The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Damped Newton Algorithms for Matrix Factorization with Missing Data
Abstract
The problem of low-rank matrix factorization in the presence of missing data has seen significant attention in recent computer vision research. The approach that dominates the literature is EM-like alternation of closed-form solutions for the two factors of the matrix. An obvious alternative is nonlinear optimization of both factors simultaneously, a strategy which has seen little published research. This paper provides a comprehensive comparison of the two strategies by evaluating previously published factorization algorithms as well as some second order methods not previously presented for this problem. We conclude that, although alternation approaches can be very quick, their propensity to glacial convergence in narrow valleys of the cost function means that average-case performance is worse than second-order strategies. Further, we demonstrate the importance of two main observations: one, that schemes based on closed-form solutions alone are not suitable and that non-linear optimization strategies are faster, more accurate and provide more flexible frameworks for continued progress; and two, that basic objective functions are not adequate and that regularization priors must be incorporated, a process that is easier with nonlinear methods.
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Cites
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Self-citationShape and motion from image streams under orthography: a factorization method
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Recovering non-rigid 3D shape from image streams
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Robust principal component analysis for computer vision
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Principal component analysis with missing data and its application to polyhedral object modeling
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Cited by
Weighted Nuclear Norm Minimization with Application to Image Denoising
Gu, S., Zhang, L., Zuo, W., & Feng, X. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.366 · Cited by 2,316
Supervised Descent Method and Its Applications to Face Alignment
Xiong, X., & De la Torre, F. (2013) · 2013 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2013.75 · Cited by 1,896
A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms
Tron, R., & Vidal, R. (2007) · 2007 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2007.382974 · Cited by 658
On Tensors, Sparsity, and Nonnegative Factorizations
Chi, E. C., & Kolda, T. G. (2012) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/110859063 · Cited by 274
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
Dai, Y., Li, H., & He, M. (2014) · International Journal of Computer Vision · doi:10.1007/s11263-013-0684-2 · Cited by 270
Metadata
- Authors
- Buchanan, A. M., & Fitzgibbon, A. W.
- Venue
- 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)
- Publisher
- IEEE
- Published
- 2005-07-27
- Volume
- 2
- Pages
- 316-322
- ISSN
- 1063-6919 (ISSN-L)
- OpenAlex
- W2126762950
- Cited by
- 299
- References
- 9
- FWCI
- 32.54
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Buchanan, A. M., & Fitzgibbon, A. W. (2005). Damped Newton Algorithms for Matrix Factorization with Missing Data. 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05). https://doi.org/10.1109/cvpr.2005.118
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