Maximum Variance Hashing via Column Generation

Algorithm 1

MVH-CG: Column generation for maximum variance hashing.

Input: Training data 𝒳={𝐱_𝑖}^𝑛_𝑖=1; balancing parameter 𝛾>0; length of hash codes ℓ.

(1) Initialize: w = 0; ℋ=∅; assign a positive constant to each element of u.

(2) for  𝑡=1,…,ℓ  do

(3)  Find a new binary hash function ℎ_𝑡(⋅) by solving (9); Add ℎ_𝑡(⋅) to ℋ and the restricted

   primal problem (10); Solve (10) by Mosek to obtain the updated w; update u by (11).

(4) Map 𝒳 to 𝒴={𝐲_𝑖}^𝑛_𝑖=1 using ℋ.

Output: The learnt hash functions ℋ, their weights w and the binary codes 𝒴.