Online Manifold Regularization by Dual Ascending Procedure

Algorithm 4

The process of getting 𝐼_𝑡 for overall update.

PROCESS: 𝐼_𝑡=∅,

    If 𝝎_𝑡−1,𝝎_𝑡−1−∑^𝑡−1_𝑖=1𝑐₁𝛼_{𝑖0𝑡−1}𝜎_𝑖>0,

       𝐼_𝑡=𝐼_𝑡∪𝜂_𝑡.

    If 1−𝑦_𝑡𝐱_𝑡,𝝎_𝑡−1>0, 𝐼_𝑡=𝐼_𝑡∪𝛼_𝑡0.

    For each 𝑖∈𝑆_𝑡

      If −𝑤_𝑡𝑖(𝐱_𝑡−𝐱_𝑖),𝝎_𝑡−1>0, 𝐼_𝑡=𝐼_𝑡∪𝛼¹_𝑡𝑖;

      If 𝑤_𝑡𝑖(𝐱_𝑡−𝐱_𝑖),𝝎_𝑡−1>0, 𝐼_𝑡=𝐼_𝑡∪𝛼²_𝑡𝑖.

    Return 𝐼_𝑡.