Editing Principal component analysis (section)

=== 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
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