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R：将函数应用于矩阵的所有行对，无需 for 循环

发布于 2024-11-14 11:17:46 字数 131 浏览 2 评论 0原文

我希望对矩阵中的所有行进行所有成对比较，显然双 for 循环可以工作，但对于大型数据集来说非常昂贵。

我查找了隐式循环，例如 apply() 等，但不知道如何避免内部循环。

如何才能实现呢？

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霓裳挽歌倾城醉 2024-11-21 11:17:46

我假设您正在尝试对矩阵的所有行对进行某种类型的比较。
您可以使用 outer() 遍历所有行索引对，并应用向量化
每个行对的比较函数。例如，您可以计算所有行对之间的平方欧几里德距离，如下所示：

m <- matrix(1:12,4,3)     
> outer(1:4,1:4, FUN = Vectorize( function(i,j) sum((m[i,]-m[j,])^2 )) )
     [,1] [,2] [,3] [,4]
[1,]    0    3   12   27
[2,]    3    0    3   12
[3,]   12    3    0    3
[4,]   27   12    3    0

I'm assuming you're trying do some type of comparison across all row-pairs of a matrix.
You could use outer() to run through all pairs of row-indices, and apply a vectorized
comparison function to each row-pair. E.g. you could calculate the squared Euclidean distance among all row-pairs as follows:

m <- matrix(1:12,4,3)     
> outer(1:4,1:4, FUN = Vectorize( function(i,j) sum((m[i,]-m[j,])^2 )) )
     [,1] [,2] [,3] [,4]
[1,]    0    3   12   27
[2,]    3    0    3   12
[3,]   12    3    0    3
[4,]   27   12    3    0

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短叹 2024-11-21 11:17:46

如果您愿意进行自我比较，outer() 效果很好 - 例如 1-1 和 2-2 等...（矩阵中的对角线值）。此外，outer() 还执行 1-2 和 2-1 比较。

大多数时候成对比较只需要三角比较，不需要自比较和镜像比较。要实现三角比较，请使用 combn() 方法。

下面是一个示例输出，显示了 outer() 和 combn() 之间的差异，

> v <- c(1,2,3,4)
> outer(v, v, function(x, y) print(paste(x, "-", y)))
 [1] "1 - 1" "2 - 1" "3 - 1" "4 - 1" "1 - 2" "2 - 2" "3 - 2" "4 - 2" "1 - 3" "2 - 3" "3 - 3" "4 - 3" "1 - 4" "2 - 4" "3 - 4" "4 - 4"

请注意上面的“1-1”自我比较。以及“1-2”和“2-1”的镜像比较。与下面的对比：

> v <- c(1,2,3,4)
> allPairs <- combn(length(v), 2) # choose a pair from 1:length(v)
> a_ply(combn(length(v), 2), 2, function(x) print(paste(x[1],"--",x[2]))) # iterate over all pairs
[1] "1 -- 2"
[1] "1 -- 3"
[1] "1 -- 4"
[1] "2 -- 3"
[1] "2 -- 4"
[1] "3 -- 4"

你可以看到上面矩阵的“上三角”部分。

当您有两个不同的向量进行成对运算时，Outer() 更合适。为了在单个向量内执行成对运算，通常可以使用combn。

例如，如果您正在执行 outer(x,x,...) 那么您可能做错了 - 您应该考虑 combn(length(x),2))代码>

outer() works fine if you are willing to do self-compare - such as 1-1 and 2-2 etc... (the diagonal values in the matrix). Also outer() performs both 1-2 and 2-1 comparisions.

Most of the times pair-wise comparisions only require triangular comparisions, without the self-comparision and mirror comparisions. To achieve triangular comparisions, use combn() method.

Here is a sample output to show the difference between outer() and combn()

> v <- c(1,2,3,4)
> outer(v, v, function(x, y) print(paste(x, "-", y)))
 [1] "1 - 1" "2 - 1" "3 - 1" "4 - 1" "1 - 2" "2 - 2" "3 - 2" "4 - 2" "1 - 3" "2 - 3" "3 - 3" "4 - 3" "1 - 4" "2 - 4" "3 - 4" "4 - 4"

Note the "1-1" self-comparisions above. And the "1-2" and "2-1" mirror comparisions. Contrast it with the below:

> v <- c(1,2,3,4)
> allPairs <- combn(length(v), 2) # choose a pair from 1:length(v)
> a_ply(combn(length(v), 2), 2, function(x) print(paste(x[1],"--",x[2]))) # iterate over all pairs
[1] "1 -- 2"
[1] "1 -- 3"
[1] "1 -- 4"
[1] "2 -- 3"
[1] "2 -- 4"
[1] "3 -- 4"

You can see the "upper triangular" part of the matrix in the above.

Outer() is more apt when you have two different vectors to do pair-wise operation. For performing pair-wise operations within a single vector, more often than not you can get away with combn.

For example, if you are doing outer(x,x,...) then you are perhaps doing it wrong - you should consider combn(length(x),2))

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杯别 2024-11-21 11:17:46

也许不是像@Prasad那么通用的解决方案，但在平方和的这种特殊情况下要快得多：

dist(m)^2

Maybe not so universal solution as @Prasad but much faster in this special case of sum of squares:

dist(m)^2

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迷荒 2024-11-21 11:17:46

@Gopalkrishna Palem

我喜欢你的解决方案！但是，我认为您应该使用combn(v, 2) 而不是comn(length(v), 2)。 commn(length(v), 2) 仅迭代 v 的不定数，

> v <- c(3,4,6,7)
> combn(v, 2)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    3    3    3    4    4    6
[2,]    4    6    7    6    7    7

> combn(length(v), 2)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    1    1    2    2    3
[2,]    2    3    4    3    4    4

> a_ply(combn(v, 2), 2, function(x) print(paste(x[1],"--",x[2])) )
[1] "3 -- 4"
[1] "3 -- 6"
[1] "3 -- 7"
[1] "4 -- 6"
[1] "4 -- 7"
[1] "6 -- 7"
> a_ply(combn(length(v), 2), 2, function(x) print(paste(x[1],"--",x[2])) )
[1] "1 -- 2"
[1] "1 -- 3"
[1] "1 -- 4"
[1] "2 -- 3"
[1] "2 -- 4"
[1] "3 -- 4"

因此最终结果与 commn(v, 2) 是正确的。

然后，如果我们有一个数据框，我们可以使用索引将函数应用于成对的行：

> df
  x  y
1 4  8
2 5  9
3 6 10
4 7 11

a_ply(combn(nrow(df), 2), 2, function(x) print(df[x[1],] - df[x[2],]))
   x  y
1 -1 -1
   x  y
1 -2 -2
   x  y
1 -3 -3
   x  y
2 -1 -1
   x  y
2 -2 -2
   x  y
3 -1 -1

但是，a_ply 会丢弃结果，那么如何将输出存储在向量中以供进一步分析呢？我不想只打印结果

@Gopalkrishna Palem

I like your solution! However, I think you should use combn(v, 2) instead of combn(length(v), 2). combn(length(v), 2) only iterates over the indecies of v

> v <- c(3,4,6,7)
> combn(v, 2)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    3    3    3    4    4    6
[2,]    4    6    7    6    7    7

> combn(length(v), 2)
     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    1    1    2    2    3
[2,]    2    3    4    3    4    4

> a_ply(combn(v, 2), 2, function(x) print(paste(x[1],"--",x[2])) )
[1] "3 -- 4"
[1] "3 -- 6"
[1] "3 -- 7"
[1] "4 -- 6"
[1] "4 -- 7"
[1] "6 -- 7"
> a_ply(combn(length(v), 2), 2, function(x) print(paste(x[1],"--",x[2])) )
[1] "1 -- 2"
[1] "1 -- 3"
[1] "1 -- 4"
[1] "2 -- 3"
[1] "2 -- 4"
[1] "3 -- 4"

so the final result is correct with combn(v, 2).

Then if we have a dataframe, we can use the indices to apply a function to pairwise rows:

> df
  x  y
1 4  8
2 5  9
3 6 10
4 7 11

a_ply(combn(nrow(df), 2), 2, function(x) print(df[x[1],] - df[x[2],]))
   x  y
1 -1 -1
   x  y
1 -2 -2
   x  y
1 -3 -3
   x  y
2 -1 -1
   x  y
2 -2 -2
   x  y
3 -1 -1

However, a_ply will discard the result, so how can I store the output in a vector for further analysis? I don't want to just print the result

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