Karhunen-Loeve decomposition in the presence of symmetry. I.
The Karhunen-Loève (KL) decomposition is widely used for data which very often exhibit some symmetry, afforded by a group action. For a finite group, we derive an algorithm using group representation theory to reduce the cost of determining the KL basis. We demonstrate the technique on a Lorenz-type ODE system. For a compact group such as tori or SO(3,R) the method also applies, and we extend results to these cases. As a short example, we consider the circle group S(1).
Lahme
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Dept. of Math., Arizona Univ., Tucson, AZ 85721, USA.
Miranda
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