Bi-cross-validation of the SVD and the nonnegative matrix factorization

  title={Bi-cross-validation of the SVD and the nonnegative matrix factorization},
  author={A. Owen and Patrick O. Perry},
  journal={The Annals of Applied Statistics},
  • A. Owen, Patrick O. Perry
  • Published 2009
  • Mathematics
  • The Annals of Applied Statistics
  • This article presents a form of bi-cross-validation (BCV) for choosing the rank in outer product models, especially the singular value decomposition (SVD) and the nonnegative matrix factorization (NMF). Instead of leaving out a set of rows of the data matrix, we leave out a set of rows and a set of columns, and then predict the left out entries by low rank operations on the retained data. We prove a self-consistency result expressing the prediction error as a residual from a low rank… CONTINUE READING
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