Multiple Kernel Spectral Regression for Dimensionality Reduction

Algorithm 1

MKL-SR algorithm.

The training procedure of MKL-SR

 Input: A set of training data, matrices 𝑊 and 𝐷, a set of base kernels 𝑘_𝑚^𝑀_𝑚=1

    and parameter 𝛾 in (21).

 Output: Sample coefficient vectors 𝐀=𝜶₁𝜶₂…𝜶_𝑐−1;

    Kernel weight vectors 𝜷;

 Make an initial guess for 𝐀 or 𝜷;

 Computing the largest 𝑐 generalized eigenvectors 𝐲^𝑘(𝑘=1,…,𝑐−1) of eigen-problem (2);

 For  𝐢←1,2,…,𝐢_𝐦𝐚𝐱  do

      (1) Compute 𝕂;

      (2) A is obtained by solving the least squares problem (21);

      (3) Compute 𝕂^′𝑇𝑊𝕂^′ in (24) and 𝕂^′𝑇𝐷𝕂^′ in (25);

      (4) 𝜷 is optimized by solving optimization problem (24) via SDP;

 Return  A and 𝜷;