【发布时间】：2025-12-25 23:10:16
【问题描述】：
当您想弄清楚哪些事件一起发生时，关联规则是一种非常常见的技术（例如汉堡和面包大多一起销售）。在营销中，这种技术被用来找出免费的产品。
我正在寻找一种提取“替代产品”的技术，并像逆关联规则一样找出哪些事件不太可能一起发生。 Spark、R、Python 等中是否有任何算法或技术可用于此？
谢谢， 阿米尔
【问题讨论】：
标签： associations rules inverse
【发布时间】：2025-12-25 23:10:16
【问题描述】：
我已经使用Teng, Hsieh and Chen (2002) for R 为替代规则挖掘做了一个非常实用的实现。也许它可以帮助你：
# Used packages:
library(arules)
SRM <- function(TransData, MinSup, MinConf, pMin, pChi, itemLabel, nTID){
# Packages ----------------------------------------------------------------
if (sum(search() %in% "package:arules") == 0) {
stop("Please load package arules")
}
# Checking Input data -----------------------------------------------------
if (missing(TransData)) {
stop("Transaction data is missing")
}
if (is.numeric(nTID) == FALSE) {
stop("nTID has to be one numeric number for the count of
Transactions")
}
if (length(nTID) > 1) {
stop("nTID has to be one number for the count of Transactions")
}
if (is.character(itemLabel) == FALSE) {
stop("itemLabel has to be a character")
}
# Concrete Item sets ---------------------------------------------------
# adding complements to transaction data
compl_trans <- addComplement(TransData,labels = itemLabel)
compl_tab <- crossTable(compl_trans,"support")
compl_tab_D <- as.data.frame(compl_tab)
# ordering matrix
compl_tab_D <- compl_tab_D[order(rownames((compl_tab))),order(colnames((compl_tab)))]
# Chi Value ---------------------------------------------------------------
# empty data frame for loop
complement_data <- data.frame(Chi = as.numeric(),
Sup_X.Y = as.numeric(),
X = as.character(),
Sup_X = as.numeric(),
Y = as.character(),
Sup_Y = as.numeric(),
CX = as.character(),
SupCX = as.numeric(),
CY = as.character(),
Sup_CY = as.numeric(),
Conf_X.CY = as.numeric(),
Sup_X.CY = as.numeric(),
Conf_Y.CX = as.numeric(),
SupY_CX = as.numeric())
# first loop for one item
for ( i in 1 : (length(itemLabel) - 1)) {
# second loop combines it with all other items
for (u in (i + 1) : length(itemLabel)) {
# getting chi value from Teng
a <- itemLabel[i]
b <- itemLabel[u]
ca <- paste0("!", itemLabel[i])
cb <- paste0("!", itemLabel[u])
chiValue <- nTID * (
compl_tab[ca, cb] ^ 2 / (compl_tab[ca, ca] * compl_tab[cb, cb]) +
compl_tab[ca, b] ^ 2 / (compl_tab[ca, ca] * compl_tab[b, b]) +
compl_tab[a, cb] ^ 2 / (compl_tab[a, a] * compl_tab[cb, cb]) +
compl_tab[a, b] ^ 2 / (compl_tab[a, a] * compl_tab[b, b]) - 1)
# condition to be dependent
if (compl_tab[a, b] > compl_tab[a, a] * compl_tab[b, b] && chiValue >= qchisq(pChi, 1) &&
compl_tab[a, a] >= MinSup && compl_tab[b, b] >= MinSup ) {
chi_sup <- data.frame(Chi = chiValue,
Sup_X.Y = compl_tab[a, b],
X = a,
Sup_X = compl_tab[a, a],
Y = b,
Sup_Y = compl_tab[b, b],
CX = ca,
SupCX = compl_tab[ca, ca],
CY = cb,
Sup_CY = compl_tab[cb, cb],
Conf_X.CY = compl_tab[a, cb] / compl_tab[a, a],
Sup_X.CY = compl_tab[a, cb],
Conf_Y.CX = compl_tab[ca, b] / compl_tab[b, b],
SupY_CX = compl_tab[ca, b])
try(complement_data <- rbind(complement_data, chi_sup))
}
}
}
if (nrow(complement_data) == 0) {
stop("No complement item sets could have been found")
}
# changing mode of
complement_data$X <- as.character(complement_data$X)
complement_data$Y <- as.character(complement_data$Y)
# calculating support for concrete itemsets with all others and their complements -------------------
## with complements
matrix_trans <- as.data.frame(as(compl_trans, "matrix"))
sup_three <- data.frame(Items = as.character(),
Support = as.numeric())
setCompl <- names(matrix_trans)
# 1. extracts all other values than that are not in the itemset
for (i in 1 : nrow(complement_data)) {
value <- setCompl[ !setCompl %in% c(complement_data$X[i],
complement_data$Y[i],
paste0("!", complement_data$X[i]),
paste0("!",complement_data$Y[i]))]
# 2. calculation of support
for (u in value) {
count <- sum(rowSums(matrix_trans[, c(complement_data$X[i], complement_data$Y[i], u )]) == 3)
sup <- count / nTID
sup_three_items <- data.frame(Items = paste0(complement_data$X[i], complement_data$Y[i], u),
Support=sup)
sup_three <- rbind(sup_three, sup_three_items)
}
}
# Correlation of single items-------------------------------------------------------------
# all items of concrete itemsets should be mixed for correlation
combis <- unique(c(complement_data$X, complement_data$Y))
# empty object
rules<- data.frame(
Substitute = as.character(),
Product = as.character(),
Support = as.numeric(),
Confidence = as.numeric(),
Correlation = as.numeric())
# first loop for one item
for (i in 1 : (length(combis) - 1)) {
# second loop combines it with all other items
for (u in (i + 1) : length(combis)) {
first <- combis[i]
second <- combis[u]
corXY <- (compl_tab[first, second] - (compl_tab[first, first] * compl_tab[second, second])) /
(sqrt((compl_tab[first, first] * (1 - compl_tab[first,first])) *
(compl_tab[second, second] * (1 - compl_tab[second, second]))))
# confidence
conf1 <- compl_tab[first, paste0("!", second)] / compl_tab[first, first]
conf2 <- compl_tab[second, paste0("!", first)] / compl_tab[second, second]
two_rules <- data.frame(
Substitute = c(paste("{", first, "}"),
paste("{", second, "}")),
Product = c(paste("=>", "{", second, "}"),
paste("=>", "{", first, "}")),
Support = c(compl_tab[first, paste0("!", second)], compl_tab[second, paste0("!", first)]),
Confidence = c(conf1, conf2),
Correlation = c(corXY, corXY)
)
# conditions
try({
if (two_rules$Correlation[1] < pMin) {
if (two_rules$Support[1] >= MinSup && two_rules$Confidence[1] >= MinConf) {
rules <- rbind(rules, two_rules[1, ])
}
if (two_rules$Support[2] >= MinSup && two_rules$Confidence[2] >= MinConf) {
rules <- rbind(rules, two_rules[2, ])
}
} })
}
}
# Correlation of concrete item pairs with single items --------------------
# adding variable for loop
complement_data$XY <- paste0(complement_data$X, complement_data$Y)
# combination of items
for (i in 1 : nrow(complement_data)){
# set of combinations from dependent items with single items
univector <- c(as.vector(unique(complement_data$X)), as.vector(unique(complement_data$Y)))
univector <- univector[!univector %in% c(complement_data$X[i], complement_data$Y[i])]
combis <- c(complement_data[i,"XY"], univector)
for (u in 2 : length(combis)) {
corXYZ <-(sup_three[sup_three$Items == paste0(combis[1], combis[u]),2] -
complement_data[complement_data$XY == combis[1],"Sup_X.Y"] *
compl_tab[combis[u],combis[u]]) /
(sqrt((complement_data[complement_data$XY == combis[1],"Sup_X.Y"] *
(1 - complement_data[complement_data$XY == combis[1],"Sup_X.Y"]) *
compl_tab[combis[u],combis[u]] * (1 - compl_tab[combis[u],combis[u]]))))
dataXYZ <- data.frame(
Substitute = paste("{", combis[1], "}"),
Product = paste("=>", "{", combis[u], "}"),
Support = sup_three[sup_three$Items == paste0(combis[1], "!", combis[u]),2],
Confidence = sup_three[sup_three$Items == paste0(combis[1], "!", combis[u]),2] /
complement_data[complement_data$XY == combis[1],"Sup_X.Y"],
Correlation = corXYZ)
# conditions
if (dataXYZ$Correlation < pMin && dataXYZ$Support >= MinSup && dataXYZ$Confidence >= MinConf) {
try(rules <- rbind(rules, dataXYZ))
}
}
}
if (nrow(rules) == 0) {
message("Sorry no rules could have been calculated. Maybe change input conditions.")
} else {
return(rules)
}
# end
}
我认为我的博客中有更好的解释： http://mattimeyer.github.io/2016-12-21-Substitution-Rule-Mining/
【讨论】：