TY - JOUR

T1 - Updating approximate principal components with applications to template tracking

AU - Lee, Geunseop

AU - Barlow, Jesse

N1 - Funding Information:
The research of Jesse L. Barlow and Geunseop Lee was funded by the National Science Foundation (NSF) under contract no. CCF-1115704.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

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U2 - 10.1002/nla.2081

DO - 10.1002/nla.2081

M3 - Article

AN - SCOPUS:85007495635

VL - 24

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

SN - 1070-5325

IS - 2

M1 - e2081

ER -