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What is the intuitive relationship between SVD and PCA

I am confused between PCA and SVD.

The wikipedia page for the PCA has this line:

"PCA can be done by eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix, usually after mean centering the data for each attribute."

Does this mean that PCA = SVD of a data matrix?

Is there an article/tutorial that explains the difference?

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1 Answers1


PCA needs SVD or Eigenvalue decomposition to calculate principal components (PCs). That is, PCs are the result of SVD of the samples.

PCA has two step.

  1. derive PCs which are axes of PCA using SVD and select n eigenvectors corresponding to the n largest eigenvalues.
  2. project some samples to these PCs (to denoise, dimensionality reduction, feature extraction)

You can find some articles using the keyword "tutorial principal component analysis".

Hope this helps

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