Imagine we have $X$, a $n\times m$ non-negative matrix. We take the rank-r SVD of X
$$ X = U\Sigma V^T$$
I'm now interested in knowing the decomposition of $X_2$, a $n_2 \times m$ matrix formed by a subset of the rows of $X$.
Can I easily obtain this decomposition from $U$, $\Sigma$ and $V$? More specifically, do I really need to calculate the decomposition from scratch?
PS: I don't require this decomposition to be the SVD, any other matrix approximation of $X$ could possibly work.
PS2: If it helps, the rows of $X_2$ are selected by "thresholding" one of the columns of $U$, i.e. after selecting a column, all the rows with score above $\tau$ form $X_2$.