmid = 20950446|pmc=2973851 |doi-access=free }}</ref> In DAPC, data is first transformed using a principal components analysis (PCA) and subsequently clusters are identified using discriminant analysis (DA). A DAPC can be realized on R using the package Adegenet. (more info: [https://adegenet.r-forge.r-project.org/ adegenet on the web]) === Directional component analysis === [[Directional component analysis]] (DCA) is a method used in the atmospheric sciences for analysing multivariate datasets.<ref name="jewson"/> Like PCA, it allows for dimension reduction, improved visualization and improved interpretability of large data-sets. Also like PCA, it is based on a covariance matrix derived from the input dataset. The difference between PCA and DCA is that DCA additionally requires the input of a vector direction, referred to as the impact. Whereas PCA maximises explained variance, DCA maximises probability density given impact. The motivation for DCA is to find components of a multivariate dataset that are both likely (measured using probability density) and important (measured using the impact). DCA has been used to find the most likely and most serious heat-wave patterns in weather prediction ensembles ,<ref name="scheretal"/> and the most likely and most impactful changes in rainfall due to climate change .<ref name="jewsonetal"/>
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)