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摘要翻译：
奇异值分解(SVD)是许多统计算法的基础，很少有用户质疑SVD是否能正确地处理它的工作。SVD的目标是在给定秩限制的情况下，评估最接近数据矩阵的分解。然而，我们往往对分解的最佳分量感兴趣，而不是对最佳近似感兴趣。目标的这种冲突导致我们引入{\em Total SVD}，其中“Total”一词被视为“Total”最小二乘。奇异值分解是一种最小二乘法，因此，对数据矩阵中的粗差非常敏感。我们通过对每个矩阵项施加一个权重来使奇异值分解鲁棒性。击穿性能优异。处理算法方面；它们依赖于高维不动点计算。
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英文标题：
《Total singular value decomposition. Robust SVD, regression and
location-scale》
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作者：
William Rey
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some rank restriction. However often we are interested in the best components of the decomposition rather than in the best approximation . This conflict of objectives leads us to introduce {\em Total SVD}, where the word "Total" is taken as in "Total" least squares. SVD is a least squares method and, therefore, is very sensitive to gross errors in the data matrix. We make SVD robust by imposing a weight to each of the matrix entries. Breakdown properties are excellent. Algorithmic aspects are handled; they rely on high dimension fixed point computations.
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PDF链接：
https://arxiv.org/pdf/706.0096
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