Similarity Measure Learning in Closed-Form Solution for Image Classification

Algorithm 1

The details of algorithm CSML.

Input: the sample set 𝑋={𝑥₁,𝑥₂,…,𝑥_𝑛} with labels 𝑌={𝑦₁,𝑦₂,…,𝑦_𝑛}

Output: the parameter set 𝑀 for the generalized correlation 𝜌

   Step  1. Construct the intrinsic graph 𝐺^𝐼 and penalty graph 𝐺^𝑃;

   Step   2. Compute the affinity weights: Δ^𝐼 and Δ^𝑃;

   Step   3. Construct the optimization problem (17);

   Step   4. For 𝑘=1 To 𝑑 Do

      If 𝑘=1 Then

       Solve 𝑆_𝛿𝑤₁=𝜆𝑆_𝑒𝑤₁ to obtain 𝑤₁

      Else

       Compute 𝐿 and solve 𝐿𝑤_𝑘=𝜆𝐿𝑤_𝑘 to obtain 𝑤_𝑘;

   Step  5. Final output 𝑀=𝑊𝑊^𝑇, where 𝑊=[𝑤₁,𝑤₂,…,𝑤_𝑑].