C1W4 final assignment: section 2.5 and onwards regarding reconstructing images

[YodaKenobi]

Hello,

1. Just above and during section 2.5 (image 1) PCA was applied to reduce from 4096 variables to 2 variables (per each of the 55 examples); that would mean for each cat image up to that point, instead of being represented by data in 4096 columns, a single cat is represented by data in 2 columns; is that interpretation correct?
   
   

1.b. It looks like the 2 dimension representations of the cats were just used when plotting that scatter plot of x,y values to show how related 2 images were, not to plot actual images. The images themselves seem to have been refernced in a preexisting imgs array. Is this interpretation correct?

[YodaKenobi]

2. Regarding the reconstruction later in 2.6; if the cat was reduced as X_red to a 55x2, meaning 2 eigenvectors for each of the 55 examples (see first image); then the dot product was applied to V_2_T (which would be of dimensions 2x55), the result would be a 55x55 matrix; meaning each of the 55 cats reconstructed images are being represented by 55 numbers now, instead of the original 4096 numbers, correct?

2.b Is there an algorithm that is determining what specific pixel values should correspond to, since the shape is now different (55 numbers instead of 4096 being used for the pixel values of the cat)?