Speeding up computation of Dice coefficient in C / Rcpp

Question

I need to compute a similarity measure call the Dice coefficient over large matrices (600,000 x 500) of binary vectors in R. For speed I use C / Rcpp. The function runs great but as I am not a computer scientist by background I would like to know if it could run faster. This code is suitable for parallelisation but I have no experience parallelising C code.

The Dice coefficient is a simple measure of similarity / dissimilarity (depending how you take it). It is intended to compare asymmetric binary vectors, meaning one of the combination (usually 0-0) is not important and agreement (1-1 pairs) have more weight than disagreement (1-0 or 0-1 pairs). Imagine the following contingency table:

   1    0
1  a    b
0  c    d

The Dice coef is: (2*a) / (2*a +b + c)

Here is my Rcpp implementation:

library(Rcpp)
cppFunction('
    NumericMatrix dice(NumericMatrix binaryMat){
        int nrows = binaryMat.nrow(), ncols = binaryMat.ncol();
        NumericMatrix results(ncols, ncols);
        for(int i=0; i < ncols-1; i++){ // columns fixed
            for(int j=i+1; j < ncols; j++){ // columns moving
                double a = 0;
                double d = 0;
                for (int l = 0; l < nrows; l++) {
                    if(binaryMat(l, i)>0){
                        if(binaryMat(l, j)>0){
                            a++;
                        }
                    }else{
                        if(binaryMat(l, j)<1){
                            d++;
                        }
                    }
                }
                // compute Dice coefficient         
                double abc = nrows - d;
                double bc = abc - a;
                results(j,i) = (2*a) / (2*a + bc);          
            }
        }
        return wrap(results);
    }
')

And here is a running example:

x <- rbinom(1:200000, 1, 0.5)
X <- matrix(x, nrow = 200, ncol = 1000)
system.time(dice(X))
  user  system elapsed
  0.814   0.000   0.814

Answer 1

The solution proposed by Roland was not entirely satisfying for my use case. So based on the source code from the arules package I implement a much faster version. The code in arules rely on an algorithm from Leisch (2005) using the tcrossproduct() function in R.

First, I wrote a Rcpp / RcppEigen version of crossprod that is 2-3 time faster. This is based on the example code in the RcppEigen vignette.

library(Rcpp)
library(RcppEigen)
library(inline)
crossprodCpp <- '
using Eigen::Map;
using Eigen::MatrixXi;
using Eigen::Lower;

const Map<MatrixXi> A(as<Map<MatrixXi> >(AA));

const int m(A.rows()), n(A.cols());

MatrixXi AtA(MatrixXi(n, n).setZero().selfadjointView<Lower>().rankUpdate(A.adjoint()));

return wrap(AtA);
'

fcprd <- cxxfunction(signature(AA = "matrix"), crossprodCpp, "RcppEigen")

Then I wrote a small R function to compute the Dice coefficient.

diceR <- function(X){
    a <- fcprd(X)

nx <- ncol(X)
rsx <- colSums(X)

c <- matrix(rsx, nrow = nx, ncol = nx) - a
# b <- matrix(rsx, nrow = nx, ncol = nx, byrow = TRUE) - a
b <- t(c)

m <- (2 * a) / (2*a + b + c)
return(m)
}

This new function is ~8 time faster than the old one and ~3 time faster than the one in arules.

m <- microbenchmark(dice(X), diceR(X), dissimilarity(t(X), method="dice"), times=100)
m
# Unit: milliseconds
#                                  expr       min       lq    median       uq      max neval
#                               dice(X) 791.34558 809.8396 812.19480 814.6735 910.1635   100
#                              diceR(X)  62.98642  76.5510  92.02528 159.2557 507.1662   100
#  dissimilarity(t(X), method = "dice") 264.07997 342.0484 352.59870 357.4632 520.0492   100

Answer 2

I cannot run your function at work, but is the result the same as this?

library(arules)
plot(dissimilarity(X,method="dice"))

system.time(dissimilarity(X,method="dice"))
#user  system elapsed 
#0.04    0.00    0.04