subject to the constraint Pn
j=1Wij = 1, one obtains the weights fWijg that
best allow to reconstruct each data point from its neighbors. With the above
constraints, Eq. (1) can be simplied to a linear system and the weights can
be computed in closed form as follows: given a particular data point Xi with
n-nearest neighbors Xj and reconstruction weights Wj that sum to one, we can
write the reconstruction error as