10、概率保序语义哈希（POSH）算法：原理、扩展与实验评估

概率保序语义哈希（POSH）算法：原理、扩展与实验评估

1. 优化算法概述

POSH的优化算法旨在获得最优离散哈希码 $B$。以下是算法的详细步骤：

Algorithm 4: Optimization Algorithm for POSH 
Require: Data X ∈ℜd×n, the expected hash code length r; label matrix G ∈{0, 1}c×n; 
maximum iterations Itern; parameters λ and η; iter = 0. 
Ensure: Optimal discrete hashing codes B. 
1: Initialize: Randomly initialize variables U, binary codes B and orthogonal matrix R. 
2: while iter < Itern & not converge do 
3:
    U-Step: Update U by using Eq. (4.16) and update the auxiliary variable tii in Eq. (4.15); 
4:
    R-Step: Update R by using Eq. (4.21); 
5:
    B-Step: Update B by using Eq. (4.19). 
6: end while 

由于 $B$ 的离散约束，可推导出简化问题：
[
\max_{B} B^{\top} (R^{\top}G