Editing Principal component analysis (section)

=== Neuroscience ===
A variant of principal components analysis is used in [[neuroscience]] to identify the specific properties of a stimulus that increases a [[neuron]]'s probability of generating an [[action potential]].<ref>{{cite journal|last1=Chapin|first1=John|last2=Nicolelis |first2=Miguel|title=Principal component analysis of neuronal ensemble activity reveals multidimensional somatosensory representations|journal=Journal of Neuroscience Methods|date=1999|volume=94|issue=1|pages=121–140|doi=10.1016/S0165-0270(99)00130-2|pmid=10638820|s2cid=17786731 }}</ref><ref name="brenner00">Brenner, N., Bialek, W., & de Ruyter van Steveninck, R.R. (2000).</ref> This technique is known as [[Spike-triggered covariance|spike-triggered covariance analysis]]. In a typical application an experimenter presents a [[white noise]] process as a stimulus (usually either as a sensory input to a test subject, or as a [[Electric current|current]] injected directly into the neuron) and records a train of action potentials, or spikes, produced by the neuron as a result. Presumably, certain features of the stimulus make the neuron more likely to spike. In order to extract these features, the experimenter calculates the [[covariance matrix]] of the ''spike-triggered ensemble'', the set of all stimuli (defined and discretized over a finite time window, typically on the order of 100 ms) that immediately preceded a spike. The [[Eigenvectors and eigenvalues|eigenvectors]] of the difference between the spike-triggered covariance matrix and the covariance matrix of the ''prior stimulus ensemble'' (the set of all stimuli, defined over the same length time window) then indicate the directions in the [[Vector space|space]] of stimuli along which the variance of the spike-triggered ensemble differed the most from that of the prior stimulus ensemble. Specifically, the eigenvectors with the largest positive eigenvalues correspond to the directions along which the variance of the spike-triggered ensemble showed the largest positive change compared to the variance of the prior. Since these were the directions in which varying the stimulus led to a spike, they are often good approximations of the sought after relevant stimulus features.

In neuroscience, PCA is also used to discern the identity of a neuron from the shape of its action potential. [[Spike sorting]] is an important procedure because [[Electrophysiology#Extracellular recording|extracellular]] recording techniques often pick up signals from more than one neuron. In spike sorting, one first uses PCA to reduce the dimensionality of the space of action potential waveforms, and then performs [[Cluster analysis|clustering analysis]] to associate specific action potentials with individual neurons.

PCA as a dimension reduction technique is particularly suited to detect coordinated activities of large neuronal ensembles. It has been used in determining collective variables, that is, [[order parameters]], during [[phase transitions]] in the brain.<ref>{{cite journal|last1=Jirsa|first1=Victor|last2=Friedrich|first2=R|last3=Haken|first3=Herman|last4=Kelso|first4=Scott|title=A theoretical model of phase transitions in the human brain|journal=Biological Cybernetics|date=1994|volume=71|issue=1|pages=27–35|doi=10.1007/bf00198909|pmid=8054384|s2cid=5155075}}</ref>