Online Manifold Regularization by Dual Ascending Procedure

Algorithm 5

Online manifold regularization algorithm based on overall update.

INPUT: two positive scalars: 𝑐₁ and 𝑐₂; edge weights 𝑤_𝑖𝑗.

INITIALIZE: a coefficient vector 𝜶₀ and its associated decision boundary vector 𝝎₀.

PROCESS: For 𝑡 =1,2,…,𝑇

      Receive an example (𝐱_𝑡,𝑦_𝑡,𝜎_𝑡),

      Get 𝐼_𝑡 using the process in Algorithm 4,

      Choose a step size 𝜌_𝑡∈0,min𝜌_𝑡^max,𝜌^∗_𝑡,

      Update the boundary vector using (33),

      If 𝜎_𝑡=0, predict 𝑦_𝑡=sign(𝝎_𝑡,𝐱_𝑡),

      Renew the buffer.