Online Manifold Regularization by Dual Ascending Procedure

Algorithm 8

The process of sparse approximation based on 𝑘-MC. The kernel representation for 𝝎_𝑡 contains 𝑘+𝜏 examples at most in this condition, where 𝜏 is the buffer size.

INPUT: the parameter 𝑘; the kernel representation of boundary on round 𝑡: 𝝎_𝑡=∑_{𝑖∈[𝑡]}𝛽_𝑖𝑡Φ𝐱_𝑖,

PROCESS: For each 𝐱_𝑖 in 𝝎_𝑡 and not in the buffer

      If 𝛽_𝑖𝑡 does not belong to the first 𝑘 maximum of the coefficients, discard the example 𝐱_𝑖 and its associated

      coefficient 𝛽_𝑖𝑡.

    Return a new boundary 𝝎_𝑡.