Can you please help me understand the following sentence:
Suppose we accumulate many millions of image patches, each of size 20×20 pixels, Clearly, every such image is a point in $R^{400}$. Let’s put these points in this 400-dim Euclidean space, in the cube $[0,1]^{400}$.
Can someone help me understand the last sentence? What does it mean to put in $400$-dim Euclidean space and in particular, the cube $[0,1]^{400}$?? I failed to picture this in my mind!
It means that all coordinates in the $400$-long vector of reals must lie in $[0,1]$.
You don't need a picture, just a vector space of $400$ dimensions: all sequences $(x_1, x_2 ,\ldots,x_{400})$ of real numbers, with coordinatewise addition and scalar multiplication. The usual Pythagorean distance formula also applies.