EVD Dualdating Based Online Subspace Learning

Algorithm 3

EVDD-base incremental PCA (EVDD-IPCA).

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

new samples 𝐵, 𝑚, 𝜇_𝐵.

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

 (1) Update the sample number and mean, 𝑛^⋆=𝑛+𝑚, 𝜇^⋆=(𝑛/(𝑛+𝑚))𝜇_𝐴+(𝑚/(𝑛+𝑚))𝜇_𝐵.

 (2) Compute the extra added sample, 𝑥_𝑎=(𝑛+𝑚)/𝑛𝑚(𝜇_𝐴−𝜇_𝐵).

 (3) Equivalent added data matrix, 𝐵=[𝐵−𝜇_𝐵𝟏_𝑚,𝑥_𝑎].

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