EVD Dualdating Based Online Subspace Learning

Algorithm 1

SVD updating.

Input: The rank-𝑘 SVD of old data 𝐴, 𝑈_𝑘, Σ_𝑘, 𝑉_𝑘, new data 𝐵.

Output: The rank-𝑘 SVD of total data 𝐴^•, 𝑈_𝑘, Σ_𝑘, 𝑉_𝑘.

 (1) Compute QR decomposition, (𝐼_𝑑−𝑈_𝑘𝑈^𝑇_𝑘)𝐵=QR;

 (2) Compute the rank-𝑘 SVD, Σ_𝑘𝑈^𝑇_𝑘𝐵=𝑈0𝑅^𝑘Σ_𝑘𝑉^𝑇_𝑘;

 (3) The rank-𝑘 SVD of 𝐴𝐵 is

        𝐴^•=𝑈_𝑘𝑄𝑈_𝑘Σ_𝑘𝑉_𝑘00𝐼_𝑚𝑉_𝑘^𝑇.