I believe SVD on a matrix A returns three matrices: U, S, and V.
Let's imagine A is a data matrix with training examples/records/whatever you call them as its rows and attributes as its columns.
I think S is a diagonal matrix, where the $i$-th diagonal value is the variation in the $i$-th attribute (column) of the matrix A. Furthermore, the diagonal values of S decrease as you go left to right/top to bottom (the matrix is sorted).
I think U says something about the records themselves. I believe each row represents one record. I often see the first two columns U graphed such that the x axis is U1 (the first column) and the y axis is U2, but I don't know what the resulting graph is telling us.
I haven't been able to figure out what V does.
Is my understanding of S correct? And what do U and V represent? Any help is appreciated!