The distinction between POD and SVD methods is in the fact that in POD we center the data matrix such that each row will be of mean zero while in SVD the rows of the data matrix are not altered.

Question

BlackTom AI · Accepted Answer

This statement mixes up how POD (Proper Orthogonal Decomposition) and SVD (Singular Value Decomposition) are typically applied.

First, POD and SVD are closely related; POD often relies on the eigen-decomposition of a covariance (or correlation) matrix and is most accurately performed on data that have been centered. Centering usually means subtracting the mean of each variable (i.e., each column) so that each feature has zero mean across observations, not centering by rows.

Second, the claim that POD centers the data by making each row have zero mean while SVD leaves the rows unaltered is not correct. Centering by rows (i.e., ensuring each observation has zero mean) is not the standard preprocessing for either POD or SVD in typical dimensionality reduction contexts. In practice, one centers by columns (features) so that the analysis captures variance around feature means.

Third, SVD itself can be applied to either centered or uncentered data, but the conventional practice in data analysis is to center the data (usually by columns) before performing SVD-based PCA/POD to ensure the principal components reflect variance about feature means rather than mean shifts.

Fourth, the core distinction between POD and SVD is not about whether you center rows versus not; it’s about the mathematical framing and what is being decomposed (covariance structure in POD versus the full data matrix in SVD). The oversimplified statement fails to capture these nuances.

In summary, the assertion misstates the centering convention and the fundamental concepts behind POD and SVD, making it incorrect.

The distinction between POD and SVD methods is in the fact that in POD we center the data matrix such that each row will be of mean zero while in SVD the rows of the data matrix are not altered.

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