在R中的稀疏矩阵上运行cor()(或任何变量)

Question

当尝试cor()在稀疏矩阵(dgCMatrix或dgTMatrix类型)上运行该函数时,我收到以下错误:

Error in cor(x) : supply both 'x' and 'y' or a matrix-like 'x'

将我的矩阵转换为密集将是非常低效的.有没有一种简单的方法来计算这种相关性(没有所有对循环？).

谢谢,

• 罗恩

Answer 1

EDITED ANSWER - 针对内存使用和速度进行了优化.

您的错误是逻辑错误,因为稀疏矩阵不被cor函数识别为矩阵,并且-yet-没有方法可以在Matrix包中进行相关.

没有我知道的功能可以让你计算这个,但你可以使用Matrix包中提供的矩阵运算符轻松地自己计算:

sparse.cor <- function(x){
  n <- nrow(x)
  m <- ncol(x)
  ii <- unique(x@i)+1 # rows with a non-zero element

  Ex <- colMeans(x)
  nozero <- as.vector(x[ii,]) - rep(Ex,each=length(ii))        # colmeans

  covmat <- ( crossprod(matrix(nozero,ncol=m)) +
              crossprod(t(Ex))*(n-length(ii))
            )/(n-1)
  sdvec <- sqrt(diag(covmat))
  covmat/crossprod(t(sdvec))
}

这covmat是你的方差 - 协方差矩阵,所以你也可以计算那个.该计算基于选择至少一个元素非零的行.对于这个的交叉乘积,您将colmeans乘以全零行的数量.这相当于

换算(X - E [X])次(X - E [X])

除以n-1,你就得到方差 - 协方差矩阵.其余的很容易.

一个测试用例:

X <- sample(0:10,1e8,replace=T,p=c(0.99,rep(0.001,10)))
xx <- Matrix(X,ncol=5)

> system.time(out1 <- sparse.cor(xx))
   user  system elapsed 
   0.50    0.09    0.59 
> system.time(out2 <- cor(as.matrix(xx)))
   user  system elapsed 
   1.75    0.28    2.05 
> all.equal(out1,out2)
[1] TRUE

Answer 2

这就是我最终使用的.感谢@Joris提供的所有帮助!

我的x矩阵非常大.假设它的大小n * p,n=200k而p=10k在我的情况.

诀窍是保持操作的稀疏性并在p * p矩阵上执行计算而不是p*n x n*p.

版本1更简单,但在时间和内存上效率较低,因为外部产品操作很昂贵:

sparse.cor2 <- function(x){
    n <- nrow(x)

    covmat <- (crossprod(x)-2*(colMeans(x) %o% colSums(x))
              +n*colMeans(x)%o%colMeans(x))/(n-1)

    sdvec <- sqrt(diag(covmat)) # standard deviations of columns
    covmat/crossprod(t(sdvec)) # correlation matrix
}

版本2在时间上(保存多个操作)和内存更有效.p=10k矩阵仍需要大量内存:

sparse.cor3 <- function(x){
    memory.limit(size=10000)
    n <- nrow(x)

    cMeans <- colMeans(x)
    cSums <- colSums(x)

    # Calculate the population covariance matrix.
    # There's no need to divide by (n-1) as the std. dev is also calculated the same way.
    # The code is optimized to minize use of memory and expensive operations
    covmat <- tcrossprod(cMeans, (-2*cSums+n*cMeans))
    crossp <- as.matrix(crossprod(x))
    covmat <- covmat+crossp

    sdvec <- sqrt(diag(covmat)) # standard deviations of columns
    covmat/crossprod(t(sdvec)) # correlation matrix
}

时序比较(sparse.cor是@Joris最新版本):

> X <- sample(0:10,1e7,replace=T,p=c(0.9,rep(0.01,10)))
> x <- Matrix(X,ncol=10)
> 
> object.size(x)
11999472 bytes
> 
> system.time(corx <- sparse.cor(x))
   user  system elapsed 
   0.50    0.06    0.56 
> system.time(corx2 <- sparse.cor2(x))
   user  system elapsed 
   0.17    0.00    0.17 
> system.time(corx3 <- sparse.cor3(x))
   user  system elapsed 
   0.13    0.00    0.12 
> system.time(correg <-cor(as.matrix(x)))
   user  system elapsed 
   0.25    0.03    0.29 
> all.equal(c(as.matrix(corx)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx2)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx3)),c(as.matrix(correg)))
[1] TRUE

更大的x矩阵:

> X <- sample(0:10,1e8,replace=T,p=c(0.9,rep(0.01,10)))
> x <- Matrix(X,ncol=10)
> object.size(x)
120005688 bytes
> system.time(corx2 <- sparse.cor2(x))
   user  system elapsed 
   1.47    0.07    1.53 
> system.time(corx3 <- sparse.cor3(x))
   user  system elapsed 
   1.18    0.09    1.29 
> system.time(corx <- sparse.cor(x))
   user  system elapsed 
   5.43    1.26    6.71

Answer 3

答案得到了@Ron的优雅解决,但对解决方案稍作修改就更清晰了,并且还返回了样本协方差矩阵.

sparse.cor4 <- function(x){
    n <- nrow(x)
    cMeans <- colMeans(x)
    covmat <- (as.matrix(crossprod(x)) - n*tcrossprod(cMeans))/(n-1)
    sdvec <- sqrt(diag(covmat)) 
    cormat <- covmat/tcrossprod(sdvec)
    list(cov=covmat,cor=cormat)
}

简化来自于:使用nxp矩阵X,并且列的nxp矩阵M表示X:

cov(X) = E[(X-M)'(X-M)] = E[X'X - M'X - X'M + M'M] 

M'X = X'M = M'M, which have (i,j) elements = sum(column i) * sum(column j) / n

= n * mean(column i) * mean(column j)

或者用列的行向量m表示,

= n * m'm

然后 cov(X) = E[X'X - n m'm]

现在它变得更快了.

> X <- sample(0:10,1e7,replace=T,p=c(0.9,rep(0.01,10)))
> x <- Matrix(X,ncol=10)
> system.time(corx <- sparse.cor(x))
   user  system elapsed 
  1.139   0.196   1.334 
> system.time(corx3 <- sparse.cor3(x))
   user  system elapsed 
  0.194   0.007   0.201 
> system.time(corx4 <- sparse.cor4(x))
   user  system elapsed 
  0.187   0.007   0.194 
> system.time(correg <-cor(as.matrix(x)))
   user  system elapsed 
  0.341   0.067   0.407 
> system.time(covreg <- cov(as.matrix(x)))
   user  system elapsed 
  0.314   0.016   0.330 
> all.equal(c(as.matrix(corx)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx3)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx4$cor)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx4$cov)),c(as.matrix(covreg)))
[1] TRUE