How to find the column means for a sparse matrix excluding 0 values?

Question

I have a sparse matrix structured similar to this, but much larger.

library(Matrix)
dfmtest<-new("dgCMatrix"
    , i = c(0L, 1L, 2L, 4L, 5L, 6L, 8L, 0L, 1L, 2L, 3L, 4L, 6L, 7L, 8L, 
0L, 2L, 3L, 6L, 7L, 8L, 1L, 2L, 4L, 5L, 6L, 7L, 8L, 9L, 0L, 1L, 
3L, 4L, 5L, 6L, 7L, 8L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 
9L, 0L, 1L, 3L, 4L, 6L, 7L, 8L, 9L, 0L, 2L, 3L, 5L, 6L, 7L, 9L, 
0L, 1L, 2L, 3L, 4L, 5L, 6L, 8L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 
7L, 9L)
    , p = c(0L, 7L, 15L, 21L, 29L, 38L, 48L, 56L, 63L, 72L, 81L)
    , Dim = c(10L, 10L)
    , Dimnames = list(NULL, NULL)
    , x = c(4, 3, 1, 2, 3, 1, 2, 1, 3, 3, 2, 3, 3, 3, 4, 2, 1, 2, 3, 2, 
1, 4, 1, 2, 2, 3, 2, 3, 4, 1, 4, 1, 3, 4, 3, 2, 2, 2, 4, 1, 2, 
2, 1, 2, 3, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 4, 3, 3, 2, 1, 2, 2, 
1, 1, 3, 3, 4, 1, 2, 4, 2, 4, 1, 2, 2, 3, 4, 2, 1, 2, 4)
    , factors = list()
)

I would like to be able to find the mean of each column (and row eventually), excluding the 0 values. If I attempt to do it manually I run into memory issues because of the size of my sparse matrix.

nzmean <- function(x) {
  mean(x[x!=0])
}


dfmmeans <- apply(dfmtest, 2, nzmean)
#       1        2        3        4        5        6        7        8 
#2.285714 2.750000 1.833333 2.625000 2.444444 1.800000 1.875000 2.000000 
#       9       10 
#2.666667 2.333333 

When I run the above on my actual matrix I get the following error:

    Error in asMethod(object) : 
      Cholmod error 'problem too large' at file ../Core/cholmod_dense.c, line 105

I have also looked into using the colMeans function, but it looks as though it is including all 0 values in the calculation.

dfmmeans <- colMeans(dfmtest)
#[1] 1.6 2.2 1.1 2.1 2.2 1.8 1.5 1.4 2.4 2.1

Is there a good way to do this on a large sparse matrix?

Answer 1

Matrix has a nice summary method that returns an i, j, x data frame of the non-zero elements in the matrix, which can easily be summarized using aggregate (or dplyr or data.table, if you like):

library(Matrix)

str(summary(dfmtest))
#> Classes 'sparseSummary' and 'data.frame':    81 obs. of  3 variables:
#>  $ i: int  1 2 3 5 6 7 9 1 2 3 ...
#>  $ j: int  1 1 1 1 1 1 1 2 2 2 ...
#>  $ x: num  4 3 1 2 3 1 2 1 3 3 ...
#>  - attr(*, "header")= chr "10 x 10 sparse Matrix of class \"dgCMatrix\", with 81 entries"

aggregate(x ~ j, summary(dfmtest), mean)
#>     j        x
#> 1   1 2.285714
#> 2   2 2.750000
#> 3   3 1.833333
#> 4   4 2.625000
#> 5   5 2.444444
#> 6   6 1.800000
#> 7   7 1.875000
#> 8   8 2.000000
#> 9   9 2.666667
#> 10 10 2.333333

If you'd like a purely matrix ops version, you can use abs(sign(...)) to turn all non-sparse elements into ones, which lets you calculate column means only with colSums:

colSums(dfmtest) / colSums(abs(sign(dfmtest)))
#>  [1] 2.285714 2.750000 1.833333 2.625000 2.444444 1.800000 1.875000
#>  [8] 2.000000 2.666667 2.333333

Answer 2

It is true that colMeans does not support removal of zeros:

getMethod("colMeans", "dgCMatrix")
#Method Definition:
#
#function (x, na.rm = FALSE, dims = 1, ...) 
#{
#    .local <- function (x, na.rm = FALSE, dims = 1, sparseResult = FALSE) 
#    .Call(dgCMatrix_colSums, x, na.rm, sparseResult, FALSE, TRUE)
#    .local(x, na.rm, dims, ...)
#}
#<environment: namespace:Matrix>

so we need to work out our own function.

colMeans_drop0 <- function (dgCMat) {
  nnz_per_col <- diff(dgCMat@p)
  ColInd <- rep.int(1:ncol(dgCMat), nnz_per_col)
  sapply(split(dgCMat@x, ColInd), mean)
  }

colMeans_drop0(dfmtest)
#       1        2        3        4        5        6        7        8 
#2.285714 2.750000 1.833333 2.625000 2.444444 1.800000 1.875000 2.000000 
#       9       10 
#2.666667 2.333333 

Note: columns with all zeros are ignored. Similarly:

rowMeans_drop0 <- function (dgCMat) {
  RowInd <- dgCMat@i + 1
  sapply(split(dgCMat@x, RowInd), mean)
  }

and rows with all zeros are ignored.

---

Remarks

alistaire's answer is also good.

The summary + aggregate approach is a different implementation of the idea in this answer.

getMethod("summary", "sparseMatrix")
#Method Definition:
#
#function (object, ...) 
#{
#    d <- dim(object)
#    T <- as(object, "TsparseMatrix")
#    r <- if (is(object, "nsparseMatrix")) 
#        data.frame(i = T@i + 1L, j = T@j + 1L)
#    else data.frame(i = T@i + 1L, j = T@j + 1L, x = T@x)
#    attr(r, "header") <- sprintf("%d x %d sparse Matrix of class \"%s\", with %d entries", 
#        d[1], d[2], class(object), length(T@i))
#    class(r) <- c("sparseSummary", class(r))
#    r
#}
#<environment: namespace:Matrix>

summary first coerces any sparse matrix class to "dgTMatrix" class, i.e., the triplet format, and the aggregate relies on split + lapply internally.

The idea of using colSums can be desirable, if you want to retain the result (which is 0 of course) for all-zero columns.

---

Discussion with 20650

An colSums / rowSums based implementation for our functions is also possible.

colMeans_drop0 <- function (dgCMat) {
  nnz_per_col <- diff(dgCMat@p)
  nnz_per_col[nnz_per_col == 0] <- 1  ## just avoid doing 0 / 0
  setNames(colSums(dgCMat) / nnz_per_col, 1:ncol(dgCMat))
  }

rowMeans_drop0 <- function (dgCMat) {
  RowInd <- dgCMat@i + 1
  nnz_per_row <- tabulate(RowInd)
  nnz_per_row[nnz_per_row == 0] <- 1  ## just avoid doing 0 / 0
  setNames(rowSums(dgCMat) / nnz_per_row, 1:nrow(dgCMat))
  }

Since colSums / rowSums drops dimnames, we add them in with setNames. These two functions retain results for all-zero columns / rows. We also use tabulate function to compute number of non-zero entries on rows efficiently.