Definition

The KL expansion is a Transformation technique allows you to find a new set of variables that are uncorrelated and can describe the original data. It does this by finding the most important patterns or modes of variation in the data and expressing the original variables as a combination of these patterns.

Karhunen Loève expansion is an instance of Model Order Reduction since it not only removes correlation but also allow to reduce the number of Random Variables.

Multivariate Gaussian PDF

Discrete KL Expansion

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Continuous Karhunen Loève Expansion

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