Editing Independent component analysis (section)

== Defining component independence ==
ICA finds the independent components (also called factors, latent variables or sources) by maximizing the statistical independence of the estimated components. We may choose one of many ways to define a proxy for independence, and this choice governs the form of the ICA algorithm. The two broadest definitions of independence for ICA are

# Minimization of mutual information
# Maximization of non-Gaussianity

The Minimization-of-[[Mutual information]] (MMI) family of ICA algorithms uses measures like [[Kullback–Leibler divergence|Kullback-Leibler Divergence]] and [[Principle of maximum entropy|maximum entropy]].  The non-Gaussianity family of ICA algorithms, motivated by the [[central limit theorem]], uses [[kurtosis]] and [[negentropy]].<ref name=comon94/>

Typical algorithms for ICA use centering (subtract the mean to create a zero mean signal), [[Whitening transformation|whitening]] (usually with the [[eigenvalue decomposition]]),<ref name="Springer">{{Cite book | author1=Holmes, M. | title=Introduction to Scientific Computing and Data Analysis, 2nd Ed | year=2023 | publisher=Springer | isbn=978-3-031-22429-4 }}</ref> and [[dimensionality reduction]] as preprocessing steps in order to simplify and reduce the complexity of the problem for the actual iterative algorithm.