TABLE I.

iITR Algorithm for Solving the Trace Ratio Problem

Initialize λ0 = 0. Compute the eigen-decomposition of Sb − λtSw as (Sb − λtSw) wi = τiwi, where wi (i = 1,2,…D) is the eigenvector of Sb − λtSw. Calculate $f_i=w_i^T{S}_b{w}_i$ and $g_i=w_i^T{S}_w{w}_i$ for i ∈ {1,2,…,D} and initialize γ0 = λt and $b^0=\left[b_1^0,b_2^0,\dots b_D^0\right]$ be a zero vector, iteratively solving the sub-problem of Eq. (5) until convergence: Sort fi − γkgi and set $b_i^k=1$ corresponding to the d largest value of fi − γkgi, $b_i^k=0$ otherwise. Update γi+1 = bkfT/bkgT. If bk = bk−1, output b* = bk and γ* = b*fT/b*gT. Form Wt by choosing the d eigenvectors of wi, with $b_i^{\ast }=1$ and Update λt+1 = γ*. Iterate the steps (2–4) until |λt+1 − λt| < ε. Output W*.