In this paper -> https://www.cs.ucsb.edu/~mturk/Papers/jcn.pdf by Turk and Pentland, 1991, pg 76, formula (8) quote "... The simplest method for determining which face class provides the best description of an input face image is to find the face class k that minimizes the euclidean distance. (epsilon_k)^2 = || omega - omega_k||^2 (8)..."
omega^T = [w_1,w_2,...,w_k] is a vector of weights that we get from projecting any face onto a face space.
To classify some unknown face f we project f onto a face space and get some vector of weights omega_f. Is this formula trying to say that we simply take the magnitude of of all weight vectors(so omega_1 -> omega_n assuming we used n faces to create the face space) minus omega_f and we get some result epsilon_i, where epsilon_i^2 = || omega_f - omega_i||^2. Now are we trying to find min(epsilon_i) and then do we say this omega_f which corresponds to face f is recognized as omega_i which corresponds to some face i if epsilon_i is less than theta_epsilon.
is my translation of this formula correct ? the author speaks of a choosing threshold theta_epsilon but I cannot see where or how it is chosen ?
