robustSvd(pcaMethods)
robustSvd()所属R语言包：pcaMethods
Alternating L1 Singular Value Decomposition
交替的L1奇异值分解
译者：生物统计家园网 机器人LoveR
描述----------Description----------
A robust approximation to the singular value decomposition of a rectangular matrix is computed using an alternating L1 norm (instead of the more usual least squares L2 norm). As the SVD is a least-squares procedure, it is highly susceptible to outliers and in the extreme case, an individual cell (if sufficiently outlying) can draw even the leading principal component toward
一个强大的近似的长方形矩阵的奇异值分解的计算使用交替L1范数（而不是更常见的L2范数最小二乘）。的SVD是一个最小二乘程序，它是高度敏感离群，在极端情况下，单个单元（如果充分离岛），甚至可以借鉴领先的主要组成部分，向
用法----------Usage----------
robustSvd(x)
参数----------Arguments----------
参数：x
A matrix whose SVD decomposition is to be computed. Missing values are allowed. </table>
要计算一个矩阵的SVD分解。遗漏值是不允许的。 </ TABLE>
Details
详情----------Details----------
See Hawkins et al (2001) for details on the robust SVD algorithm. Briefly, the idea is to sequentially estimate the left and right eigenvectors using an L1 (absolute value) norm minimization.
强大的SVD算法的详细信息，请参阅霍金斯等人（2001）。简单地说，这个想法是使用L1（绝对值）范数最小化的左，右特征向量顺序估计。
Note that the robust SVD is able to accomodate missing values in the matrix x, unlike the usual svd function.
需要注意的是强劲的SVD是能够容纳在矩阵缺失值x，不像通常的svd功能。
Also note that the eigenvectors returned by the robust SVD algorithm are NOT (in general) orthogonal and the eigenvalues need
还注意到，强大的SVD算法返回的特征向量是（一般）正交的特征值所需要的
值----------Value----------
The robust SVD of the matrix is x = u d v'.
强大的矩阵奇异值是X = U D V。
参数：d
A vector containing the singular values of x. <tr valign="top"><td>u</td>
含有x奇异值的一个向量。 <tr valign="top"> <TD>u</ TD>
A matrix whose columns are the left singular vectors of x.
矩阵的列是x的左奇异向量。
参数：v
A matrix whose columns are the right singular vectors of x. </table>
矩阵的列是x的右奇异向量。 </ TABLE>
注意----------Note----------
Two differences from the usual SVD may be noted. One relates to orthogonality. In the conventional SVD, all the eigenvectors are orthogonal even if not explicitly imposed. Those returned by the AL1 algorithm (used here) are (in general) not orthogonal. Another difference is that, in the L2 analysis of the conventional SVD, the successive eigen triples (eigenvalue, left eigenvector, right eigenvector) are found in descending order of eigenvalue. This is not necessarily the case with the AL1 algorithm. Hawkins et al (2001) note that a larger eigen value
从平时的SVD差异可能会注意到。一个涉及到正交。在传统的SVD，所有的特征向量是正交的，即使没有明确征收。返回的控制AL1算法（这里使用）（一般）不正交。另一个区别是，在L2传统的SVD分析，连续的特征三元组（特征值，左特征向量，右特征向量）的特征值降序排列。这不一定与控制AL1算法的情况下。霍金斯等人（2001）注较大的特征值
作者（S）----------Author(s)----------
Kevin Wright, modifications by Wolfram Stacklies
参考文献----------References----------
Robust Singular Value Decomposition, National Institute of Statistical Sciences, Technical Report Number
参见----------See Also----------
svd, nipals for
svd，nipals
举例----------Examples----------
data(metaboliteDataComplete)
mdc <- prep(metaboliteDataComplete, center=TRUE, scale="none")
## Now create 5% of outliers.[＃现在创建5离群％。]
cond <- runif(length(mdc)) < 0.05;
mdcOut <- mdc
mdcOut[cond] <- 10
## Now we do a conventional SVD and a robustSvd on both, the original and the [＃现在我们做一个传统的SVD和上都robustSvd，原来和]
## data with outliers.[离群＃数据。]
resSvd <- svd(mdc)
resSvdOut <- svd(mdcOut)
resRobSvd <- robustSvd(mdc)
resRobSvdOut <- robustSvd(mdcOut)
## Now we plot the results for the original data against those with outliers[＃现在我们针对离群的原始数据绘制的结果]
## We can see that robustSvd is hardly affected by the outliers.[＃我们可以看到，robustSvd几乎不受离群值的影响。]
plot(resSvd$v[,1], resSvdOut$v[,1])
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注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-2-26 10:53:20
