Association rules
Natalia Miela
2023-02-02
Market Basket Analysis
Explore the data
Aim of this report is to analyze relationship between products in the basket. Data was downloaded from Kaggle website.
Summary of the data set:
summary(raw_data)## transactions as itemMatrix in sparse format with
## 9039 rows (elements/itemsets/transactions) and
## 168 columns (items) and a density of 0.02621708
##
## most frequent items:
## whole milk other vegetables rolls/buns soda
## 2325 1740 1656 1579
## yogurt (Other)
## 1258 31254
##
## element (itemset/transaction) length distribution:
## sizes
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 1981 1513 1210 919 775 594 504 405 319 219 166 112 72 71 48 44
## 17 18 19 20 21 22 23 24 27 28 29
## 25 13 14 9 10 4 6 1 1 1 3
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 4.404 6.000 29.000
##
## includes extended item information - examples:
## labels
## 1 abrasive cleaner
## 2 artif. sweetener
## 3 baby cosmeticsData summary: There are 9039 transactions and 168 unique items.
Whole milk, other vegetables, rolls/ buns, soda and yoghurt are the most
frequently bought products.
Most of the transactions (1981) include only a single item and the
largest shopping basket includes 29 items.
hist(size(raw_data), main = 'Number of items per basket', xlab = '# Items', col = 'cornflowerblue')
Let’s check the top products:
Items which belong to 5% of all transactions:
itemFrequencyPlot(raw_data, support = 0.05, col = 'pink', xlab = 'Item name', ylab = 'Frequency', main = 'Frequency plot with 5% support' )
Top 10 items with highest (absolute) frequency:
itemFrequencyPlot(raw_data, topN = 10, type = 'absolute', col = 'lightslateblue', xlab = 'Item name', ylab = 'Absolute frequency', main = 'Absolute item frequency plot- top 10')
Top 10 items with highest (relative) frequency:
itemFrequencyPlot(raw_data, topN = 10, type = 'relative', col = 'coral1', xlab = 'Item name', ylab = 'Relative frequency', main = 'Relative item frequency plot- top 10' )
Below is a list of items absolute frequency in the data set:
sort(round(itemFrequency(raw_data, type = 'absolute'),4), decreasing = TRUE)## whole milk other vegetables rolls/buns
## 2325 1740 1656
## soda yogurt root vegetables
## 1579 1258 990
## bottled water tropical fruit shopping bags
## 969 949 902
## sausage pastry bottled beer
## 855 795 732
## citrus fruit newspapers pip fruit
## 730 726 701
## canned beer fruit/vegetable juice whipped/sour cream
## 699 648 646
## brown bread domestic eggs frankfurter
## 585 577 531
## margarine pork coffee
## 528 528 514
## butter napkins curd
## 501 476 472
## beef chocolate frozen vegetables
## 469 461 433
## chicken white bread cream cheese
## 395 378 355
## waffles long life bakery product dessert
## 348 342 337
## salty snack sugar berries
## 336 300 299
## UHT-milk hamburger meat hygiene articles
## 297 289 287
## onions specialty chocolate candy
## 286 281 267
## frozen meals butter milk misc. beverages
## 256 252 251
## oil specialty bar beverages
## 245 245 241
## meat ham ice cream
## 237 232 230
## hard cheese sliced cheese cat food
## 222 221 211
## grapes chewing gum white wine
## 196 186 173
## detergent red/blush wine semi-finished bread
## 171 164 163
## baking powder pickled vegetables dishes
## 162 162 161
## soft cheese potted plants flour
## 159 158 156
## herbs processed cheese canned fish
## 147 144 138
## seasonal products pasta cake bar
## 134 130 122
## mustard packaged fruit/vegetables frozen fish
## 113 111 110
## cling film/bags liquor spread cheese
## 105 104 102
## canned vegetables salt flower (seeds)
## 101 99 98
## condensed milk frozen dessert dish cleaner
## 95 95 91
## roll products pet care sweet spreads
## 91 87 86
## chocolate marshmallow candles dog food
## 84 83 83
## mayonnaise photo/film house keeping products
## 82 82 78
## specialty cheese turkey frozen potato products
## 76 76 75
## Instant food products popcorn liquor (appetizer)
## 72 69 68
## rice instant coffee finished products
## 67 66 62
## soups zwieback vinegar
## 62 61 60
## female sanitary products jam dental care
## 57 53 52
## kitchen towels cereals sauces
## 52 50 50
## cleaner softener sparkling wine
## 49 49 49
## liver loaf spices curd cheese
## 47 47 44
## male cosmetics ketchup brandy
## 40 39 38
## meat spreads rum tea
## 38 38 37
## light bulbs nuts/prunes specialty fat
## 35 32 31
## artif. sweetener canned fruit skin care
## 30 30 30
## syrup nut snack fish
## 30 29 28
## snack products abrasive cleaner potato products
## 28 27 27
## cooking chocolate cookware organic sausage
## 24 23 22
## pudding powder tidbits bathroom cleaner
## 22 22 21
## cocoa drinks soap flower soil/fertilizer
## 21 21 19
## prosecco ready soups specialty vegetables
## 19 17 16
## decalcifier organic products cream
## 15 15 13
## honey frozen fruits hair spray
## 13 12 9
## liqueur make up remover rubbing alcohol
## 9 8 8
## salad dressing whisky toilet cleaner
## 8 8 6
## frozen chicken baby cosmetics bags
## 5 4 4
## kitchen utensil preservation products sound storage medium
## 4 2 1Apriori algorithm
Here I apply Apriori algorithm, with support 2% and confidence value of 40%.
# creating the rules - 2% support, 40% confidence
rules <- apriori(raw_data, parameter=list(supp=0.02, conf=0.4, minlen = 2))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.4 0.1 1 none FALSE TRUE 5 0.02 2
## 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: 180
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[168 item(s), 9039 transaction(s)] done [0.00s].
## sorting and recoding items ... [59 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 done [0.00s].
## writing ... [15 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].Support tells us how popular an item is, as measured by the
proportion of transactions in which an item appears.
Rules with highest support value:
inspect(sort(rules, by = 'support'))## lhs rhs support
## [1] {yogurt} => {whole milk} 0.05675407
## [2] {root vegetables} => {whole milk} 0.05000553
## [3] {root vegetables} => {other vegetables} 0.04746100
## [4] {tropical fruit} => {whole milk} 0.04270384
## [5] {whipped/sour cream} => {whole milk} 0.03219383
## [6] {domestic eggs} => {whole milk} 0.03064498
## [7] {whipped/sour cream} => {other vegetables} 0.02876424
## [8] {butter} => {whole milk} 0.02810045
## [9] {curd} => {whole milk} 0.02522403
## [10] {margarine} => {whole milk} 0.02433898
## [11] {other vegetables, root vegetables} => {whole milk} 0.02345392
## [12] {root vegetables, whole milk} => {other vegetables} 0.02345392
## [13] {other vegetables, yogurt} => {whole milk} 0.02267950
## [14] {beef} => {whole milk} 0.02090939
## [15] {frozen vegetables} => {whole milk} 0.02057750
## confidence coverage lift count
## [1] 0.4077901 0.13917469 1.585383 513
## [2] 0.4565657 0.10952539 1.775009 452
## [3] 0.4333333 0.10952539 2.251092 429
## [4] 0.4067439 0.10498949 1.581315 386
## [5] 0.4504644 0.07146808 1.751289 291
## [6] 0.4800693 0.06383449 1.866386 277
## [7] 0.4024768 0.07146808 2.090797 260
## [8] 0.5069860 0.05542649 1.971031 254
## [9] 0.4830508 0.05221817 1.877977 228
## [10] 0.4166667 0.05841354 1.619892 220
## [11] 0.4941725 0.04746100 1.921215 212
## [12] 0.4690265 0.05000553 2.436512 212
## [13] 0.5242967 0.04325700 2.038330 205
## [14] 0.4029851 0.05188627 1.566702 189
## [15] 0.4295612 0.04790353 1.670023 186The highest support value is equal to almost 5.7%, which can be
understood as the pair { yoghurt -> whole milk} occurs in 5.7% of
transactions.
Lift tells us what is the ratio between confidence of the rule and
the expected confidence of the rule.
Rules with highest lift value:
inspect(sort(rules, by = 'lift'))## lhs rhs support
## [1] {root vegetables, whole milk} => {other vegetables} 0.02345392
## [2] {root vegetables} => {other vegetables} 0.04746100
## [3] {whipped/sour cream} => {other vegetables} 0.02876424
## [4] {other vegetables, yogurt} => {whole milk} 0.02267950
## [5] {butter} => {whole milk} 0.02810045
## [6] {other vegetables, root vegetables} => {whole milk} 0.02345392
## [7] {curd} => {whole milk} 0.02522403
## [8] {domestic eggs} => {whole milk} 0.03064498
## [9] {root vegetables} => {whole milk} 0.05000553
## [10] {whipped/sour cream} => {whole milk} 0.03219383
## [11] {frozen vegetables} => {whole milk} 0.02057750
## [12] {margarine} => {whole milk} 0.02433898
## [13] {yogurt} => {whole milk} 0.05675407
## [14] {tropical fruit} => {whole milk} 0.04270384
## [15] {beef} => {whole milk} 0.02090939
## confidence coverage lift count
## [1] 0.4690265 0.05000553 2.436512 212
## [2] 0.4333333 0.10952539 2.251092 429
## [3] 0.4024768 0.07146808 2.090797 260
## [4] 0.5242967 0.04325700 2.038330 205
## [5] 0.5069860 0.05542649 1.971031 254
## [6] 0.4941725 0.04746100 1.921215 212
## [7] 0.4830508 0.05221817 1.877977 228
## [8] 0.4800693 0.06383449 1.866386 277
## [9] 0.4565657 0.10952539 1.775009 452
## [10] 0.4504644 0.07146808 1.751289 291
## [11] 0.4295612 0.04790353 1.670023 186
## [12] 0.4166667 0.05841354 1.619892 220
## [13] 0.4077901 0.13917469 1.585383 513
## [14] 0.4067439 0.10498949 1.581315 386
## [15] 0.4029851 0.05188627 1.566702 189The highest lift value is equal to around 2.44 for the rule {root
vegetables, whole milk -> other vegetables}.
Confidence tells us about some probability relationship.
inspect(sort(rules, by = 'confidence'))## lhs rhs support
## [1] {other vegetables, yogurt} => {whole milk} 0.02267950
## [2] {butter} => {whole milk} 0.02810045
## [3] {other vegetables, root vegetables} => {whole milk} 0.02345392
## [4] {curd} => {whole milk} 0.02522403
## [5] {domestic eggs} => {whole milk} 0.03064498
## [6] {root vegetables, whole milk} => {other vegetables} 0.02345392
## [7] {root vegetables} => {whole milk} 0.05000553
## [8] {whipped/sour cream} => {whole milk} 0.03219383
## [9] {root vegetables} => {other vegetables} 0.04746100
## [10] {frozen vegetables} => {whole milk} 0.02057750
## [11] {margarine} => {whole milk} 0.02433898
## [12] {yogurt} => {whole milk} 0.05675407
## [13] {tropical fruit} => {whole milk} 0.04270384
## [14] {beef} => {whole milk} 0.02090939
## [15] {whipped/sour cream} => {other vegetables} 0.02876424
## confidence coverage lift count
## [1] 0.5242967 0.04325700 2.038330 205
## [2] 0.5069860 0.05542649 1.971031 254
## [3] 0.4941725 0.04746100 1.921215 212
## [4] 0.4830508 0.05221817 1.877977 228
## [5] 0.4800693 0.06383449 1.866386 277
## [6] 0.4690265 0.05000553 2.436512 212
## [7] 0.4565657 0.10952539 1.775009 452
## [8] 0.4504644 0.07146808 1.751289 291
## [9] 0.4333333 0.10952539 2.251092 429
## [10] 0.4295612 0.04790353 1.670023 186
## [11] 0.4166667 0.05841354 1.619892 220
## [12] 0.4077901 0.13917469 1.585383 513
## [13] 0.4067439 0.10498949 1.581315 386
## [14] 0.4029851 0.05188627 1.566702 189
## [15] 0.4024768 0.07146808 2.090797 260The highest confidence value achieved is 52.4% for the rule {other
vegetables, yoghurt -> whole milk}, which means that if someone buys
other vegetables and yoghurt, they will also buy whole milk with 52.4%
probability.
Visualize association rules
Below is a simple scatter plot with support and lift on the axes and
confidence represented by the color of the points.
plot(rules, measure = c('support','lift'), shading = 'confidence')
The next visualization represents the rules as a graph. The rules are
represented as items connected by arrows.
plot(rules, method = 'graph')
The rules can be also visualized as a grouped matrix- based visualization. Support measure is represented as the size of the balloons, and the lift measure is represented by color of the balloons.
plot(rules, method = 'grouped')
Conclusion
Association rules can help us to find interesting patterns in
customer buying preferences and habits. In the analyzed data set, it has
been discovered that whole milk, other vegetables, rolls/buns, soda and
yoghurt are most frequently bought products.
{yoghurt -> whole milk}, {root vegetables -> whole milk}, {root
vegetables -> other vegetables} are the rules with highest support
measure.
{root vegetables, whole milk -> other vegetables}, {root vegetables
-> other vegetables}, {whipped/ sour cream -> other vegetables}
are the rules with highest lift measure.
{other vegetables, yoghurt -> whole milk}, {butter -> whole milk},
{other vegetables, root vegetables -> whole milk} are the rules with
highest confidence measure.