Calculate document similarity with SVD for unseen documents?

Question

Is it possible to transform a document into a latent semantic space calculated with SVD without recomputing the SVD, or even doing a rank one update? I don't care about updating the $U$, $\Sigma$, or $V$ matrices, but I am interested in being able to calculate document similarity for an unseen document.

My linear algebra is very weak (apologies :), but given the SVD equation, $X = U \Sigma V^T$, my first thought was to calculate $U_{n+1} = X_{n+1} \left(\Sigma V^T\right)^{-1}$, but my solver fails because $\Sigma V^T$ is singular. Does this mean that I must do an update to get the new document into the same space?

Answer 1

I solved all my misconceptions by studying the Derivations section of the Wikipedia page on latent semantic analysis. In particular, a document in the latent semantic space is $\Sigma^{-1} U^T x$.