TITLE: What is the intuitive relationship between SVD and PCA?
QUESTION [439 upvotes]: Singular value decomposition (SVD) and principal component analysis (PCA) are two eigenvalue methods used to reduce a high-dimensional data set into fewer dimensions while retaining important information. Online articles say that these methods are 'related' but never specify the exact relation.
What is the intuitive relationship between PCA and SVD? As PCA uses the SVD in its calculation, clearly there is some 'extra' analysis done. What does PCA 'pay attention' to differently than the SVD? What kinds of relationships do each method utilize more in their calculations? Is one method 'blind' to a certain type of data that the other is not?

REPLY [4 votes]: There is a way to do an SVD on a sparse matrix that treats missing features as missing (using gradient search). I don't know any way to do PCA on a sparse matrix except by treating missing features as zero.