最有效的R余弦计算 [英] most efficient R cosine calculation
问题描述
我有两个值向量和一个权重向量，我需要计算余弦相似度.由于复杂的原因，我一次只能计算一对余弦.但是我必须做数百万次.
I have two vectors of values and one vector of weights, and I need to calculate the cosine similarity. For complicated reasons, I can only calculate the cosine for one pair at a time. But I have to do it many millions of times.
cosine_calc <- function(a,b,wts) {
#scale both vectors by the weights, then compute the cosine of the scaled vectors
a = a*wts
b = b*wts
(a %*% b)/(sqrt(a%*%a)*sqrt(b%*%b))
}
可行，但是我想尝试从中获得更好的性能.
works, but I want to try to eke better performance out of it.
示例数据:
a = c(-1.2092420, -0.7053822, 1.4364633, 1.3612304, -0.3029147, 1.0319704, 0.6707610, -2.2128987, -0.9839970, -0.4302205)
b = c(-0.69042619, 0.05811749, -0.17836802, 0.15699691, 0.78575477, 0.27925779, -0.08552864, -1.31031219, -1.92756861, -1.36350112)
w = c(0.26333839, 0.12803180, 0.62396023, 0.37393705, 0.13539926, 0.09199102, 0.37347546, 1.36790007, 0.64978409, 0.46256891)
> cosine_calc(a,b,w)[,1]
[1,] 0.8390671
此问题指出R中还有其他可用的预定义余弦函数，但是他们的相对效率什么也没说.
This question points out that there are other predefined cosine functions available in R, but says nothing about their relative efficiency.
推荐答案
您正在使用的所有函数都是.Primitive(因此已经直接调用了编译代码)，因此很难在re之外找到一致的速度提升.用优化的BLAS构建R.话虽如此，对于较大的向量，这是一个可能更快的选择:
All the functions you're using are .Primitive (therefore already call compiled code directly), so it will be hard to find consistent speed gains outside of re-building R with an optimized BLAS. With that said, here is one option that might be faster for larger vectors:
cosine_calc2 <- function(a,b,wts) {
a = a*wts
b = b*wts
crossprod(a,b)/sqrt(crossprod(a)*crossprod(b))
}
all.equal(cosine_calc1(a,b,w),cosine_calc2(a,b,w))
# [1] TRUE
# Check some timings
library(rbenchmark)
# cosine_calc2 is slower on my machine in this case
benchmark(
cosine_calc1(a,b,w),
cosine_calc2(a,b,w), replications=1e5, columns=1:4 )
# test replications user.self sys.self
# 1 cosine_calc1(a, b, w) 100000 1.06 0.02
# 2 cosine_calc2(a, b, w) 100000 1.21 0.00
# but cosine_calc2 is faster for larger vectors
set.seed(21)
a <- rnorm(1000)
b <- rnorm(1000)
w <- runif(1000)
benchmark(
cosine_calc1(a,b,w),
cosine_calc2(a,b,w), replications=1e5, columns=1:4 )
# test replications user.self sys.self
# 1 cosine_calc1(a, b, w) 100000 3.83 0
# 2 cosine_calc2(a, b, w) 100000 2.12 0
更新:
UPDATE:
分析表明，将每个向量乘以权重向量需要花费大量时间.
Profiling reveals that quite a bit of time is spent multiplying each vector by the weight vector.
> Rprof(); for(i in 1:100000) cosine_calc2(a,b,w); Rprof(NULL); summaryRprof()
$by.self
self.time self.pct total.time total.pct
* 0.80 45.98 0.80 45.98
crossprod 0.56 32.18 0.56 32.18
cosine_calc2 0.32 18.39 1.74 100.00
sqrt 0.06 3.45 0.06 3.45
$by.total
total.time total.pct self.time self.pct
cosine_calc2 1.74 100.00 0.32 18.39
* 0.80 45.98 0.80 45.98
crossprod 0.56 32.18 0.56 32.18
sqrt 0.06 3.45 0.06 3.45
$sample.interval
[1] 0.02
$sampling.time
[1] 1.74
如果可以在必须调用该函数数百万次之前进行加权，则可以节省大量时间. cosine_calc3比带有小向量的原始函数要快一些.字节编译功能应该为您提供另一种边际加速.
If you can do the weighting before you have to call the function millions of times, it could save you quite a bit of time. cosine_calc3 is marginally faster than your original function with small vectors. Byte-compiling the function should give you another marginal speedup.
cosine_calc3 <- function(a,b) {
crossprod(a,b)/sqrt(crossprod(a)*crossprod(b))
}
A = a*w
B = b*w
# Run again on the 1000-element vectors
benchmark(
cosine_calc1(a,b,w),
cosine_calc2(a,b,w),
cosine_calc3(A,B), replications=1e5, columns=1:4 )
# test replications user.self sys.self
# 1 cosine_calc1(a, b, w) 100000 3.85 0.00
# 2 cosine_calc2(a, b, w) 100000 2.13 0.02
# 3 cosine_calc3(A, B) 100000 1.31 0.00
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