We see that almost 99% of the variability is explained by the first three columns of Y V = UD. So we get the sense that we should be able to explain much of the variability and structure we found...

We see that almost 99% of the variability is explained by the first three columns of Y V = UD. So we get the sense that we should be able to explain much of the variability and structure we found while exploring the data with a few columns. Before we continue, let’s show a useful computational trick to avoid creating the matrix diag(s$d). To motivate this, we note that if we write U out in its columns [U1, U2, . . . , Up] then UD is equal to

Use the sweep function to compute UD without constructing diag(s$d) nor matrix multiplication.