# PCA vs SVD - understanding difference and preference of SVD over PCA [duplicate]

I understand that PCA and SVD are similar - PCA removes the mean and SVD doesn't? I think I have an understanding of PCA - you would use it to reduce dimensions of data and separate it out into linear combinations of variables that explain the largest variance of the SS.

But I can't grasp that same concept for SVD - and especially can't understand when you would use SVD over PCA if they are supposed to be very similar.

Can someone explain in very basic terms why I would pick SVD vs PCA, and how SVD works? What is a real world application where SVD is better than PCA?

• Read stats.stackexchange.com/q/79043/3277. PCA and SVD are not comparable at all. PCA is a data analytic method. SVD is a mathematical operation. PCA is often done via SVD (BTW PCA does not necessarily remove means). Some other analytical methods, similar to PCA - Correspondence analysis, Principal Coordinate analysis, Procrustes rotation etc. - use SVD also. Aug 14, 2014 at 6:52
• Mar 16, 2016 at 20:43

From what I understand. SVD has to do with general matrix factorization in some sense. It can be called as a numerical method to do factorization such the we can decompose $A = UDV^T$ such that D is diagonal and U and V are orthogonal. Thats it.
• look at page 5 footnote. Now it turns down to solving $Ax=\lambda x$ and this is an eigen value problem. There are many ways to solve $Ax=\lambda x$ and you can use any one of them. Solutions to this is called eigen vectors(for x) and eigen values(for $\lambda$). You should look into linear algebra for more perspectives. Nov 16, 2015 at 7:06