Hi,
The point here is to actually first project the data to a lower dimension, and then back to the higher dimension. This is also elaborated upon in slides 27-29. What we achieve by doing this is getting rid of the noise in the data (because when we map to the lower dimension, the transform lets us keep only the most essential parts of the data). Then, when we map the data back to the original dimension (so now we are going from low dimension to high dimension), we have removed the noise from the data, and should have a cleaner reconstruction.
Best,
Sena
