# What are the differences among Proper Orthogonal Decomposition (POD), Singular value decomposition (SVD) and principal component analysis (PCA)?

Proper Orthogonal Decomposition (POD), singular value decomposition (SVD), and principal component analysis (PCA) are three eigenvalue methods used to reduce a high-dimensional data set into fewer dimensions while retaining important information. Online articles,e.g., this Wikipedia article, say that these methods are 'related' but does not specify the exact relation.

What is the intuitive relationship between POD, and SVD, PCA? How to decide which one to choose?

• This is not a proper answer, but I believe the 3 are the same mathematically. In particular, SVD is the operation of decomposing a matrix into orthogonal modes. If the data is a time series, then it is referred to as POD; if the data is sampled from some statistical measure, then it is referred to as PCA. Apr 18 at 21:36