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Updating approximate principal components with applications to template tracking
Author(s) -
Lee Geunseop,
Barlow Jesse
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2081
Subject(s) - singular value decomposition , principal component analysis , algorithm , computation , matrix (chemical analysis) , mathematics , subspace topology , robust principal component analysis , qr decomposition , matrix decomposition , decomposition , tracking (education) , computer science , mathematical optimization , artificial intelligence , psychology , ecology , pedagogy , eigenvalues and eigenvectors , materials science , physics , quantum mechanics , composite material , biology
Summary Adaptive principal component analysis is prohibitively expensive when a large‐scale data matrix must be updated frequently. Therefore, we consider the truncated URV decomposition that allows faster updates to its approximation to the singular value decomposition while still producing a good enough approximation to recover principal components. Specifically, we suggest an efficient algorithm for the truncated URV decomposition when a rank 1 matrix updates the data matrix. After the algorithm development, the truncated URV decomposition is successfully applied to the template tracking problem in a video sequence proposed by Matthews et al. [IEEE Trans. Pattern Anal. Mach. Intell., 26:810‐815 2004], which requires computation of the principal components of the augmented image matrix at every iteration. From the template tracking experiments, we show that, in adaptive applications, the truncated URV decomposition maintains a good approximation to the principal component subspace more efficiently than other procedures.