]>Gene-Based Multiclass Cancer Diagnosis with Class-Selective Rejections : Algorithm 1
1     𝜽 ∶ = ∅
2    𝐶 ∶ = ∅
3    for 𝜎 ← 𝜎 0 to 𝜎 𝑠 do
4          / ∗ Using the Training Set ∗ /
5         for 𝑗 ← 1 to 𝑁 do
6    Train 𝜈 - 1 -SVM on 𝑤 𝑗 , namely solving the QP (16)
7    Derive the regularization path for 𝑤 𝑗 , namely compute the 𝜶 𝜆 𝑗 s
8         end
9          / ∗ Using the Validation Set ∗ /
10      𝝀 ∶ = 𝝀 0
11      𝜷 ∶ = 𝜷 0
12     repeat
13          𝑑 𝜆 𝑗 1 ( 𝑥 ) ∶ = 𝜆 𝑗 ∑ 𝑛 𝑗 𝑝 = 1 𝛼 𝜆 𝑗 𝑝 𝐾 ( 𝑥 𝑝 , 𝑥 ) / 𝑏 𝜆 𝑗
14          𝑃 𝑗 ∶ = | 𝑤 𝑗 ∑ | / 𝑁 𝑗 = 1 | 𝑤 𝑗 | / ∗ | | = cardinality ∗ /
15         Assign 𝑥 to a decision 𝜓 𝑖 according to (19)
16          𝑃 ( 𝐷 𝑖 / 𝑤 𝑗 ) ∶ = | { 𝑥 o f 𝑤 𝑗 a s s i g n e d t o 𝜓 𝑖 } | / | { 𝑥 / 𝑥 ∈ 𝑤 𝑗 } |
17          ∑ ̂ 𝑐 ( 𝑍 ) ∶ = 𝐼 𝑖 = 1 ∑ 𝑁 𝑗 = 1 𝑐 𝑖 𝑗 𝑃 𝑗 𝑃 ( 𝐷 𝑖 / 𝑤 𝑗 )
18        𝝀 ∶ = 𝝀 n e w / ∗ construct the new vector according to the
     direction of greatest decrease ∗ /
19        𝜷 ∶ = 𝜷 n e w
20     until ̂ 𝑐 ( 𝑍 ) is minimum
21      𝜽 ∶ = 𝜽 ∪ { 𝜎 , 𝝀 , 𝜷 }
22    𝐶 ∶ = 𝐶 ∪ { ̂ 𝑐 ( 𝑍 ) }
23     end
24     index := min { 𝐶 }
25     𝜽 o p t i m a l ∶ = 𝜽 i n d e x
Algorithm 1: Multiclass SVM minimizing an asymmetric loss function.