EVD Dualdating Based Online Subspace Learning

Table 1

Expansions of EVD dualdating.

	Old data	New data	Φ	Miscellanea
Update	𝐴𝑑×𝑛	𝐴𝑑×𝑛𝐵𝑑×𝑚	𝐼𝑘𝐼𝑚
Downdate	𝐶𝑑×(𝑛−𝑝)𝐷𝑑×𝑝	𝐶𝑑×(𝑛−𝑝)	𝐼𝑘−𝐼𝑝
Dualdate	𝐶𝑑×(𝑛−𝑝)𝐷𝑑×𝑝	𝐶𝑑×(𝑛−𝑝)𝐵𝑑×𝑚	𝐼𝑘𝐼𝑚−𝐼𝑝
Revise	𝐶𝑑×(𝑛−𝑝)𝐷𝑑×𝑝	𝐶𝑑×(𝑛−𝑝)𝐵𝑑×𝑝	𝐼𝑘𝐼𝑝−𝐼𝑝
Weighted update	𝐴𝑑×𝑛	𝑤1𝐴𝑑×𝑛𝑊𝐵𝑑×𝑚	𝑤1𝐼𝑘𝑊	𝑊=diag(𝑤2,…,𝑤𝑚+1)