I would like to know what do i have to do for the input of Kmeans Clustering if I use Dimensionality Reduction (SVD in this case) after TF-IDF? Does these three matrices become my input (A = USVt)? or do i need to transform it again into something else?
Note: the dataset i use is a set of document and would like to do text clustering
If you do dimensionality reduction via SVD, you will go from having a dataset matrix $X\in\mathbb{R}^{N\times M}$ to one $\tilde{X}\in\mathbb{R}^{N\times K}$ where $K<M$ (see also here). Essentially you get $N$ vectors but with fewer features. Mathematically you have projected your data onto the principal components of the data (the columns of $V$). You can then cluster them with exactly the same algorithms you would normally use. (Clearly if you use all three full matrices, you will just end up with the original dataset).
For SVD specifically, if $X=U\Lambda V^T$, then you reduce the dimensionality (i.e. set all but the first $K$ singular values to zero in $\Lambda$) to get $\Lambda_r$ (which removes all the zero columns and rows) and $U_r$ (remove columns of $U$ to match $\Lambda$), and then you take $\tilde{X}=U_r \Lambda_r$ to cluster. (In other words, $\tilde{X}\in\mathbb{R}^{N\times K}$ with $U_r\in\mathbb{R}^{N\times K},\Lambda_r\in\mathbb{R}^{K\times K}$. See also reduced SVDs.)