EVD Dualdating Based Online Subspace Learning

Algorithm 4

EVDD-base decremental PCA (EVDD-DPCA).

Input: The sample number, mean, eigenvectors, eigenvalues of old data, 𝑛, 𝜇_𝐴, 𝑈_𝑘, Λ_𝑘, the sample number and mean of

deleted samples 𝐷, 𝑝, 𝜇_𝐷.

Output: The sample number, mean, eigenvectors, eigenvalues of remained data, 𝑛^⋆, 𝜇^⋆, Λ^⋆_𝑘, 𝑈^⋆_𝑘.

 (1) Update the sample number and mean, 𝑛^⋆=𝑛−𝑝, 𝜇^⋆=(𝑛/(𝑛−𝑝))𝜇_𝐴−(𝑝/(𝑛−𝑝))𝜇_𝐷.

 (2) Compute the extra deleted sample, 𝑥_𝑑=𝑛𝑝/(𝑛−𝑝)(𝜇_𝐴−𝜇_𝐷).

 (3) Equivalent deleted data matrix, 𝐷=[𝐷−𝜇_𝐷𝟏_𝑝,𝑥_𝑑].

 (4) Compute 𝑈^⋆_𝑘, Λ^⋆_𝑘 via EVD-Dualdating with 𝑈_𝑘, Λ_𝑘 and deleted data 𝐷.