全奇异值分解稳健的SVD、回归和位置-尺度
Total singular value decomposition. Robust SVD, regression and location-scale
摘要：
奇异值分解（SVD）是许多统计算法的基础，很少有用户质疑SVD是否正确处理了它的工作。SVD的目的是评估分解，最好的近似数据矩阵，给定一定的秩限制。然而，我们通常对分解的最佳分量感兴趣，而不是对最佳近似感兴趣。这种目标的冲突导致我们引入{ \em Total SVD}，其中“Total”一词取为“Total”最小二乘。SVD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权重来使SVD鲁棒。击穿性能优异。数学方面的处理，他们依赖于高维不动点计算。
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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