Context-Aware and Locality-Constrained Coding for Image Categorization

Algorithm 2

Codebook optimization.

input: 𝐗∈𝐑^𝐷×𝑁,𝐗_𝑠∈𝐑^{𝐷×𝑁𝑠}

output: B

(1) {Codebook initialization stage}

(2)  {𝑠₁,…,𝑠_𝐾}← clustering the randomly sampled

  data 𝐗_𝑠 into 𝑘 sets by 𝑘-means

(3)  𝐵_init←𝑧𝑒𝑟𝑜𝑠(𝐷,𝐾)

(4)  for  𝑖=1  to  𝐾  do

(5)  𝐵_init(∶,𝑖)←∑^𝑁𝑖_𝑗=1𝑠_𝑖𝑗/𝑁_𝑖,𝑁_𝑖←𝑠𝑖𝑧𝑒(𝑠_𝑖,2)

(6)  end for

(7)  𝐵←𝐵_init

(8)  while (not stopping criterion)

  {sparse coding stage}

(9)  for 𝑖=1 to 𝑁 do

(10)  Solving (18) with B fixed. The solution  𝑐_𝑖=(1^𝑇Ψ1)⁻¹(Ψ)⁻¹1.

      when 𝑤=1. The calculation of  Ψ  can be seen in Section 4.2

(11)  end for

  {codebook updating stage}

(12) Solving (18) with C fixed. The analytical solution can be referred in [18].

(13) End while