【发布时间】：2016-02-27 19:39:35
【问题描述】：
我刚刚对我的数据执行了 SVD (M = U.D.V^t)，我有 3 个 svd 矩阵 U、D、Vt。这些矩阵按 D 的最高奇异值排序（即U和V的第一行对应最高的奇异值等）
我想根据特定的排序标准交换这个顺序：我对按绝对奇异值排序不感兴趣，而是对奇异值 di 乘以 Vt 中其对应向量的第一个元素进行排序
示例（伪代码，R代码如下）：
Singular_values = [ sV[1]=100, sV[2]=1, sv[3]=50 ]
Dt = [
0.1, xxx, ... # 1st row Dt1 associated to 1st singular Value
100, yyy, ... # 2nd row Dt2 associated to 2nd singular Value
1 , zzz, ... #
]
产品sV[i]*Dti[1]给：
100*0.1 = 10, # sV1*Dt1[1]
1*100 = 100, # sV2*Dt2[1]
50*1 = 50 # sv3*Dt3[1]
应该按照 [1,2,3] > [2,3,1] 降序排列
100 # sV2*Dt2[1]
50 # sv3*Dt3[1]
10 # sV1*Dt1[1]
...并将这些更改传播到 Matrix Dt
Dt_reordered [
100, yyy, ... # 2nd row Dt2 associated to 2nd singular Value
1, zzz, ... # 3rd row Dt3 associated to 3rd singular Value
0.1, xxx, ... #
]
R 代码
dataToSVD = matrix(rexp(200), 10)
theSVD = svd(dataToSVD) # Generates ...
# theSVD$u (Matrix U : I don't care about this one),
# theSVD$d (List D : singularValues),
# theSVD$v (Matrix V : Right singular vectors, not transposed)
theSVD$newValues <- theSVD$d*theSVD$v[1,] # This is a list of the "new" values that should be used for sorting
# The idea is now to sort theSVD$newValues by decreasing values, and the corresponding permutation must be applied also to theSVD$d and theSVD$v[1,]
【问题讨论】：
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这看起来不像 R 代码。你在使用一些伪代码吗？制作reproducible example 会有所帮助。
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对不起，我使用伪代码来描述问题，我对 R 不是很好，但我想它可以生成一个随机矩阵并对其执行 svd...