I have an n x n similarity matrix which I'd like to reduce to a smaller square matrix. I am aware of this answer:
The answer shows how you can use SVD to reduce the number of columns of a matrix. Essentially, if $A= USV^T$, then taking $US$, gives a matrix with fewer columns than the original.
Therefore, I know how to reduce the number of columns using SVD, but how about the number of rows and columns?
Can I apply the procedure twice, first to reduce the columns, then to the transpose of the result to reduce the rows?
If my similarity matrix is symmetrical; does it make the problem simpler?