A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis.

@article{Witten2009APM,
  title={A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis.},
  author={Daniela M. Witten and Robert Tibshirani and Trevor J. Hastie},
  journal={Biostatistics},
  year={2009},
  volume={10 3},
  pages={
          515-34
        }
}
We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as circumflexX = sigma(k=1)(K) d(k)u(k)v(k)(T), where d(k), u(k), and v(k) minimize the squared Frobenius norm of X - circumflexX, subject to penalties on u(k) and v(k). This results in a regularized version of the singular value decomposition. Of particular interest is the use of L(1)-penalties on u(k) and v(k), which yields a decomposition of X… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 32 REFERENCES

Projected gradient approach to the numerical solution of the SCoTLASS

  • Computational Statistics & Data Analysis
  • 2006
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Plaid models for gene expression data

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

A path algorithm for the fused lasso (in preparation)

H. HOEFLING
  • 2009
VIEW 1 EXCERPT

Identifying copy number changes in CGH data for multiple samples (in preparation)

G. NOWAK, T. HASTIE, J. POLLACK, R. TIBSHIRANI
  • 2009