Business Intelligent 10/29/2023
| Student ID Number | 136346 127559 134775 135863 134141 |
| Student Name | Ngumi Joshua Joseph Watunu Hakeem Alavi Muema Ian Aicha Mbongo |
| BBIT 4.2 Group | C |
| BI Project Group Name/ID (if applicable) | Business Intelligent |
Note: the following KnitR options have been set as
the global defaults:
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, eval = TRUE, collapse = FALSE, tidy = TRUE).
More KnitR options are documented here https://bookdown.org/yihui/rmarkdown-cookbook/chunk-options.html and here https://yihui.org/knitr/options/.
if (require("arulesViz")) {
require("arulesViz")
} else {
install.packages("arulesViz",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
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## Loading required package: arules
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if (require("tidyverse")) {
require("tidyverse")
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install.packages("tidyverse",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors## readxl ----
if (require("readxl")) {
require("readxl")
} else {
install.packages("readxl",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}## Loading required package: readxl## knitr ----
if (require("knitr")) {
require("knitr")
} else {
install.packages("knitr",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}## Loading required package: knitr## ggplot2 ----
if (require("ggplot2")) {
require("ggplot2")
} else {
install.packages("ggplot2",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}
## lubridate ----
if (require("lubridate")) {
require("lubridate")
} else {
install.packages("lubridate",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}
## plyr ----
if (require("plyr")) {
require("plyr")
} else {
install.packages("plyr",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}## Loading required package: plyr
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if (require("dplyr")) {
require("dplyr")
} else {
install.packages("dplyr",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}
## naniar ----
if (require("naniar")) {
require("naniar")
} else {
install.packages("naniar",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}## Loading required package: naniar## RColorBrewer ----
if (require("RColorBrewer")) {
require("RColorBrewer")
} else {
install.packages("RColorBrewer",
dependencies = TRUE,
repos = "https://cloud.r-project.org"
)
}## Loading required package: RColorBrewer# STEP 2a. Load and pre-process the dataset ----
#groceries_basket_format <- read.transactions("data/groceries_basket_format.csv", format = "single", cols = c(1,2, 3))
#groceries_basket_format <- read.transactions("data/groceries_basket_format.csv", format = "basket", header = TRUE, sep = ",")
## FORMAT 2: Basket Format----
# An example of the single format transaction data is presented
# here: "data/groceries_basket_format.csv" and loaded as follows:
groceries_basket_format <-
read.transactions("../data/Groceries_dataset.csv",
format = "basket",
header = TRUE,
rm.duplicates = TRUE,
sep = ",")
#view(groceries_basket_format)
print(groceries_basket_format)## transactions in sparse format with
## 38765 transactions (rows) and
## 4793 items (columns)## transactions as itemMatrix in sparse format with
## 38765 rows (elements/itemsets/transactions) and
## 4793 columns (items) and a density of 0.0006259128
##
## most frequent items:
## whole milk other vegetables rolls/buns soda
## 2502 1898 1716 1514
## yogurt (Other)
## 1334 107331
##
## element (itemset/transaction) length distribution:
## sizes
## 3
## 38765
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3 3 3 3 3 3
##
## includes extended item information - examples:
## labels
## 1 01-01-2014
## 2 01-01-2015
## 3 01-02-2014## transactions in sparse format with
## 6 transactions (rows) and
## 4793 items (columns)# Handle missing values in the groceries_basket_format transactions object
# We can read data from an Excel spreadsheet as follows:
groceries_basket_format<- read_excel("../data/Groceries_dataset.xlsx")
dim(groceries_basket_format)## [1] 38765 3### Handle missing values ----
# Are there missing values in the dataset?
any_na(groceries_basket_format)## [1] FALSE## [1] 0## [1] 0# What is the number and percentage of missing values grouped by
# each variable?
miss_var_summary(groceries_basket_format)## # A tibble: 3 × 3
## variable n_miss pct_miss
## <chr> <int> <dbl>
## 1 Member_number 0 0
## 2 Date 0 0
## 3 itemDescription 0 0
# Which combinations of variables are missing together?
#gg_miss_upset(groceries_basket_format)
#### OPTION 1: Remove the observations with missing values ----
groceries_cleaned <- groceries_basket_format%>% dplyr::filter(complete.cases(.))
# We end up with 406,829 observations to create the association rules
# instead of the initial 541,909 observations.
dim(groceries_cleaned)## [1] 38765 3# Also ensure that the description (name of the product purchased) is recorded
# as categorical data
# Now you can use mutate on the data frame
groceries_cleaned <- groceries_cleaned %>% mutate(itemDescription = as.factor(itemDescription))
str(groceries_cleaned)## tibble [38,765 × 3] (S3: tbl_df/tbl/data.frame)
## $ Member_number : num [1:38765] 1808 2552 2300 1187 3037 ...
## $ Date : chr [1:38765] "21-07-2015" "2015-05-01" "19-09-2015" "2015-12-12" ...
## $ itemDescription: Factor w/ 167 levels "abrasive cleaner",..: 156 165 109 102 165 122 102 112 165 156 ...## [1] 38765 3## # A tibble: 6 × 3
## Member_number Date itemDescription
## <dbl> <chr> <fct>
## 1 1808 21-07-2015 tropical fruit
## 2 2552 2015-05-01 whole milk
## 3 2300 19-09-2015 pip fruit
## 4 1187 2015-12-12 other vegetables
## 5 3037 2015-01-02 whole milk
## 6 4941 14-02-2015 rolls/buns## Record the date and time variables in the correct format ----
# Ensure that InvoiceDate is stored in the correct date format.
# We can separate the date and the time into 2 different variables.
groceries_cleaned$trans_date <-
as.Date(groceries_cleaned$Date)
## Record the InvoiceNo in the correct format (numeric) ----
# Convert InvoiceNo into numeric
groceries_cleaned$Member_number<-
as.numeric(as.character(groceries_cleaned$Member_number))
# Are there missing values in the dataset?
any_na(groceries_cleaned)## [1] FALSE# What is the number and percentage of missing values grouped by
# each variable?
miss_var_summary(groceries_cleaned)## # A tibble: 4 × 3
## variable n_miss pct_miss
## <chr> <int> <dbl>
## 1 Member_number 0 0
## 2 Date 0 0
## 3 itemDescription 0 0
## 4 trans_date 0 0## [1] 38765 4# We now remove the observations that do not have a numeric value for the
# invoice_no variable, i.e., the cancelled invoices that did not lead to a
# complete purchase. There are a total of 9,291 cancelled invoices.
groceries_cleaned <- groceries_cleaned %>%
dplyr::filter(complete.cases(.))
dim(groceries_cleaned)## [1] 38765 4# We then remove the duplicate variables that we do not need
groceries_cleaned<-
groceries_cleaned %>%
select(-trans_date) %>%
mutate_all(~str_replace_all(., "/", " or "))
dim(groceries_cleaned)## [1] 38765 3#view(groceries_cleaned)
# We can save the pre-processing progress made so far
write.csv(groceries_cleaned,
file = "../data/groceries_cleaned_before_single_transaction_format.csv",
row.names = FALSE)
groceries_cleaned<-
read.csv(file = "../data/groceries_cleaned_before_single_transaction_format.csv")
# Check the structure of the data frame after the transformation
str(groceries_cleaned)## 'data.frame': 38765 obs. of 3 variables:
## $ Member_number : int 1808 2552 2300 1187 3037 4941 4501 3803 2762 4119 ...
## $ Date : chr "21-07-2015" "2015-05-01" "19-09-2015" "2015-12-12" ...
## $ itemDescription: chr "tropical fruit" "whole milk" "pip fruit" "other vegetables" ...### OPTION 1 ----
transaction_data <-
plyr::ddply(groceries_cleaned,
c("Member_number", "Date"),
function(df1) {
paste(df1$itemDescription, collapse = ",")
}
)
#view(transaction_data)
## Record only the `items` variable ----
# Notice that at this point, the basket format ensures that each transaction is
# recorded in one row. We therefore no longer require the
# `invoice_no` variable and all the other variables in the data frame except
# the itemsets.
### OPTION 1 ----
transaction_data <-
transaction_data %>%
dplyr::select("items" = V1)
#view(transaction_data)
## Save the transactions in CSV format ----
### OPTION 1 ----
write.csv(transaction_data,
"../data/transactions_basket_format_groceries_dataset.csv",
quote = FALSE, row.names = FALSE)
## Read the transactions fromm the CSV file ----
# We can now, finally, read the basket format transaction data as a
# transaction object.
### OPTION 1 ----
tr <-
read.transactions("../data/transactions_basket_format_groceries_dataset.csv",
format = "basket",
header = TRUE,
rm.duplicates = TRUE,
sep = ","
)## distribution of transactions with duplicates:
## items
## 1 2 3 4
## 662 39 5 1## transactions in sparse format with
## 14963 transactions (rows) and
## 167 items (columns)## transactions as itemMatrix in sparse format with
## 14963 rows (elements/itemsets/transactions) and
## 167 columns (items) and a density of 0.01520957
##
## most frequent items:
## whole milk other vegetables rolls or buns soda
## 2363 1827 1646 1453
## yogurt (Other)
## 1285 29432
##
## element (itemset/transaction) length distribution:
## sizes
## 1 2 3 4 5 6 7 8 9 10
## 205 10012 2727 1273 338 179 113 96 19 1
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 2.00 2.00 2.54 3.00 10.00
##
## includes extended item information - examples:
## labels
## 1 abrasive cleaner
## 2 artif. sweetener
## 3 baby cosmetics# STEP 2b. Basic EDA ----
# Create an item frequency plot for the top 10 items
itemFrequencyPlot(tr, topN = 10, type = "absolute",
col = brewer.pal(8, "Pastel2"),
main = "Absolute Item Frequency Plot",
horiz = TRUE,
mai = c(2, 2, 2, 2))
itemFrequencyPlot(tr, topN = 10, type = "relative",
col = brewer.pal(8, "Pastel2"),
main = "Relative Item Frequency Plot",
horiz = TRUE,
mai = c(2, 2, 2, 2))
## OPTION 1 ----
association_rules <- apriori(tr,
parameter = list(support = 0.0001,
confidence = 0.8,
maxlen = 10))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 1e-04 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 1
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[167 item(s), 14963 transaction(s)] done [0.00s].
## sorting and recoding items ... [165 item(s)] done [0.00s].
## creating transaction tree ... done [0.01s].
## checking subsets of size 1 2 3 4 5 done [0.00s].
## writing ... [647 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].association_rules_prod_name <- apriori(tr,
parameter = list(support = 0.0001,
confidence = 0.8,
maxlen = 10))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 1e-04 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 1
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[167 item(s), 14963 transaction(s)] done [0.00s].
## sorting and recoding items ... [165 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 done [0.01s].
## writing ... [647 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].# STEP 3. Print the association rules ----
## OPTION 2 ----
# Threshold values of support = 0.0001, confidence = 0.8, and
# product name to identify the products.
summary(association_rules_prod_name)## set of 647 rules
##
## rule length distribution (lhs + rhs):sizes
## 3 4 5
## 135 438 74
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 4.000 4.000 3.906 4.000 5.000
##
## summary of quality measures:
## support confidence coverage lift
## Min. :0.0001337 Min. :0.8000 Min. :0.0001337 Min. : 5.066
## 1st Qu.:0.0001337 1st Qu.:1.0000 1st Qu.:0.0001337 1st Qu.: 8.190
## Median :0.0001337 Median :1.0000 Median :0.0001337 Median : 11.644
## Mean :0.0001373 Mean :0.9988 Mean :0.0001377 Mean : 19.285
## 3rd Qu.:0.0001337 3rd Qu.:1.0000 3rd Qu.:0.0001337 3rd Qu.: 20.386
## Max. :0.0003342 Max. :1.0000 Max. :0.0004010 Max. :364.951
## count
## Min. :2.000
## 1st Qu.:2.000
## Median :2.000
## Mean :2.054
## 3rd Qu.:2.000
## Max. :5.000
##
## mining info:
## data ntransactions support confidence
## tr 14963 1e-04 0.8
## call
## apriori(data = tr, parameter = list(support = 1e-04, confidence = 0.8, maxlen = 10))## lhs rhs support confidence coverage lift count
## [1] {domestic eggs,
## rubbing alcohol} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [2] {frankfurter,
## rubbing alcohol} => {domestic eggs} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [3] {soap,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [4] {soap,
## whole milk} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [5] {domestic eggs,
## skin care} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [6] {bottled water,
## cookware} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [7] {frankfurter,
## potato products} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [8] {syrup,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [9] {ice cream,
## prosecco} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [10] {prosecco,
## waffles} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [11] {prosecco,
## waffles} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [12] {prosecco,
## waffles} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [13] {prosecco,
## whole milk} => {waffles} 0.0001336630 1.0000000 0.0001336630 54.018051 2
## [14] {prosecco,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [15] {prosecco,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [16] {canned fruit,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [17] {cat food,
## tea} => {frozen vegetables} 0.0001336630 1.0000000 0.0001336630 35.711217 2
## [18] {frozen vegetables,
## tea} => {cat food} 0.0001336630 1.0000000 0.0001336630 84.536723 2
## [19] {cream cheese,
## nut snack} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [20] {curd,
## nut snack} => {cream cheese} 0.0001336630 1.0000000 0.0001336630 42.268362 2
## [21] {newspapers,
## nut snack} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [22] {nut snack,
## other vegetables} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [23] {jam,
## pip fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [24] {cereals,
## packaged fruit or vegetables} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [25] {dental care,
## napkins} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [26] {dental care,
## pip fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [27] {artif. sweetener,
## bottled water} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [28] {brown bread,
## sauces} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [29] {shopping bags,
## spices} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [30] {softener,
## vinegar} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [31] {softener,
## vinegar} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [32] {pip fruit,
## softener} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [33] {house keeping products,
## semi-finished bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [34] {house keeping products,
## margarine} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [35] {canned beer,
## house keeping products} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [36] {bottled water,
## house keeping products} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [37] {house keeping products,
## other vegetables} => {whole milk} 0.0002673261 1.0000000 0.0002673261 6.332205 4
## [38] {citrus fruit,
## soups} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [39] {ice cream,
## popcorn} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [40] {oil,
## popcorn} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [41] {grapes,
## vinegar} => {frozen vegetables} 0.0001336630 1.0000000 0.0001336630 35.711217 2
## [42] {frozen vegetables,
## vinegar} => {grapes} 0.0001336630 1.0000000 0.0001336630 69.273148 2
## [43] {vinegar,
## white bread} => {beef} 0.0001336630 1.0000000 0.0001336630 29.454724 2
## [44] {beef,
## vinegar} => {white bread} 0.0001336630 1.0000000 0.0001336630 41.679666 2
## [45] {sausage,
## vinegar} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [46] {chocolate marshmallow,
## sugar} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [47] {chocolate marshmallow,
## domestic eggs} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [48] {canned beer,
## Instant food products} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [49] {frankfurter,
## liver loaf} => {condensed milk} 0.0001336630 1.0000000 0.0001336630 152.683673 2
## [50] {liver loaf,
## sausage} => {white bread} 0.0001336630 1.0000000 0.0001336630 41.679666 2
## [51] {liver loaf,
## shopping bags} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [52] {berries,
## zwieback} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [53] {frankfurter,
## zwieback} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [54] {flower (seeds),
## pork} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [55] {candles,
## white bread} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [56] {candles,
## curd} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [57] {finished products,
## onions} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [58] {chocolate,
## finished products} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [59] {chocolate,
## finished products} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [60] {curd,
## finished products} => {whipped or sour cream} 0.0001336630 1.0000000 0.0001336630 22.879205 2
## [61] {butter,
## finished products} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [62] {frozen potato products,
## UHT-milk} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [63] {fruit or vegetable juice,
## specialty cheese} => {long life bakery product} 0.0001336630 1.0000000 0.0001336630 55.832090 2
## [64] {dog food,
## sliced cheese} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [65] {dog food,
## fruit or vegetable juice} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [66] {dog food,
## fruit or vegetable juice} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [67] {cling film or bags,
## newspapers} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [68] {cling film or bags,
## shopping bags} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [69] {mayonnaise,
## oil} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [70] {mayonnaise,
## newspapers} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [71] {mayonnaise,
## pip fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [72] {curd,
## pet care} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [73] {specialty chocolate,
## sweet spreads} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [74] {butter milk,
## sweet spreads} => {berries} 0.0001336630 1.0000000 0.0001336630 45.898773 2
## [75] {hamburger meat,
## sweet spreads} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [76] {curd,
## sweet spreads} => {hamburger meat} 0.0001336630 1.0000000 0.0001336630 45.758410 2
## [77] {napkins,
## sweet spreads} => {chocolate} 0.0001336630 1.0000000 0.0001336630 42.388102 2
## [78] {canned vegetables,
## domestic eggs} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [79] {bottled beer,
## salt} => {misc. beverages} 0.0001336630 1.0000000 0.0001336630 63.402542 2
## [80] {misc. beverages,
## turkey} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [81] {bottled beer,
## turkey} => {misc. beverages} 0.0001336630 1.0000000 0.0001336630 63.402542 2
## [82] {ham,
## turkey} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [83] {ham,
## turkey} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [84] {beef,
## turkey} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [85] {pork,
## turkey} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [86] {pork,
## turkey} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [87] {citrus fruit,
## turkey} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [88] {hamburger meat,
## mustard} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [89] {cake bar,
## frozen vegetables} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [90] {frozen dessert,
## pip fruit} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [91] {flour,
## liquor} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [92] {flour,
## liquor} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [93] {frankfurter,
## liquor} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [94] {frozen fish,
## napkins} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [95] {frozen meals,
## spread cheese} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [96] {frozen meals,
## spread cheese} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [97] {spread cheese,
## UHT-milk} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [98] {frankfurter,
## spread cheese} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [99] {canned beer,
## spread cheese} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [100] {condensed milk,
## pip fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [101] {canned fish,
## pasta} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [102] {canned fish,
## chocolate} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [103] {hygiene articles,
## pot plants} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [104] {pork,
## pot plants} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [105] {baking powder,
## specialty bar} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [106] {baking powder,
## sliced cheese} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [107] {pickled vegetables,
## processed cheese} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [108] {detergent,
## oil} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [109] {cream cheese,
## detergent} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [110] {citrus fruit,
## detergent} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [111] {cat food,
## dishes} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [112] {fruit or vegetable juice,
## semi-finished bread} => {rolls or buns} 0.0002673261 0.8000000 0.0003341576 7.272418 4
## [113] {flour,
## salty snack} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [114] {flour,
## margarine} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [115] {butter,
## processed cheese} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [116] {pastry,
## processed cheese} => {whole milk} 0.0002673261 0.8000000 0.0003341576 5.065764 4
## [117] {soft cheese,
## specialty bar} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [118] {cat food,
## long life bakery product} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [119] {chewing gum,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [120] {coffee,
## specialty bar} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [121] {hygiene articles,
## misc. beverages} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [122] {frozen meals,
## hygiene articles} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [123] {frozen meals,
## hygiene articles} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [124] {hygiene articles,
## salty snack} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [125] {butter milk,
## candy} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [126] {beverages,
## ice cream} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [127] {fruit or vegetable juice,
## grapes} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [128] {oil,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [129] {ham,
## oil} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [130] {hard cheese,
## specialty chocolate} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [131] {beverages,
## hard cheese} => {fruit or vegetable juice} 0.0001336630 1.0000000 0.0001336630 29.396857 2
## [132] {berries,
## specialty chocolate} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [133] {ham,
## salty snack} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [134] {ham,
## pip fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [135] {hamburger meat,
## long life bakery product} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [136] {prosecco,
## sausage,
## waffles} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [137] {other vegetables,
## prosecco,
## waffles} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [138] {other vegetables,
## prosecco,
## sausage} => {waffles} 0.0001336630 1.0000000 0.0001336630 54.018051 2
## [139] {prosecco,
## sausage,
## waffles} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [140] {prosecco,
## waffles,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [141] {prosecco,
## sausage,
## whole milk} => {waffles} 0.0001336630 1.0000000 0.0001336630 54.018051 2
## [142] {other vegetables,
## prosecco,
## waffles} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [143] {prosecco,
## waffles,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [144] {other vegetables,
## prosecco,
## whole milk} => {waffles} 0.0001336630 1.0000000 0.0001336630 54.018051 2
## [145] {other vegetables,
## prosecco,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [146] {prosecco,
## sausage,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [147] {other vegetables,
## prosecco,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [148] {nuts or prunes,
## rolls or buns,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [149] {nuts or prunes,
## sausage,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [150] {nuts or prunes,
## rolls or buns,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [151] {frankfurter,
## softener,
## vinegar} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [152] {softener,
## vinegar,
## whole milk} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [153] {frankfurter,
## softener,
## whole milk} => {vinegar} 0.0001336630 1.0000000 0.0001336630 293.392157 2
## [154] {frankfurter,
## vinegar,
## whole milk} => {softener} 0.0001336630 1.0000000 0.0001336630 364.951220 2
## [155] {other vegetables,
## rolls or buns,
## softener} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [156] {rolls or buns,
## softener,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [157] {bottled water,
## pip fruit,
## popcorn} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [158] {pip fruit,
## popcorn,
## rolls or buns} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [159] {bottled water,
## pip fruit,
## rolls or buns} => {popcorn} 0.0001336630 1.0000000 0.0001336630 311.729167 2
## [160] {canned beer,
## sausage,
## zwieback} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [161] {canned beer,
## whole milk,
## zwieback} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [162] {sausage,
## whole milk,
## zwieback} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [163] {chocolate,
## finished products,
## other vegetables} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [164] {chocolate,
## finished products,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [165] {dog food,
## fruit or vegetable juice,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [166] {dog food,
## fruit or vegetable juice,
## rolls or buns} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [167] {dog food,
## rolls or buns,
## yogurt} => {fruit or vegetable juice} 0.0001336630 1.0000000 0.0001336630 29.396857 2
## [168] {dog food,
## rolls or buns,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [169] {dog food,
## soda,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [170] {dog food,
## rolls or buns,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [171] {bottled water,
## other vegetables,
## pet care} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [172] {bottled water,
## pet care,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [173] {berries,
## pip fruit,
## sweet spreads} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [174] {berries,
## sweet spreads,
## whole milk} => {pip fruit} 0.0001336630 1.0000000 0.0001336630 20.385559 2
## [175] {berries,
## pip fruit,
## whole milk} => {sweet spreads} 0.0001336630 1.0000000 0.0001336630 220.044118 2
## [176] {other vegetables,
## soda,
## sweet spreads} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [177] {other vegetables,
## sweet spreads,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [178] {meat,
## roll products,
## tropical fruit} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [179] {meat,
## other vegetables,
## roll products} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [180] {other vegetables,
## roll products,
## tropical fruit} => {meat} 0.0001336630 1.0000000 0.0001336630 59.376984 2
## [181] {ham,
## pastry,
## turkey} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [182] {ham,
## soda,
## turkey} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [183] {pastry,
## soda,
## turkey} => {ham} 0.0001336630 1.0000000 0.0001336630 58.449219 2
## [184] {ham,
## pastry,
## soda} => {turkey} 0.0001336630 1.0000000 0.0001336630 187.037500 2
## [185] {pork,
## soda,
## turkey} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [186] {pork,
## turkey,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [187] {mustard,
## other vegetables,
## root vegetables} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [188] {mustard,
## root vegetables,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [189] {mustard,
## other vegetables,
## whole milk} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [190] {cake bar,
## curd,
## tropical fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [191] {cake bar,
## curd,
## rolls or buns} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [192] {cake bar,
## rolls or buns,
## tropical fruit} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [193] {cake bar,
## curd,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [194] {cake bar,
## curd,
## whole milk} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [195] {cake bar,
## tropical fruit,
## whole milk} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [196] {cake bar,
## curd,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [197] {cake bar,
## curd,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [198] {brown bread,
## cake bar,
## canned beer} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [199] {brown bread,
## cake bar,
## sausage} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [200] {cake bar,
## canned beer,
## sausage} => {brown bread} 0.0001336630 1.0000000 0.0001336630 26.577265 2
## [201] {cake bar,
## rolls or buns,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [202] {cake bar,
## tropical fruit,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [203] {flour,
## liquor,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [204] {flour,
## liquor,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [205] {liquor,
## soda,
## whole milk} => {flour} 0.0001336630 1.0000000 0.0001336630 102.486301 2
## [206] {frozen meals,
## root vegetables,
## spread cheese} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [207] {frozen meals,
## soda,
## spread cheese} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [208] {root vegetables,
## soda,
## spread cheese} => {frozen meals} 0.0001336630 1.0000000 0.0001336630 59.613546 2
## [209] {frozen meals,
## root vegetables,
## soda} => {spread cheese} 0.0001336630 1.0000000 0.0001336630 149.630000 2
## [210] {condensed milk,
## root vegetables,
## tropical fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [211] {condensed milk,
## rolls or buns,
## root vegetables} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [212] {condensed milk,
## rolls or buns,
## tropical fruit} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [213] {coffee,
## pastry,
## seasonal products} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [214] {coffee,
## seasonal products,
## whole milk} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [215] {pastry,
## seasonal products,
## whole milk} => {coffee} 0.0001336630 1.0000000 0.0001336630 31.634249 2
## [216] {bottled beer,
## canned fish,
## onions} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [217] {canned fish,
## onions,
## whole milk} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [218] {bottled beer,
## canned fish,
## whole milk} => {onions} 0.0001336630 1.0000000 0.0001336630 49.382838 2
## [219] {bottled beer,
## onions,
## whole milk} => {canned fish} 0.0001336630 1.0000000 0.0001336630 130.113043 2
## [220] {canned fish,
## frankfurter,
## UHT-milk} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [221] {canned fish,
## UHT-milk,
## whole milk} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [222] {frankfurter,
## UHT-milk,
## whole milk} => {canned fish} 0.0001336630 1.0000000 0.0001336630 130.113043 2
## [223] {other vegetables,
## pot plants,
## shopping bags} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [224] {other vegetables,
## pot plants,
## tropical fruit} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [225] {pastry,
## pot plants,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [226] {pastry,
## pot plants,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [227] {fruit or vegetable juice,
## pasta,
## pip fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [228] {fruit or vegetable juice,
## pasta,
## rolls or buns} => {pip fruit} 0.0001336630 1.0000000 0.0001336630 20.385559 2
## [229] {pasta,
## pastry,
## soda} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [230] {pasta,
## soda,
## tropical fruit} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [231] {detergent,
## dishes,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [232] {detergent,
## dishes,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [233] {dishes,
## frankfurter,
## whipped or sour cream} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [234] {citrus fruit,
## dishes,
## frankfurter} => {whipped or sour cream} 0.0001336630 1.0000000 0.0001336630 22.879205 2
## [235] {dishes,
## whipped or sour cream,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [236] {dishes,
## pip fruit,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [237] {dishes,
## rolls or buns,
## whole milk} => {pip fruit} 0.0001336630 1.0000000 0.0001336630 20.385559 2
## [238] {fruit or vegetable juice,
## semi-finished bread,
## tropical fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [239] {rolls or buns,
## semi-finished bread,
## tropical fruit} => {fruit or vegetable juice} 0.0001336630 1.0000000 0.0001336630 29.396857 2
## [240] {sausage,
## semi-finished bread,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [241] {flour,
## specialty chocolate,
## whipped or sour cream} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [242] {flour,
## onions,
## tropical fruit} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [243] {flour,
## onions,
## yogurt} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [244] {flour,
## tropical fruit,
## yogurt} => {onions} 0.0001336630 1.0000000 0.0001336630 49.382838 2
## [245] {flour,
## rolls or buns,
## whipped or sour cream} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [246] {flour,
## rolls or buns,
## tropical fruit} => {whipped or sour cream} 0.0001336630 1.0000000 0.0001336630 22.879205 2
## [247] {citrus fruit,
## herbs,
## pork} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [248] {citrus fruit,
## herbs,
## other vegetables} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [249] {frankfurter,
## herbs,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [250] {frankfurter,
## herbs,
## other vegetables} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [251] {pastry,
## processed cheese,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [252] {citrus fruit,
## shopping bags,
## white wine} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [253] {shopping bags,
## white wine,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [254] {citrus fruit,
## white wine,
## whole milk} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [255] {cat food,
## citrus fruit,
## frozen vegetables} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [256] {cat food,
## frozen vegetables,
## other vegetables} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [257] {cat food,
## citrus fruit,
## other vegetables} => {frozen vegetables} 0.0001336630 1.0000000 0.0001336630 35.711217 2
## [258] {chewing gum,
## hamburger meat,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [259] {chewing gum,
## hamburger meat,
## soda} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [260] {chewing gum,
## citrus fruit,
## root vegetables} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [261] {chewing gum,
## citrus fruit,
## whole milk} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [262] {candy,
## ham,
## specialty bar} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [263] {candy,
## specialty bar,
## whole milk} => {ham} 0.0001336630 1.0000000 0.0001336630 58.449219 2
## [264] {ham,
## specialty bar,
## whole milk} => {candy} 0.0001336630 1.0000000 0.0001336630 69.595349 2
## [265] {beverages,
## curd,
## specialty bar} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [266] {curd,
## other vegetables,
## specialty bar} => {beverages} 0.0001336630 1.0000000 0.0001336630 60.334677 2
## [267] {beverages,
## rolls or buns,
## specialty bar} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [268] {other vegetables,
## rolls or buns,
## specialty bar} => {beverages} 0.0001336630 1.0000000 0.0001336630 60.334677 2
## [269] {bottled water,
## specialty bar,
## tropical fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [270] {soda,
## specialty bar,
## tropical fruit} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [271] {bottled water,
## specialty bar,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [272] {frozen meals,
## hygiene articles,
## sausage} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [273] {frozen meals,
## hygiene articles,
## rolls or buns} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [274] {hygiene articles,
## rolls or buns,
## sausage} => {frozen meals} 0.0001336630 1.0000000 0.0001336630 59.613546 2
## [275] {canned beer,
## chicken,
## hygiene articles} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [276] {chicken,
## hygiene articles,
## whole milk} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [277] {canned beer,
## curd,
## hygiene articles} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [278] {frankfurter,
## hygiene articles,
## other vegetables} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [279] {frankfurter,
## hygiene articles,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [280] {bottled beer,
## hygiene articles,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [281] {bottled beer,
## hygiene articles,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [282] {canned beer,
## hygiene articles,
## soda} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [283] {citrus fruit,
## hygiene articles,
## shopping bags} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [284] {citrus fruit,
## hygiene articles,
## whole milk} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [285] {pastry,
## sliced cheese,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [286] {bottled beer,
## candy,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [287] {candy,
## rolls or buns,
## whole milk} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [288] {candy,
## citrus fruit,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [289] {candy,
## root vegetables,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [290] {candy,
## rolls or buns,
## root vegetables} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [291] {fruit or vegetable juice,
## ice cream,
## pip fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [292] {fruit or vegetable juice,
## ice cream,
## rolls or buns} => {pip fruit} 0.0001336630 1.0000000 0.0001336630 20.385559 2
## [293] {citrus fruit,
## frankfurter,
## ice cream} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [294] {frankfurter,
## ice cream,
## yogurt} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [295] {frankfurter,
## ice cream,
## rolls or buns} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [296] {frankfurter,
## ice cream,
## other vegetables} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [297] {ice cream,
## other vegetables,
## rolls or buns} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [298] {grapes,
## meat,
## other vegetables} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [299] {grapes,
## meat,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [300] {dessert,
## grapes,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [301] {dessert,
## grapes,
## soda} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [302] {frozen meals,
## oil,
## pork} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [303] {frozen meals,
## oil,
## other vegetables} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [304] {brown bread,
## oil,
## pork} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [305] {brown bread,
## oil,
## whole milk} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [306] {oil,
## pork,
## root vegetables} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [307] {oil,
## pork,
## rolls or buns} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [308] {canned beer,
## oil,
## rolls or buns} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [309] {citrus fruit,
## frankfurter,
## oil} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [310] {citrus fruit,
## frankfurter,
## soda} => {oil} 0.0001336630 1.0000000 0.0001336630 67.098655 2
## [311] {oil,
## root vegetables,
## shopping bags} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [312] {oil,
## shopping bags,
## soda} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [313] {misc. beverages,
## sausage,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [314] {misc. beverages,
## other vegetables,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [315] {misc. beverages,
## other vegetables,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [316] {misc. beverages,
## sausage,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [317] {misc. beverages,
## other vegetables,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [318] {misc. beverages,
## other vegetables,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [319] {misc. beverages,
## other vegetables,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [320] {misc. beverages,
## other vegetables,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [321] {curd,
## hard cheese,
## sausage} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [322] {curd,
## hard cheese,
## root vegetables} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [323] {hard cheese,
## newspapers,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [324] {hard cheese,
## other vegetables,
## soda} => {newspapers} 0.0001336630 1.0000000 0.0001336630 25.709622 2
## [325] {hard cheese,
## other vegetables,
## pip fruit} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [326] {hard cheese,
## tropical fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [327] {citrus fruit,
## hamburger meat,
## specialty chocolate} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [328] {hamburger meat,
## other vegetables,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [329] {citrus fruit,
## dessert,
## specialty chocolate} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [330] {dessert,
## sausage,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [331] {citrus fruit,
## sausage,
## specialty chocolate} => {dessert} 0.0001336630 1.0000000 0.0001336630 42.388102 2
## [332] {citrus fruit,
## dessert,
## sausage} => {specialty chocolate} 0.0001336630 1.0000000 0.0001336630 62.606695 2
## [333] {chicken,
## cream cheese,
## specialty chocolate} => {citrus fruit} 0.0002004946 1.0000000 0.0002004946 18.821384 3
## [334] {chicken,
## citrus fruit,
## cream cheese} => {specialty chocolate} 0.0002004946 1.0000000 0.0002004946 62.606695 3
## [335] {chicken,
## curd,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [336] {chicken,
## citrus fruit,
## curd} => {specialty chocolate} 0.0001336630 1.0000000 0.0001336630 62.606695 2
## [337] {chicken,
## specialty chocolate,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [338] {curd,
## pastry,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [339] {citrus fruit,
## pastry,
## specialty chocolate} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [340] {curd,
## pastry,
## specialty chocolate} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [341] {other vegetables,
## pastry,
## specialty chocolate} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [342] {citrus fruit,
## pastry,
## specialty chocolate} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [343] {other vegetables,
## pastry,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [344] {specialty chocolate,
## tropical fruit,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [345] {beverages,
## hamburger meat,
## yogurt} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [346] {beverages,
## soda,
## yogurt} => {hamburger meat} 0.0001336630 1.0000000 0.0001336630 45.758410 2
## [347] {beverages,
## canned beer,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [348] {beverages,
## pip fruit,
## sausage} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [349] {beverages,
## pip fruit,
## rolls or buns} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [350] {beverages,
## rolls or buns,
## sausage} => {pip fruit} 0.0001336630 1.0000000 0.0001336630 20.385559 2
## [351] {beverages,
## sausage,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [352] {beverages,
## other vegetables,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [353] {beverages,
## other vegetables,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [354] {citrus fruit,
## ham,
## onions} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [355] {ham,
## onions,
## yogurt} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [356] {citrus fruit,
## onions,
## yogurt} => {ham} 0.0001336630 1.0000000 0.0001336630 58.449219 2
## [357] {citrus fruit,
## frozen vegetables,
## ham} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [358] {frozen vegetables,
## ham,
## yogurt} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [359] {citrus fruit,
## frozen vegetables,
## ham} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [360] {frozen vegetables,
## ham,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [361] {frozen vegetables,
## ham,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [362] {frozen vegetables,
## ham,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [363] {canned beer,
## ham,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [364] {ham,
## other vegetables,
## yogurt} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [365] {canned beer,
## ham,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [366] {ham,
## tropical fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [367] {ham,
## other vegetables,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [368] {frozen meals,
## long life bakery product,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [369] {frozen meals,
## long life bakery product,
## soda} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [370] {long life bakery product,
## sausage,
## soda} => {frozen meals} 0.0001336630 1.0000000 0.0001336630 59.613546 2
## [371] {frozen meals,
## other vegetables,
## salty snack} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [372] {frozen meals,
## salty snack,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [373] {frozen meals,
## margarine,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [374] {frozen meals,
## margarine,
## sausage} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [375] {margarine,
## other vegetables,
## yogurt} => {frozen meals} 0.0001336630 1.0000000 0.0001336630 59.613546 2
## [376] {bottled water,
## curd,
## frozen meals} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [377] {bottled water,
## frozen meals,
## rolls or buns} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [378] {frozen meals,
## sausage,
## tropical fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [379] {butter milk,
## rolls or buns,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [380] {butter milk,
## curd,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [381] {butter milk,
## curd,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [382] {butter milk,
## curd,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [383] {butter milk,
## curd,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [384] {brown bread,
## butter milk,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [385] {brown bread,
## butter milk,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [386] {butter milk,
## canned beer,
## sausage} => {yogurt} 0.0002004946 1.0000000 0.0002004946 11.644358 3
## [387] {butter milk,
## canned beer,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [388] {butter milk,
## rolls or buns,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [389] {butter milk,
## rolls or buns,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [390] {sugar,
## tropical fruit,
## white bread} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [391] {other vegetables,
## sugar,
## white bread} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [392] {rolls or buns,
## soda,
## sugar} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [393] {other vegetables,
## rolls or buns,
## sugar} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [394] {long life bakery product,
## other vegetables,
## rolls or buns} => {domestic eggs} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [395] {curd,
## waffles,
## white bread} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [396] {frankfurter,
## waffles,
## white bread} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [397] {sausage,
## tropical fruit,
## waffles} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [398] {other vegetables,
## root vegetables,
## waffles} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [399] {pip fruit,
## root vegetables,
## waffles} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [400] {bottled beer,
## domestic eggs,
## salty snack} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [401] {canned beer,
## rolls or buns,
## salty snack} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [402] {rolls or buns,
## salty snack,
## soda} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [403] {root vegetables,
## salty snack,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [404] {root vegetables,
## salty snack,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [405] {bottled water,
## margarine,
## onions} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [406] {margarine,
## onions,
## other vegetables} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [407] {bottled water,
## onions,
## other vegetables} => {margarine} 0.0001336630 1.0000000 0.0001336630 31.043568 2
## [408] {onions,
## pork,
## tropical fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [409] {onions,
## pork,
## soda} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [410] {onions,
## sausage,
## whipped or sour cream} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [411] {onions,
## rolls or buns,
## whipped or sour cream} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [412] {bottled beer,
## onions,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [413] {bottled beer,
## onions,
## other vegetables} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [414] {beef,
## pip fruit,
## UHT-milk} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [415] {beef,
## UHT-milk,
## whole milk} => {pip fruit} 0.0001336630 1.0000000 0.0001336630 20.385559 2
## [416] {berries,
## fruit or vegetable juice,
## pip fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [417] {berries,
## pip fruit,
## soda} => {fruit or vegetable juice} 0.0001336630 1.0000000 0.0001336630 29.396857 2
## [418] {berries,
## fruit or vegetable juice,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [419] {hamburger meat,
## other vegetables,
## white bread} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [420] {coffee,
## frankfurter,
## hamburger meat} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [421] {coffee,
## hamburger meat,
## root vegetables} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [422] {coffee,
## frankfurter,
## hamburger meat} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [423] {coffee,
## hamburger meat,
## soda} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [424] {coffee,
## hamburger meat,
## root vegetables} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [425] {coffee,
## hamburger meat,
## soda} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [426] {domestic eggs,
## hamburger meat,
## soda} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [427] {domestic eggs,
## hamburger meat,
## rolls or buns} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [428] {frankfurter,
## hamburger meat,
## root vegetables} => {soda} 0.0002004946 1.0000000 0.0002004946 10.298004 3
## [429] {frankfurter,
## hamburger meat,
## soda} => {root vegetables} 0.0002004946 1.0000000 0.0002004946 14.373679 3
## [430] {frankfurter,
## root vegetables,
## soda} => {hamburger meat} 0.0002004946 1.0000000 0.0002004946 45.758410 3
## [431] {hamburger meat,
## soda,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [432] {hamburger meat,
## rolls or buns,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [433] {hamburger meat,
## other vegetables,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [434] {curd,
## dessert,
## pastry} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [435] {curd,
## dessert,
## sausage} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [436] {citrus fruit,
## curd,
## dessert} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [437] {butter,
## dessert,
## soda} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [438] {butter,
## dessert,
## whole milk} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [439] {dessert,
## shopping bags,
## whole milk} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [440] {dessert,
## pip fruit,
## yogurt} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [441] {dessert,
## pip fruit,
## soda} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [442] {dessert,
## pip fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [443] {dessert,
## pip fruit,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [444] {dessert,
## pip fruit,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [445] {dessert,
## pip fruit,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [446] {dessert,
## pastry,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [447] {dessert,
## sausage,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [448] {chocolate,
## margarine,
## napkins} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [449] {butter,
## margarine,
## napkins} => {chocolate} 0.0001336630 1.0000000 0.0001336630 42.388102 2
## [450] {butter,
## chocolate,
## margarine} => {napkins} 0.0001336630 1.0000000 0.0001336630 45.205438 2
## [451] {butter,
## cream cheese,
## frankfurter} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [452] {cream cheese,
## frankfurter,
## soda} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [453] {chocolate,
## frozen vegetables,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [454] {bottled water,
## chocolate,
## margarine} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [455] {chocolate,
## margarine,
## soda} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [456] {bottled water,
## chocolate,
## soda} => {margarine} 0.0001336630 1.0000000 0.0001336630 31.043568 2
## [457] {bottled beer,
## chocolate,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [458] {chocolate,
## pip fruit,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [459] {chocolate,
## pastry,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [460] {frozen vegetables,
## sausage,
## white bread} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [461] {frozen vegetables,
## root vegetables,
## white bread} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [462] {root vegetables,
## sausage,
## white bread} => {frozen vegetables} 0.0001336630 1.0000000 0.0001336630 35.711217 2
## [463] {beef,
## frankfurter,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [464] {beef,
## rolls or buns,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [465] {shopping bags,
## white bread,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [466] {sausage,
## white bread,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [467] {rolls or buns,
## sausage,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [468] {chicken,
## margarine,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [469] {chicken,
## margarine,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [470] {chicken,
## domestic eggs,
## frankfurter} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [471] {chicken,
## other vegetables,
## root vegetables} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [472] {frozen vegetables,
## margarine,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [473] {frozen vegetables,
## margarine,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [474] {brown bread,
## frozen vegetables,
## pip fruit} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [475] {frankfurter,
## frozen vegetables,
## pip fruit} => {brown bread} 0.0001336630 1.0000000 0.0001336630 26.577265 2
## [476] {brown bread,
## frozen vegetables,
## pip fruit} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [477] {frankfurter,
## frozen vegetables,
## pip fruit} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [478] {beef,
## coffee,
## other vegetables} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [479] {coffee,
## pork,
## root vegetables} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [480] {coffee,
## pork,
## soda} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [481] {coffee,
## frankfurter,
## pastry} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [482] {coffee,
## frankfurter,
## pastry} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [483] {coffee,
## frankfurter,
## sausage} => {soda} 0.0002004946 1.0000000 0.0002004946 10.298004 3
## [484] {coffee,
## sausage,
## soda} => {frankfurter} 0.0002004946 1.0000000 0.0002004946 26.483186 3
## [485] {bottled beer,
## coffee,
## rolls or buns} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [486] {coffee,
## pastry,
## root vegetables} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [487] {bottled water,
## coffee,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [488] {coffee,
## root vegetables,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [489] {curd,
## margarine,
## pip fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [490] {curd,
## margarine,
## other vegetables} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [491] {butter,
## citrus fruit,
## margarine} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [492] {butter,
## margarine,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [493] {citrus fruit,
## margarine,
## whole milk} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [494] {domestic eggs,
## frankfurter,
## margarine} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [495] {brown bread,
## frankfurter,
## margarine} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [496] {brown bread,
## margarine,
## soda} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [497] {citrus fruit,
## margarine,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [498] {citrus fruit,
## margarine,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [499] {citrus fruit,
## sausage,
## yogurt} => {margarine} 0.0001336630 1.0000000 0.0001336630 31.043568 2
## [500] {margarine,
## other vegetables,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [501] {beef,
## curd,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [502] {beef,
## bottled beer,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [503] {beef,
## pip fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [504] {curd,
## fruit or vegetable juice,
## tropical fruit} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [505] {fruit or vegetable juice,
## newspapers,
## pastry} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [506] {fruit or vegetable juice,
## newspapers,
## whole milk} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [507] {bottled beer,
## fruit or vegetable juice,
## sausage} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [508] {bottled beer,
## fruit or vegetable juice,
## tropical fruit} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [509] {citrus fruit,
## fruit or vegetable juice,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [510] {curd,
## newspapers,
## sausage} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [511] {curd,
## newspapers,
## other vegetables} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [512] {newspapers,
## other vegetables,
## sausage} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [513] {curd,
## pip fruit,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [514] {citrus fruit,
## curd,
## pastry} => {other vegetables} 0.0002004946 1.0000000 0.0002004946 8.189929 3
## [515] {citrus fruit,
## curd,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [516] {curd,
## soda,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [517] {bottled beer,
## frankfurter,
## soda} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [518] {bottled beer,
## butter,
## citrus fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [519] {bottled beer,
## citrus fruit,
## soda} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [520] {bottled beer,
## butter,
## root vegetables} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [521] {butter,
## root vegetables,
## sausage} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [522] {butter,
## canned beer,
## sausage} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [523] {butter,
## rolls or buns,
## shopping bags} => {soda} 0.0002004946 1.0000000 0.0002004946 10.298004 3
## [524] {butter,
## citrus fruit,
## pip fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [525] {citrus fruit,
## pip fruit,
## whole milk} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [526] {butter,
## pastry,
## tropical fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [527] {canned beer,
## pork,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [528] {pork,
## sausage,
## shopping bags} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [529] {pork,
## sausage,
## shopping bags} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [530] {citrus fruit,
## pip fruit,
## pork} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [531] {citrus fruit,
## pork,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [532] {pork,
## root vegetables,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [533] {brown bread,
## domestic eggs,
## frankfurter} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [534] {citrus fruit,
## domestic eggs,
## frankfurter} => {brown bread} 0.0001336630 1.0000000 0.0001336630 26.577265 2
## [535] {brown bread,
## domestic eggs,
## frankfurter} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [536] {citrus fruit,
## domestic eggs,
## whole milk} => {brown bread} 0.0001336630 1.0000000 0.0001336630 26.577265 2
## [537] {bottled beer,
## domestic eggs,
## shopping bags} => {newspapers} 0.0001336630 1.0000000 0.0001336630 25.709622 2
## [538] {citrus fruit,
## domestic eggs,
## frankfurter} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [539] {citrus fruit,
## domestic eggs,
## whole milk} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [540] {domestic eggs,
## sausage,
## shopping bags} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [541] {bottled water,
## domestic eggs,
## sausage} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [542] {bottled water,
## domestic eggs,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [543] {domestic eggs,
## root vegetables,
## whole milk} => {other vegetables} 0.0002004946 1.0000000 0.0002004946 8.189929 3
## [544] {brown bread,
## citrus fruit,
## shopping bags} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [545] {bottled beer,
## newspapers,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [546] {newspapers,
## pastry,
## rolls or buns} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [547] {newspapers,
## rolls or buns,
## soda} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [548] {bottled water,
## frankfurter,
## pastry} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [549] {frankfurter,
## pastry,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [550] {frankfurter,
## tropical fruit,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [551] {citrus fruit,
## frankfurter,
## rolls or buns} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [552] {bottled water,
## frankfurter,
## sausage} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [553] {bottled beer,
## citrus fruit,
## whipped or sour cream} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [554] {other vegetables,
## pip fruit,
## whipped or sour cream} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [555] {citrus fruit,
## rolls or buns,
## whipped or sour cream} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [556] {other vegetables,
## tropical fruit,
## whipped or sour cream} => {sausage} 0.0002004946 1.0000000 0.0002004946 16.570321 3
## [557] {soda,
## whipped or sour cream,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [558] {bottled beer,
## rolls or buns,
## shopping bags} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [559] {bottled beer,
## other vegetables,
## shopping bags} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [560] {bottled beer,
## pastry,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [561] {canned beer,
## citrus fruit,
## tropical fruit} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [562] {canned beer,
## citrus fruit,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [563] {canned beer,
## citrus fruit,
## yogurt} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [564] {canned beer,
## tropical fruit,
## yogurt} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [565] {citrus fruit,
## shopping bags,
## yogurt} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [566] {citrus fruit,
## pip fruit,
## soda} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [567] {citrus fruit,
## pastry,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [568] {pastry,
## root vegetables,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [569] {pastry,
## rolls or buns,
## sausage} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [570] {other vegetables,
## pastry,
## soda} => {whole milk} 0.0003341576 0.8333333 0.0004009891 5.276837 5
## [571] {bottled water,
## citrus fruit,
## tropical fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [572] {citrus fruit,
## other vegetables,
## tropical fruit} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [573] {rolls or buns,
## tropical fruit,
## yogurt} => {sausage} 0.0002673261 0.8000000 0.0003341576 13.256257 4
## [574] {other vegetables,
## prosecco,
## sausage,
## waffles} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [575] {prosecco,
## sausage,
## waffles,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [576] {other vegetables,
## prosecco,
## waffles,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [577] {other vegetables,
## prosecco,
## sausage,
## whole milk} => {waffles} 0.0001336630 1.0000000 0.0001336630 54.018051 2
## [578] {cake bar,
## curd,
## rolls or buns,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [579] {cake bar,
## curd,
## tropical fruit,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [580] {cake bar,
## curd,
## rolls or buns,
## whole milk} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [581] {cake bar,
## rolls or buns,
## tropical fruit,
## whole milk} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [582] {curd,
## rolls or buns,
## tropical fruit,
## whole milk} => {cake bar} 0.0001336630 1.0000000 0.0001336630 162.641304 2
## [583] {misc. beverages,
## other vegetables,
## sausage,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [584] {misc. beverages,
## sausage,
## whole milk,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [585] {misc. beverages,
## other vegetables,
## sausage,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [586] {misc. beverages,
## other vegetables,
## whole milk,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [587] {citrus fruit,
## curd,
## pastry,
## specialty chocolate} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [588] {curd,
## other vegetables,
## pastry,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [589] {citrus fruit,
## curd,
## other vegetables,
## specialty chocolate} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [590] {citrus fruit,
## other vegetables,
## pastry,
## specialty chocolate} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [591] {citrus fruit,
## frozen vegetables,
## ham,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [592] {citrus fruit,
## frozen vegetables,
## ham,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [593] {frozen vegetables,
## ham,
## whole milk,
## yogurt} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [594] {citrus fruit,
## ham,
## whole milk,
## yogurt} => {frozen vegetables} 0.0001336630 1.0000000 0.0001336630 35.711217 2
## [595] {citrus fruit,
## frozen vegetables,
## whole milk,
## yogurt} => {ham} 0.0001336630 1.0000000 0.0001336630 58.449219 2
## [596] {frozen meals,
## margarine,
## sausage,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [597] {frozen meals,
## margarine,
## other vegetables,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [598] {frozen meals,
## margarine,
## other vegetables,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [599] {frozen meals,
## other vegetables,
## sausage,
## yogurt} => {margarine} 0.0001336630 1.0000000 0.0001336630 31.043568 2
## [600] {margarine,
## other vegetables,
## sausage,
## yogurt} => {frozen meals} 0.0001336630 1.0000000 0.0001336630 59.613546 2
## [601] {butter milk,
## rolls or buns,
## sausage,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [602] {butter milk,
## sausage,
## whole milk,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [603] {butter milk,
## rolls or buns,
## sausage,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [604] {butter milk,
## rolls or buns,
## whole milk,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [605] {onions,
## root vegetables,
## tropical fruit,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [606] {root vegetables,
## tropical fruit,
## whole milk,
## yogurt} => {onions} 0.0001336630 1.0000000 0.0001336630 49.382838 2
## [607] {coffee,
## frankfurter,
## hamburger meat,
## root vegetables} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [608] {coffee,
## frankfurter,
## hamburger meat,
## soda} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [609] {coffee,
## hamburger meat,
## root vegetables,
## soda} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [610] {coffee,
## frankfurter,
## root vegetables,
## soda} => {hamburger meat} 0.0001336630 1.0000000 0.0001336630 45.758410 2
## [611] {dessert,
## pip fruit,
## soda,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [612] {dessert,
## pip fruit,
## whole milk,
## yogurt} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [613] {dessert,
## pip fruit,
## soda,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [614] {pip fruit,
## soda,
## whole milk,
## yogurt} => {dessert} 0.0001336630 1.0000000 0.0001336630 42.388102 2
## [615] {brown bread,
## canned beer,
## frankfurter,
## frozen vegetables} => {pip fruit} 0.0001336630 1.0000000 0.0001336630 20.385559 2
## [616] {brown bread,
## frankfurter,
## frozen vegetables,
## pip fruit} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [617] {brown bread,
## canned beer,
## frozen vegetables,
## pip fruit} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [618] {canned beer,
## frankfurter,
## frozen vegetables,
## pip fruit} => {brown bread} 0.0001336630 1.0000000 0.0001336630 26.577265 2
## [619] {brown bread,
## canned beer,
## frankfurter,
## pip fruit} => {frozen vegetables} 0.0001336630 1.0000000 0.0001336630 35.711217 2
## [620] {coffee,
## frankfurter,
## pastry,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [621] {coffee,
## frankfurter,
## pastry,
## soda} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [622] {coffee,
## pastry,
## sausage,
## soda} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [623] {frankfurter,
## pastry,
## sausage,
## soda} => {coffee} 0.0001336630 1.0000000 0.0001336630 31.634249 2
## [624] {curd,
## sausage,
## whole milk,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [625] {curd,
## rolls or buns,
## whole milk,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [626] {pork,
## sausage,
## shopping bags,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [627] {pork,
## sausage,
## shopping bags,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [628] {pork,
## shopping bags,
## soda,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [629] {pork,
## sausage,
## soda,
## yogurt} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [630] {pork,
## soda,
## whole milk,
## yogurt} => {sausage} 0.0002004946 1.0000000 0.0002004946 16.570321 3
## [631] {pork,
## rolls or buns,
## sausage,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [632] {pork,
## rolls or buns,
## sausage,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [633] {brown bread,
## citrus fruit,
## domestic eggs,
## frankfurter} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [634] {brown bread,
## domestic eggs,
## frankfurter,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [635] {brown bread,
## citrus fruit,
## domestic eggs,
## whole milk} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [636] {citrus fruit,
## domestic eggs,
## frankfurter,
## whole milk} => {brown bread} 0.0001336630 1.0000000 0.0001336630 26.577265 2
## [637] {brown bread,
## citrus fruit,
## frankfurter,
## whole milk} => {domestic eggs} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [638] {citrus fruit,
## rolls or buns,
## whipped or sour cream,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [639] {citrus fruit,
## whipped or sour cream,
## whole milk,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [640] {rolls or buns,
## whipped or sour cream,
## whole milk,
## yogurt} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [641] {citrus fruit,
## rolls or buns,
## whole milk,
## yogurt} => {whipped or sour cream} 0.0001336630 1.0000000 0.0001336630 22.879205 2
## [642] {canned beer,
## citrus fruit,
## tropical fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [643] {canned beer,
## citrus fruit,
## tropical fruit,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [644] {other vegetables,
## pastry,
## sausage,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [645] {other vegetables,
## pastry,
## sausage,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [646] {citrus fruit,
## other vegetables,
## tropical fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [647] {citrus fruit,
## other vegetables,
## whole milk,
## yogurt} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2## lhs rhs support
## [1] {domestic eggs, rubbing alcohol} => {frankfurter} 0.000133663
## [2] {frankfurter, rubbing alcohol} => {domestic eggs} 0.000133663
## [3] {soap, tropical fruit} => {whole milk} 0.000133663
## [4] {soap, whole milk} => {tropical fruit} 0.000133663
## [5] {domestic eggs, skin care} => {other vegetables} 0.000133663
## [6] {bottled water, cookware} => {canned beer} 0.000133663
## [7] {frankfurter, potato products} => {other vegetables} 0.000133663
## [8] {syrup, tropical fruit} => {whole milk} 0.000133663
## [9] {ice cream, prosecco} => {other vegetables} 0.000133663
## [10] {prosecco, waffles} => {sausage} 0.000133663
## confidence coverage lift count
## [1] 1 0.000133663 26.483186 2
## [2] 1 0.000133663 26.960360 2
## [3] 1 0.000133663 6.332205 2
## [4] 1 0.000133663 14.756410 2
## [5] 1 0.000133663 8.189929 2
## [6] 1 0.000133663 21.314815 2
## [7] 1 0.000133663 8.189929 2
## [8] 1 0.000133663 6.332205 2
## [9] 1 0.000133663 8.189929 2
## [10] 1 0.000133663 16.570321 2## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
### Remove redundant rules ----
# We can remove the redundant rules as follows:
subset_rules <-
which(colSums(is.subset(association_rules_prod_name,
association_rules_prod_name)) > 1)
length(subset_rules)## [1] 407association_rules_prod_no_reps <- association_rules_prod_name[-subset_rules]
# This results in 8 non-redundant rules (instead of the initial 3 rules)
summary(association_rules_prod_no_reps)## set of 240 rules
##
## rule length distribution (lhs + rhs):sizes
## 3 4
## 117 123
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 3.000 4.000 3.513 4.000 4.000
##
## summary of quality measures:
## support confidence coverage lift
## Min. :0.0001337 Min. :0.8000 Min. :0.0001337 Min. : 5.066
## 1st Qu.:0.0001337 1st Qu.:1.0000 1st Qu.:0.0001337 1st Qu.: 6.332
## Median :0.0001337 Median :1.0000 Median :0.0001337 Median : 9.091
## Mean :0.0001409 Mean :0.9968 Mean :0.0001420 Mean : 12.789
## 3rd Qu.:0.0001337 3rd Qu.:1.0000 3rd Qu.:0.0001337 3rd Qu.: 15.187
## Max. :0.0003342 Max. :1.0000 Max. :0.0004010 Max. :152.684
## count
## Min. :2.000
## 1st Qu.:2.000
## Median :2.000
## Mean :2.108
## 3rd Qu.:2.000
## Max. :5.000
##
## mining info:
## data ntransactions support confidence
## tr 14963 1e-04 0.8
## call
## apriori(data = tr, parameter = list(support = 1e-04, confidence = 0.8, maxlen = 10))## lhs rhs support confidence coverage lift count
## [1] {domestic eggs,
## skin care} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [2] {bottled water,
## cookware} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [3] {frankfurter,
## potato products} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [4] {syrup,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [5] {ice cream,
## prosecco} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [6] {prosecco,
## waffles} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [7] {prosecco,
## waffles} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [8] {prosecco,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [9] {prosecco,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [10] {canned fruit,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [11] {newspapers,
## nut snack} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [12] {nut snack,
## other vegetables} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [13] {jam,
## pip fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [14] {cereals,
## packaged fruit or vegetables} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [15] {dental care,
## napkins} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [16] {dental care,
## pip fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [17] {artif. sweetener,
## bottled water} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [18] {brown bread,
## sauces} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [19] {shopping bags,
## spices} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [20] {softener,
## vinegar} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [21] {softener,
## vinegar} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [22] {pip fruit,
## softener} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [23] {house keeping products,
## semi-finished bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [24] {house keeping products,
## margarine} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [25] {canned beer,
## house keeping products} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [26] {bottled water,
## house keeping products} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [27] {house keeping products,
## other vegetables} => {whole milk} 0.0002673261 1.0000000 0.0002673261 6.332205 4
## [28] {citrus fruit,
## soups} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [29] {ice cream,
## popcorn} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [30] {oil,
## popcorn} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [31] {sausage,
## vinegar} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [32] {chocolate marshmallow,
## sugar} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [33] {chocolate marshmallow,
## domestic eggs} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [34] {canned beer,
## Instant food products} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [35] {frankfurter,
## liver loaf} => {condensed milk} 0.0001336630 1.0000000 0.0001336630 152.683673 2
## [36] {liver loaf,
## sausage} => {white bread} 0.0001336630 1.0000000 0.0001336630 41.679666 2
## [37] {liver loaf,
## shopping bags} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [38] {berries,
## zwieback} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [39] {frankfurter,
## zwieback} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [40] {flower (seeds),
## pork} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [41] {candles,
## white bread} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [42] {candles,
## curd} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [43] {finished products,
## onions} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [44] {chocolate,
## finished products} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [45] {chocolate,
## finished products} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [46] {curd,
## finished products} => {whipped or sour cream} 0.0001336630 1.0000000 0.0001336630 22.879205 2
## [47] {butter,
## finished products} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [48] {frozen potato products,
## UHT-milk} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [49] {fruit or vegetable juice,
## specialty cheese} => {long life bakery product} 0.0001336630 1.0000000 0.0001336630 55.832090 2
## [50] {dog food,
## sliced cheese} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [51] {dog food,
## fruit or vegetable juice} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [52] {dog food,
## fruit or vegetable juice} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [53] {cling film or bags,
## newspapers} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [54] {cling film or bags,
## shopping bags} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [55] {mayonnaise,
## oil} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [56] {mayonnaise,
## newspapers} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [57] {mayonnaise,
## pip fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [58] {curd,
## pet care} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [59] {specialty chocolate,
## sweet spreads} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [60] {butter milk,
## sweet spreads} => {berries} 0.0001336630 1.0000000 0.0001336630 45.898773 2
## [61] {napkins,
## sweet spreads} => {chocolate} 0.0001336630 1.0000000 0.0001336630 42.388102 2
## [62] {canned vegetables,
## domestic eggs} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [63] {bottled beer,
## salt} => {misc. beverages} 0.0001336630 1.0000000 0.0001336630 63.402542 2
## [64] {ham,
## turkey} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [65] {ham,
## turkey} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [66] {beef,
## turkey} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [67] {pork,
## turkey} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [68] {pork,
## turkey} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [69] {citrus fruit,
## turkey} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [70] {hamburger meat,
## mustard} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [71] {cake bar,
## frozen vegetables} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [72] {frozen dessert,
## pip fruit} => {pork} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [73] {flour,
## liquor} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [74] {flour,
## liquor} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [75] {frankfurter,
## liquor} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [76] {frozen fish,
## napkins} => {frankfurter} 0.0001336630 1.0000000 0.0001336630 26.483186 2
## [77] {frozen meals,
## spread cheese} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [78] {frozen meals,
## spread cheese} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [79] {spread cheese,
## UHT-milk} => {root vegetables} 0.0001336630 1.0000000 0.0001336630 14.373679 2
## [80] {frankfurter,
## spread cheese} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [81] {canned beer,
## spread cheese} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [82] {condensed milk,
## pip fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [83] {canned fish,
## pasta} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [84] {canned fish,
## chocolate} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [85] {hygiene articles,
## pot plants} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [86] {pork,
## pot plants} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [87] {baking powder,
## specialty bar} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [88] {baking powder,
## sliced cheese} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [89] {pickled vegetables,
## processed cheese} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [90] {detergent,
## oil} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [91] {cream cheese,
## detergent} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [92] {citrus fruit,
## detergent} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [93] {cat food,
## dishes} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [94] {fruit or vegetable juice,
## semi-finished bread} => {rolls or buns} 0.0002673261 0.8000000 0.0003341576 7.272418 4
## [95] {flour,
## salty snack} => {bottled water} 0.0001336630 1.0000000 0.0001336630 16.479075 2
## [96] {flour,
## margarine} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [97] {butter,
## processed cheese} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [98] {pastry,
## processed cheese} => {whole milk} 0.0002673261 0.8000000 0.0003341576 5.065764 4
## [99] {soft cheese,
## specialty bar} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [100] {cat food,
## long life bakery product} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [101] {chewing gum,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [102] {coffee,
## specialty bar} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [103] {hygiene articles,
## misc. beverages} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [104] {frozen meals,
## hygiene articles} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [105] {frozen meals,
## hygiene articles} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [106] {hygiene articles,
## salty snack} => {curd} 0.0001336630 1.0000000 0.0001336630 29.688492 2
## [107] {butter milk,
## candy} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [108] {beverages,
## ice cream} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [109] {fruit or vegetable juice,
## grapes} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [110] {oil,
## specialty chocolate} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [111] {ham,
## oil} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [112] {hard cheese,
## specialty chocolate} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [113] {beverages,
## hard cheese} => {fruit or vegetable juice} 0.0001336630 1.0000000 0.0001336630 29.396857 2
## [114] {berries,
## specialty chocolate} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [115] {ham,
## salty snack} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [116] {ham,
## pip fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [117] {hamburger meat,
## long life bakery product} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [118] {dishes,
## whipped or sour cream,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [119] {sausage,
## semi-finished bread,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [120] {flour,
## specialty chocolate,
## whipped or sour cream} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [121] {bottled water,
## specialty bar,
## whole milk} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [122] {canned beer,
## curd,
## hygiene articles} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [123] {canned beer,
## hygiene articles,
## soda} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [124] {pastry,
## sliced cheese,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [125] {candy,
## citrus fruit,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [126] {oil,
## pork,
## root vegetables} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [127] {misc. beverages,
## sausage,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [128] {curd,
## hard cheese,
## sausage} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [129] {curd,
## hard cheese,
## root vegetables} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [130] {hard cheese,
## other vegetables,
## pip fruit} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [131] {hard cheese,
## tropical fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [132] {chicken,
## specialty chocolate,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [133] {specialty chocolate,
## tropical fruit,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [134] {beverages,
## canned beer,
## whole milk} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [135] {canned beer,
## ham,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [136] {ham,
## tropical fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [137] {ham,
## other vegetables,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [138] {frozen meals,
## margarine,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [139] {frozen meals,
## margarine,
## sausage} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [140] {margarine,
## other vegetables,
## yogurt} => {frozen meals} 0.0001336630 1.0000000 0.0001336630 59.613546 2
## [141] {bottled water,
## curd,
## frozen meals} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [142] {bottled water,
## frozen meals,
## rolls or buns} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [143] {frozen meals,
## sausage,
## tropical fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [144] {butter milk,
## rolls or buns,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [145] {butter milk,
## canned beer,
## sausage} => {yogurt} 0.0002004946 1.0000000 0.0002004946 11.644358 3
## [146] {butter milk,
## canned beer,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [147] {butter milk,
## rolls or buns,
## sausage} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [148] {butter milk,
## rolls or buns,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [149] {long life bakery product,
## other vegetables,
## rolls or buns} => {domestic eggs} 0.0001336630 1.0000000 0.0001336630 26.960360 2
## [150] {sausage,
## tropical fruit,
## waffles} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [151] {other vegetables,
## root vegetables,
## waffles} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [152] {pip fruit,
## root vegetables,
## waffles} => {tropical fruit} 0.0001336630 1.0000000 0.0001336630 14.756410 2
## [153] {bottled beer,
## domestic eggs,
## salty snack} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [154] {onions,
## sausage,
## whipped or sour cream} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [155] {onions,
## rolls or buns,
## whipped or sour cream} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [156] {berries,
## fruit or vegetable juice,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [157] {hamburger meat,
## other vegetables,
## white bread} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [158] {hamburger meat,
## soda,
## whole milk} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [159] {hamburger meat,
## rolls or buns,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [160] {hamburger meat,
## other vegetables,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [161] {citrus fruit,
## curd,
## dessert} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [162] {butter,
## dessert,
## soda} => {shopping bags} 0.0001336630 1.0000000 0.0001336630 21.015449 2
## [163] {dessert,
## pastry,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [164] {dessert,
## sausage,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [165] {chocolate,
## frozen vegetables,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [166] {bottled beer,
## chocolate,
## sausage} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [167] {chocolate,
## pip fruit,
## yogurt} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [168] {chocolate,
## pastry,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [169] {beef,
## frankfurter,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [170] {beef,
## rolls or buns,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [171] {shopping bags,
## white bread,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [172] {sausage,
## white bread,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [173] {rolls or buns,
## sausage,
## white bread} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [174] {chicken,
## domestic eggs,
## frankfurter} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [175] {chicken,
## other vegetables,
## root vegetables} => {bottled beer} 0.0001336630 1.0000000 0.0001336630 22.069322 2
## [176] {brown bread,
## frozen vegetables,
## pip fruit} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [177] {frankfurter,
## frozen vegetables,
## pip fruit} => {canned beer} 0.0001336630 1.0000000 0.0001336630 21.314815 2
## [178] {beef,
## coffee,
## other vegetables} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [179] {coffee,
## frankfurter,
## pastry} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [180] {coffee,
## frankfurter,
## pastry} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [181] {bottled beer,
## coffee,
## rolls or buns} => {pastry} 0.0001336630 1.0000000 0.0001336630 19.332041 2
## [182] {coffee,
## pastry,
## root vegetables} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [183] {bottled water,
## coffee,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [184] {coffee,
## root vegetables,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [185] {curd,
## margarine,
## pip fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [186] {curd,
## margarine,
## other vegetables} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [187] {domestic eggs,
## frankfurter,
## margarine} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [188] {margarine,
## other vegetables,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [189] {beef,
## curd,
## rolls or buns} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [190] {beef,
## bottled beer,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [191] {beef,
## pip fruit,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [192] {curd,
## fruit or vegetable juice,
## tropical fruit} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [193] {citrus fruit,
## fruit or vegetable juice,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [194] {curd,
## pip fruit,
## yogurt} => {sausage} 0.0001336630 1.0000000 0.0001336630 16.570321 2
## [195] {citrus fruit,
## curd,
## pastry} => {other vegetables} 0.0002004946 1.0000000 0.0002004946 8.189929 3
## [196] {citrus fruit,
## curd,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [197] {curd,
## soda,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [198] {bottled beer,
## frankfurter,
## soda} => {butter} 0.0001336630 1.0000000 0.0001336630 28.392789 2
## [199] {butter,
## canned beer,
## sausage} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [200] {butter,
## rolls or buns,
## shopping bags} => {soda} 0.0002004946 1.0000000 0.0002004946 10.298004 3
## [201] {butter,
## pastry,
## tropical fruit} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [202] {canned beer,
## pork,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [203] {pork,
## sausage,
## shopping bags} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [204] {pork,
## sausage,
## shopping bags} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [205] {citrus fruit,
## pip fruit,
## pork} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [206] {citrus fruit,
## pork,
## soda} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [207] {pork,
## root vegetables,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [208] {brown bread,
## domestic eggs,
## frankfurter} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [209] {citrus fruit,
## domestic eggs,
## whole milk} => {brown bread} 0.0001336630 1.0000000 0.0001336630 26.577265 2
## [210] {bottled beer,
## domestic eggs,
## shopping bags} => {newspapers} 0.0001336630 1.0000000 0.0001336630 25.709622 2
## [211] {domestic eggs,
## sausage,
## shopping bags} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [212] {bottled water,
## domestic eggs,
## sausage} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [213] {bottled water,
## domestic eggs,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [214] {domestic eggs,
## root vegetables,
## whole milk} => {other vegetables} 0.0002004946 1.0000000 0.0002004946 8.189929 3
## [215] {brown bread,
## citrus fruit,
## shopping bags} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [216] {bottled beer,
## newspapers,
## yogurt} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [217] {bottled water,
## frankfurter,
## pastry} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [218] {frankfurter,
## pastry,
## whole milk} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [219] {frankfurter,
## tropical fruit,
## whole milk} => {citrus fruit} 0.0001336630 1.0000000 0.0001336630 18.821384 2
## [220] {citrus fruit,
## frankfurter,
## rolls or buns} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [221] {bottled water,
## frankfurter,
## sausage} => {other vegetables} 0.0001336630 1.0000000 0.0001336630 8.189929 2
## [222] {bottled beer,
## citrus fruit,
## whipped or sour cream} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [223] {other vegetables,
## pip fruit,
## whipped or sour cream} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [224] {citrus fruit,
## rolls or buns,
## whipped or sour cream} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [225] {other vegetables,
## tropical fruit,
## whipped or sour cream} => {sausage} 0.0002004946 1.0000000 0.0002004946 16.570321 3
## [226] {soda,
## whipped or sour cream,
## yogurt} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [227] {bottled beer,
## pastry,
## whole milk} => {rolls or buns} 0.0001336630 1.0000000 0.0001336630 9.090522 2
## [228] {canned beer,
## citrus fruit,
## tropical fruit} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [229] {canned beer,
## citrus fruit,
## tropical fruit} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [230] {canned beer,
## citrus fruit,
## yogurt} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [231] {canned beer,
## tropical fruit,
## yogurt} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [232] {citrus fruit,
## shopping bags,
## yogurt} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [233] {citrus fruit,
## pip fruit,
## soda} => {yogurt} 0.0001336630 1.0000000 0.0001336630 11.644358 2
## [234] {citrus fruit,
## pastry,
## soda} => {whole milk} 0.0001336630 1.0000000 0.0001336630 6.332205 2
## [235] {pastry,
## root vegetables,
## sausage} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [236] {pastry,
## rolls or buns,
## sausage} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [237] {other vegetables,
## pastry,
## soda} => {whole milk} 0.0003341576 0.8333333 0.0004009891 5.276837 5
## [238] {bottled water,
## citrus fruit,
## tropical fruit} => {soda} 0.0001336630 1.0000000 0.0001336630 10.298004 2
## [239] {citrus fruit,
## other vegetables,
## tropical fruit} => {whole milk} 0.0002004946 1.0000000 0.0002004946 6.332205 3
## [240] {rolls or buns,
## tropical fruit,
## yogurt} => {sausage} 0.0002673261 0.8000000 0.0003341576 13.256257 4write(association_rules_prod_no_reps,
file = "../rules/association_rules_based_on_product_name.csv")# STEP 4. Find specific rules ----
# Which product(s), if bought, result in a customer purchasing
rolls_and_buns_association_rules <-
apriori(tr, parameter = list(supp = 0.00001, conf = 0.8),
appearance = list(default = "lhs",
rhs = "rolls or buns"))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 1e-05 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 0
##
## set item appearances ...[1 item(s)] done [0.00s].
## set transactions ...[167 item(s), 14963 transaction(s)] done [0.00s].
## sorting and recoding items ... [167 item(s)] done [0.00s].
## creating transaction tree ... done [0.01s].
## checking subsets of size 1 2 3 4 5 6 7 8 9 10 done [0.03s].
## writing ... [6348 rule(s)] done [0.01s].
## creating S4 object ... done [0.01s].## lhs rhs support confidence
## [1] {kitchen utensil} => {rolls or buns} 6.683152e-05 1
## [2] {kitchen utensil, pasta} => {rolls or buns} 6.683152e-05 1
## [3] {bottled water, kitchen utensil} => {rolls or buns} 6.683152e-05 1
## [4] {hamburger meat, toilet cleaner} => {rolls or buns} 6.683152e-05 1
## [5] {chocolate, hair spray} => {rolls or buns} 6.683152e-05 1
## [6] {pastry, rubbing alcohol} => {rolls or buns} 6.683152e-05 1
## coverage lift count
## [1] 6.683152e-05 9.090522 1
## [2] 6.683152e-05 9.090522 1
## [3] 6.683152e-05 9.090522 1
## [4] 6.683152e-05 9.090522 1
## [5] 6.683152e-05 9.090522 1
## [6] 6.683152e-05 9.090522 1# Which product(s) are bought if a customer purchases
kitchen_pasta_association_rules <- # nolint
apriori(tr, parameter = list(supp = 0.00001, conf = 0.8),
appearance = list(lhs = c("kitchen utensil", "pasta"), # nolint
default = "rhs"))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 1e-05 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 0
##
## set item appearances ...[2 item(s)] done [0.00s].
## set transactions ...[167 item(s), 14963 transaction(s)] done [0.00s].
## sorting and recoding items ... [167 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 done [0.00s].
## writing ... [4 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].## lhs rhs support confidence
## [1] {kitchen utensil} => {bottled water} 6.683152e-05 1
## [2] {kitchen utensil} => {rolls or buns} 6.683152e-05 1
## [3] {kitchen utensil, pasta} => {bottled water} 6.683152e-05 1
## [4] {kitchen utensil, pasta} => {rolls or buns} 6.683152e-05 1
## coverage lift count
## [1] 6.683152e-05 16.479075 1
## [2] 6.683152e-05 9.090522 1
## [3] 6.683152e-05 16.479075 1
## [4] 6.683152e-05 9.090522 1# STEP 5. Visualize the rules ----
# Filter rules with confidence greater than 0.85 or 85%
rules_to_plot <-
association_rules_prod_no_reps[quality(association_rules_prod_no_reps)$confidence > 0.85] # nolint
#Plot SubRules
plot(rules_to_plot)## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
top_10_rules_to_plot <- head(rules_to_plot, n = 10, by = "confidence")
plot(top_10_rules_to_plot, method = "graph", engine = "htmlwidget")
saveAsGraph(head(rules_to_plot, n = 1000, by = "lift"),
file = "../graph/association_rules_prod_no_reps.graphml")
# Filter top 20 rules with highest lift
rules_to_plot_by_lift <- head(rules_to_plot, n = 20, by = "lift")
plot(rules_to_plot_by_lift, method = "paracoord")
