Iterative Reweighted Noninteger Norm Regularizing SVM for Gene Expression Data Classification

Algorithm 1

Iterative re-weighted 𝑝-norm regularization SVM.

input: data 𝑆=𝑥_𝑖,𝑦_𝑖^𝑚_𝑖=1⊆𝑅^𝑛×{±1}, stop criterion 𝜍, maximum iteration limit 𝑇

Output: Weight vector 𝑤 and bias Term 𝑏

Set an initial estimation 𝑤_𝑗⁽⁰⁾=1√𝑛+1, for 𝑗=1,…,𝑛,𝑛+1

Repeat

Determine 𝑎^(𝑡) via the solution of Platt’s “sequential minimal optimization” until convergence of 𝑎^(𝑡)

Calculate 𝑤^𝑇=𝑎^𝑇diag(𝑦)𝑋𝑉⁻¹

calculate bias Term 1𝑏=|𝑆|_𝑘∑_∈𝑆𝑤^𝑇𝑥_𝑘−𝑦_𝑘

until 𝑎^(𝑡)−𝑎^(𝑡−1)≤𝜍 or reach maximum iteration limit 𝑇