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.
Discrete KL Expansion
Continuous Karhunen Loève Expansion
Truncation Error