Karhunen-Loeve Decomposition

For microfluidic systems with strong nonlinear effects, proper orthogonal decomposition (POD)-based MOR (also called Karhunen-Loeve decomposition) is employed to locate the low-dimensional subspace for modeling. POD is... 

For POD, the Karhunen-Loeve procedure decomposes a set of distributions or functions into an optimal, orthonormal set of eigenfunctions able to represent the distributions of interest [4-6]. These eigenfunctions can offer highly efficient representations of important variables and structures in combustion systems. Furthermore, the potential for a rednced-order model utilizing these basis functions can be evaluated from the associated eigenvalue spectrum derived from decomposition. 

The basic idea of the Karhunen-Loeve Transform (KLT) is that, if the correlation in the image is known, then it is possible to calculate the optimal mathematical basis by using an eigen-decomposition. The optimal basis is defined here as the one that minimises the overall root-mean-square distortion. 

Karhunen-Loeve (K-L) approach Karhunen-Loeve (K-L) decomposition Karhunen-Loeve (K-L) expansion... 

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