Online Manifold Regularization by Dual Ascending Procedure

Algorithm 1

A template online manifold regularization algorithm for semi-supervised binary classification. Based on dual ascending procedure, this template algorithm aims for an increment of the dual function on each round.

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),

      Choose a new coefficient vector 𝜶_𝑡 that satisfies 𝐷𝜶_𝑡≥𝐷𝜶_𝑡−1,

      Return a new associated boundary vector 𝝎_𝑡 in (18),

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