a <- c(1,3,5)
b <- c(2,4,6)
x <- sum(a*b)/(sqrt(sum(a^2))*sqrt(sum(b^2)))

## 用户,Item,Score
x <- read.csv(textConnection("
  1,101,5.0
  1,102,3.0
  1,103,2.5
  2,101,2.0
  2,102,2.5
  2,103,5.0
  2,104,2.0
  3,101,2.5
  3,104,4.0
  3,105,4.5
  3,107,5.0
  4,101,5.0
  4,103,3.0
  4,104,4.5
  4,106,4.0
  5,101,4.0
  5,102,3.0
  5,103,2.0
  5,104,4.0
  5,105,3.5
  5,106,4.0  
"), header = FALSE)

rn <- sort(unique(x$V1))
cn <- sort(unique(x$V2))
library(Matrix)
y <- sparseMatrix(i = match(x$V1, rn), j = match(x$V2, cn), x = x$V3)    
h <- as.matrix(dist(t(y), diag = TRUE)^2)
h <- 1/(1 + h)
diag(h) <- 0
## 推荐引擎的四个参数：相似矩阵、购买了什么，得分是多少，推荐几个
recommend <- function(h = h, k = c(3, 5), score = c(4, 5), m = 1) {
  if(length(k) > 1) {
    v <- colSums(h[k,] * score)/colSums(h[k,])
  } else {
    v <- h[k,]
  }
  v[k] <- 0
  od <- order(v, decreasing=T)[1:m]
  return(list(colnames(h)[od], v[od]))
}
recommend(h, k = c(1,3), score = c(1, 5),  m = 2)

参考资料

[1]. http://www.bjt.name/2013/06/recommendation-system/
[2]. http://zh.wikipedia.org/wiki/%E4%BD%99%E5%BC%A6%E7%9B%B8%E4%BC%BC%E6%80%A7