我已经编写了一些 Rcpp 代码和 R 代码，它们可以计算出二进制矩阵的二进制/Jaccard 距离。比 dist(x, method = "binary") 快 80 倍。它将输入矩阵转换为原始矩阵，这是输入的转置（以便位模式在内部处于正确的顺序）。然后在一些 C++ 代码中使用它，将数据作为 64 位无符号整数处理以提高速度。两个向量 x 和 y 的 Jaccard 距离等于 x ^ y / (x | y)，其中 ^ 是 xor 运算符。如果xor 或or 的结果非零，则Hamming Weight 计算用于计算设置的位数。
我已将代码放在 github 上 https://github.com/NikNakk/binaryDist/ 上，并复制了下面的两个文件。我已经确认，一些随机数据集的结果与dist(x, method = "binary") 相同。
在 39000 行 x 14000 列（每行 1-5 个）的数据集上，大约需要 11 分钟。输出距离矩阵为 5.7 GB。
bDist.cpp
#include <Rcpp.h>
using namespace Rcpp;
//countBits function taken from https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
const uint64_t m1 = 0x5555555555555555; //binary: 0101...
const uint64_t m2 = 0x3333333333333333; //binary: 00110011..
const uint64_t m4 = 0x0f0f0f0f0f0f0f0f; //binary: 4 zeros, 4 ones ...
const uint64_t h01 = 0x0101010101010101; //the sum of 256 to the power of 0,1,2,3...
int countBits(uint64_t x) {
x -= (x >> 1) & m1; //put count of each 2 bits into those 2 bits
x = (x & m2) + ((x >> 2) & m2); //put count of each 4 bits into those 4 bits
x = (x + (x >> 4)) & m4; //put count of each 8 bits into those 8 bits
return (x * h01)>>56; //returns left 8 bits of x + (x<<8) + (x<<16) + (x<<24) + ...
}
// [[Rcpp::export]]
int countBitsFromRaw(RawVector rv) {
uint64_t* x = (uint64_t*)RAW(rv);
return(countBits(*x));
}
// [[Rcpp::export]]
NumericVector bDist(RawMatrix mat) {
int nr(mat.nrow()), nc(mat.ncol());
int nw = nr / 8;
NumericVector res(nc * (nc - 1) / 2);
// Access the raw data as unsigned 64 bit integers
uint64_t* data = (uint64_t*)RAW(mat);
uint64_t a(0);
// Work through each possible combination of columns (rows in the original integer matrix)
for (int i = 0; i < nc - 1; i++) {
for (int j = i + 1; j < nc; j++) {
uint64_t sx = 0;
uint64_t so = 0;
// Work through each 64 bit integer and calculate the sum of (x ^ y) and (x | y)
for (int k = 0; k < nw; k++) {
uint64_t o = data[nw * i + k] | data[nw * j + k];
// If (x | y == 0) then (x ^ y) will also be 0
if (o) {
// Use Hamming weight method to calculate number of set bits
so = so + countBits(o);
uint64_t x = data[nw * i + k] ^ data[nw * j + k];
if (x) {
sx = sx + countBits(x);
}
}
}
res(a++) = (double)sx / so;
}
}
return (res);
}
R 源码
library("Rcpp")
library("plyr")
sourceCpp("bDist.cpp")
# Converts a binary integer vector into a packed raw vector,
# padding out at the end to make the input length a multiple of packWidth
packRow <- function(row, packWidth = 64L) {
packBits(as.raw(c(row, rep(0, (packWidth - length(row)) %% packWidth))))
}
as.PackedMatrix <- function(x, packWidth = 64L) {
UseMethod("as.PackedMatrix")
}
# Converts a binary integer matrix into a packed raw matrix
# padding out at the end to make the input length a multiple of packWidth
as.PackedMatrix.matrix <- function(x, packWidth = 64L) {
stopifnot(packWidth %% 8 == 0, class(x) %in% c("matrix", "Matrix"))
storage.mode(x) <- "raw"
if (ncol(x) %% packWidth != 0) {
x <- cbind(x, matrix(0L, nrow = nrow(x), ncol = packWidth - (ncol(x) %% packWidth)))
}
out <- packBits(t(x))
dim(out) <- c(ncol(x) %/% 8, nrow(x))
class(out) <- "PackedMatrix"
out
}
# Converts back to an integer matrix
as.matrix.PackedMatrix <- function(x) {
out <- rawToBits(x)
dim(out) <- c(nrow(x) * 8L, ncol(x))
storage.mode(out) <- "integer"
t(out)
}
# Generates random sparse data for testing the main function
makeRandomData <- function(nObs, nVariables, maxBits, packed = FALSE) {
x <- replicate(nObs, {
y <- integer(nVariables)
y[sample(nVariables, sample(maxBits, 1))] <- 1L
if (packed) {
packRow(y, 64L)
} else {
y
}
})
if (packed) {
class(x) <- "PackedMatrix"
x
} else {
t(x)
}
}
# Reads a binary matrix from file or character vector
# Borrows the first bit of code from read.table
readPackedMatrix <- function(file = NULL, text = NULL, packWidth = 64L) {
if (missing(file) && !missing(text)) {
file <- textConnection(text)
on.exit(close(file))
}
if (is.character(file)) {
file <- file(file, "rt")
on.exit(close(file))
}
if (!inherits(file, "connection"))
stop("'file' must be a character string or connection")
if (!isOpen(file, "rt")) {
open(file, "rt")
on.exit(close(file))
}
lst <- list()
i <- 1
while(length(line <- readLines(file, n = 1)) > 0) {
lst[[i]] <- packRow(as.integer(strsplit(line, "", fixed = TRUE)[[1]]), packWidth = packWidth)
i <- i + 1
}
out <- do.call("cbind", lst)
class(out) <- "PackedMatrix"
out
}
# Wrapper for the C++ code which
binaryDist <- function(x) {
if (class(x) != "PackedMatrix") {
x <- as.PackedMatrix(x)
}
dst <- bDist(x)
attr(dst, "Size") <- ncol(x)
attr(dst, "Diag") <- attr(dst, "Upper") <- FALSE
attr(dst, "method") <- "binary"
attr(dst, "call") <- match.call()
class(dst) <- "dist"
dst
}
x <- makeRandomData(2000, 400, maxBits = 5, packed = TRUE)
system.time(bd <- binaryDist(x))
来自原始答案：
要考虑的其他事情是对两行与单行之间的比较进行一些预过滤，因为距离将是 0 表示重复或 1 表示任何其他可能性。
vegan 包中的vegdist 函数和amap 包。如果您有多个内核并利用它支持并行化的事实，后者可能只会更快。