Robust Singular Value Decomposition BaLsed on Weighted Least Absolute Deviation Regression Jung, Kang-Mo;
The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.
Outliers;robust statistics;singular value decomposition;weighted least absolute deviation;
A robust AMMI model for the analysis of genotype-by-environment data, Bioinformatics, 2015, btv533
Bradu, D. and Gabriel, K. R. (1978). The biplot as a diagnostic tool for models of two-way tables, Technometrics, 20, 47-68.
Chen, C; He, X. and Wei, Y. (2008). Lower rank approximation of matrices based on fast and robust alternating regression, Journal of Computational and Graphical Statistics, 17, 186-200.
Croux, C; Filzmoser, P., Pison, G. and Rousseeuw, P. J. (2003). Fitting multiplicative models by robust alternating regressions, Statistics and Computing, 13, 23-36.
Gabriel, K. R. and Zamir, S. (1979). Lower rank approximation of matrices by least squares with any choice of weights, Technometrics, 21, 489-498.
Gilnoi, A., Simonoff, J. S. and Sengupta, B. (2006). Robust weighted LAD regression, Computational Statistics and Data Analysis, 50, 3124-3140.
Greenacre, M. J. (1984). Theory and Applications of Correspondence Analysis, Academic Press, London.
Hawkins, D. M., Liu, L. and Young, S. S. (2001). Robust singular value decomposition, National Institute of Statistical Sciences Technical Report 122.
Liu, L., Hawkins, D. W., Ghosh, S. and Young, S. S. (2003). Robust singular value decomposition analysis of microarray data, Proceedings of the National Academy of Sciences of the USA, 100, 13167-13172.
Rousseeuw, P. J. (1984). Least median of squares regression, Journal of the American Statistical Association, 79, 871-880.
Rousseeuw, P. J. and van Zomeren, B. C. (1990). Unmasking multivariate outliers and leverage points, Journal of the American Statistical Association, 85, 633-639.