Proper orthogonal decomposition
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In statistics, the proper orthogonal decomposition (POD) is a powerful method for system identification aiming at obtaining low-dimensional approximate descriptions for multidimensional systems.
The proper orthogonal decomposition provides a basis for the modal decomposition of a system of functions, usually data obtained from experiments, measurements or numerical simulations. The basis functions retrieved are called proper orthogonal modes. It provides an efficient way of capturing the dominant components of a multidimensional system and representing it to the desired precision by using the relevant set of modes, thus reducing the order of the system.
The POD is an empirical version of the Karhunen-Loève decomposition (KLD). The singular value decomposition (SVD) is essential in efficient implementation of POD. The principal components analysis (PCA) is an important application of POD.
