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Continuous Iteratively Reweighted Least Squares Algorithm for Solving Linear Models by Convex Relaxation

DOI: 10.4236/apm.2019.96024, PP. 523-533

Keywords: Linear Models, Continuous Iteratively Reweighted Least Squares, Convex Relaxation, Principal Component Analysis

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Abstract:

In this paper, we present continuous iteratively reweighted least squares algorithm (CIRLS) for solving the linear models problem by convex relaxation, and prove the convergence of this algorithm. Under some conditions, we give an error bound for the algorithm. In addition, the numerical result shows the efficiency of the algorithm.

References

[1]  Torre, F.D. and Black, M.J. (2001) Robust Principal Component Analysis for Computer Vision. Proceedings of Eighth IEEE International Conference on Computer Vision, Vancouver, 7-14 July 2001, 362-369.
https://doi.org/10.1109/ICCV.2001.937541
[2]  Wanger, A., Wright, J. and Ganesh, A. (2009) Towards a Practical Face Recongnition System: Robust Registration Tillumination by Sparse Represention. 2009 IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, 20-25 June 2009, 20-25.
https://doi.org/10.1109/CVPR.2009.5206654
[3]  Ho, J., Yang, M., Lim, J., Lee, K. and Kriegman, D. (2003) Clustering Appearances of Objects under Varying Illumination Conditions. 2003 IEEE Computer Vision and Pattern Recognition, Madison, WI, 18-20 June 2003, 11-18.
[4]  Jolliffe, I.T. (2002) Principal Component Analysis. Journal of Marketing Research, 25, 513.
[5]  Watson, G.A. (2002) On the Gauss-Newton Method for l1 Orthogonal Distance Regression. IMA Journal of Numerical Analysis, 22, 345-357.
https://doi.org/10.1093/imanum/22.3.345
[6]  Ding, C., Zhou, D., He, X. and Zha, H. (2006) R1-PCA: Rotational Invariant L1-Norm Principal Component Analysis for Robust Subspace Factorization. The 23rd International Conference on Machine Learning, 23, 281-288.
https://doi.org/10.1145/1143844.1143880
[7]  Kwak, N. (2008) Principal Component Analysis Based on L1-Norm Maximization. IEEE Transactions on Pattern Analysis and Machine Intelligence, Pittsburgh, PA, 25-29 June 2006, 1672-1680.
https://doi.org/10.1109/TPAMI.2008.114
[8]  Maronna, R.A., Martin, D.R. and Yohai, V.J. (2006) Robust Statistics. Wiley Series in Probability and Statistics. Wiley, Chichester.
https://doi.org/10.1002/0470010940
[9]  Zhang, T., Szlam, A. and Lerman, G. (2009) Median K-Flats for Hybrid Linear Modeling with Many Outliers. IEEE International Conference on Computer Vision Workshops, 12, 234-241.
[10]  Wright, J., Peng, Y.G. and Ma, Y. (2009) Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices by Convex Optimization. 2009 23rd Annual Conference on Neural Information Processing Systems, Vancouver, Canada, 7-10 December 2009, 2080-2088.
[11]  Candes, E.J., Li, X., Ma, Y. and Wright, J. (2011) Robust Principal Component Analysis? Journal of the ACM, 58, Article No. 11.
https://doi.org/10.1145/1970392.1970395
[12]  Lerman, G., McCoy, M.B., Tropp, J.T. and Zhang, T. (2015) Robust Computation of Linear Models by Convex Relaxation. Foundations of Computational Mathematics, 15, 363-410.
https://doi.org/10.1007/s10208-014-9221-0

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