Updating approximate principal components with applications to template tracking

Geunseop Lee, Jesse Barlow

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article numbere2081
JournalNumerical Linear Algebra with Applications
Volume24
Issue number2
DOIs
StatePublished - Mar 1 2017

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

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