Revisit the notes on association rule mining and the R example on music playlists: playlists.R and playlists.csv. Then use the data on grocery purchases in groceries.txt and find some interesting association rules for these shopping baskets. The data file is a list of shopping baskets: one person’s basket for each row, with multiple items per row separated by commas. Pick your own thresholds for lift and confidence; just be clear what these thresholds are and say why you picked them. Do your discovered item sets make sense? Present your discoveries in an interesting and visually appealing way.
Note: This is an exercise in visual and numerical story-telling. Do be clear in your description of what you’ve done, but keep the focus on the data, the figures, and the insights your analysis has drawn from the data, rather than technical details. The data file is a list of baskets: one row per basket, with multiple items per row separated by commas. You’ll have to cobble together your own code for processing this into the format expected by the “arules” package. This is not intrinsically all that hard, but it is the kind of data-wrangling wrinkle you’ll encounter frequently on real problems, where your software package expects data in one format and the data comes in a different format. Figuring out how to bridge that gap is part of the assignment, and so we won’t be giving tips on this front.
Solution:
## Loading required package: Matrix
##
## Attaching package: 'arules'
## The following objects are masked from 'package:base':
##
## abbreviate, write
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## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.2 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ tidyr::expand() masks Matrix::expand()
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## ✖ tidyr::pack() masks Matrix::pack()
## ✖ dplyr::recode() masks arules::recode()
## ✖ tidyr::unpack() masks Matrix::unpack()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
summary(groceries)## transactions as itemMatrix in sparse format with
## 9835 rows (elements/itemsets/transactions) and
## 169 columns (items) and a density of 0.02609146
##
## most frequent items:
## whole milk other vegetables rolls/buns soda
## 2513 1903 1809 1715
## yogurt (Other)
## 1372 34055
##
## element (itemset/transaction) length distribution:
## sizes
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 2159 1643 1299 1005 855 645 545 438 350 246 182 117 78 77 55 46
## 17 18 19 20 21 22 23 24 26 27 28 29 32
## 29 14 14 9 11 4 6 1 1 1 1 3 1
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 4.409 6.000 32.000
##
## includes extended item information - examples:
## labels
## 1 abrasive cleaner
## 2 artif. sweetener
## 3 baby cosmetics
The most frequent items bought: whole milk, other vegetables, rolls/buns, soda, yogurt.
Apriori Algorithm:
rules = apriori(groceries, parameter = list(support = 0.001, confidence = 0.1, maxlen=3))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.1 0.1 1 none FALSE TRUE 5 0.001 1
## maxlen target ext
## 3 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 9
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [157 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3
## Warning in apriori(groceries, parameter = list(support = 0.001, confidence =
## 0.1, : Mining stopped (maxlen reached). Only patterns up to a length of 3
## returned!
## done [0.00s].
## writing ... [18597 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].
top_20_rules <- rules[1:20]
inspect(top_20_rules)## lhs rhs support confidence
## [1] {} => {bottled water} 0.110523640 0.1105236
## [2] {} => {tropical fruit} 0.104931368 0.1049314
## [3] {} => {root vegetables} 0.108998475 0.1089985
## [4] {} => {soda} 0.174377224 0.1743772
## [5] {} => {yogurt} 0.139501779 0.1395018
## [6] {} => {rolls/buns} 0.183934926 0.1839349
## [7] {} => {other vegetables} 0.193492628 0.1934926
## [8] {} => {whole milk} 0.255516014 0.2555160
## [9] {honey} => {whole milk} 0.001118454 0.7333333
## [10] {soap} => {whole milk} 0.001118454 0.4230769
## [11] {tidbits} => {soda} 0.001016777 0.4347826
## [12] {tidbits} => {rolls/buns} 0.001220132 0.5217391
## [13] {cocoa drinks} => {whole milk} 0.001321810 0.5909091
## [14] {snack products} => {soda} 0.001118454 0.3666667
## [15] {snack products} => {rolls/buns} 0.001118454 0.3666667
## [16] {pudding powder} => {whole milk} 0.001321810 0.5652174
## [17] {cooking chocolate} => {whole milk} 0.001321810 0.5200000
## [18] {bathroom cleaner} => {soda} 0.001016777 0.3703704
## [19] {bathroom cleaner} => {other vegetables} 0.001016777 0.3703704
## [20] {nuts/prunes} => {rolls/buns} 0.001016777 0.3030303
## coverage lift count
## [1] 1.000000000 1.000000 1087
## [2] 1.000000000 1.000000 1032
## [3] 1.000000000 1.000000 1072
## [4] 1.000000000 1.000000 1715
## [5] 1.000000000 1.000000 1372
## [6] 1.000000000 1.000000 1809
## [7] 1.000000000 1.000000 1903
## [8] 1.000000000 1.000000 2513
## [9] 0.001525165 2.870009 11
## [10] 0.002643620 1.655775 11
## [11] 0.002338587 2.493345 10
## [12] 0.002338587 2.836542 12
## [13] 0.002236909 2.312611 13
## [14] 0.003050330 2.102721 11
## [15] 0.003050330 1.993459 11
## [16] 0.002338587 2.212062 13
## [17] 0.002541942 2.035097 13
## [18] 0.002745297 2.123961 10
## [19] 0.002745297 1.914132 10
## [20] 0.003355363 1.647486 10
summary(rules)## set of 18597 rules
##
## rule length distribution (lhs + rhs):sizes
## 1 2 3
## 8 2121 16468
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 3.000 3.000 2.885 3.000 3.000
##
## summary of quality measures:
## support confidence coverage lift
## Min. :0.001017 Min. :0.1000 Min. :0.001118 Min. : 0.4193
## 1st Qu.:0.001220 1st Qu.:0.1471 1st Qu.:0.005084 1st Qu.: 1.7695
## Median :0.001627 Median :0.2083 Median :0.008032 Median : 2.2620
## Mean :0.002553 Mean :0.2523 Mean :0.012901 Mean : 2.5042
## 3rd Qu.:0.002542 3rd Qu.:0.3182 3rd Qu.:0.012913 3rd Qu.: 2.9558
## Max. :0.255516 Max. :1.0000 Max. :1.000000 Max. :35.7158
## count
## Min. : 10.00
## 1st Qu.: 12.00
## Median : 16.00
## Mean : 25.11
## 3rd Qu.: 25.00
## Max. :2513.00
##
## mining info:
## data ntransactions support confidence
## groceries 9835 0.001 0.1
## call
## apriori(data = groceries, parameter = list(support = 0.001, confidence = 0.1, maxlen = 3))
The most frequent individual items purchased are bottled water, tropical fruit, root vegetables, soda, yogurt, rolls/buns, other vegetables, and whole milk. These items have high support values, indicating their prevalence in the transactions. The lift value of 1.0 indicates that these items are purchased independently, as their presence or absence doesn’t influence each other.
{honey} => {whole milk}: Customers buying “honey” are likely to buy “whole milk” with a confidence of 73.33%, suggesting a common combination, while the support for {whole milk} individually is just 25.5%
{tidbits} => {soda}: Customers purchasing “tidbits” tend to purchase “soda” as well with a confidence of 43.48%, and the support for getting {soda} individually is shown as 17.4%
Related Categories: {cooking chocolate} => {whole milk}: Customers buying “cooking chocolate” are likely to buy “whole milk” with a confidence of 52%. This suggests an association between cooking ingredients and dairy products.
Unrelated Categories: Rules like {bathroom cleaner} => {soda} and {bathroom cleaner} => {other vegetables} might indicate that customers who buy cleaning products like “bathroom cleaner” also tend to buy food items like “soda” and “other vegetables.”
Pick your own thresholds for lift and confidence; just be clear what these thresholds are and say why you picked them
-
lift > 15 : A high lift value indicates a strong association between items. Generally, a lift value greater than 1 signifies a positive association. Choosing a threshold like 15 filters out rules that are significantly stronger than random chance, ensuring that we focus on the most valuable relationships.
-
confidence > 0.3 : By setting a confidence threshold of 30%, we can filter out weaker associations and focus on the more significant and reliable relationships between items, and Including all rules might lead to numerous less meaningful associations. Sub-setting allows us to highlight the most relevant insights.
-
lift > 10 & confidence > 0.5 : This subset is chosen based on two criteria: rules with a “lift” value greater than 10, indicating strong associations, and rules with a “confidence” value higher than 0.5, indicating reliable predictions. By applying these filters, the code focuses on extracting rules that not only represent strong connections between items but also provide dependable insights. This approach is useful for uncovering significant and practically relevant patterns in transaction data, which can be valuable for decision-making in fields like marketing and recommendation systems.
Do your discovered item sets make sense? Present your discoveries in an interesting and visually appealing way.
inspect(subset(rules, subset=lift > 15))## lhs rhs support
## [1] {bottled beer, liquor} => {red/blush wine} 0.001931876
## [2] {bottled beer, red/blush wine} => {liquor} 0.001931876
## [3] {popcorn, soda} => {salty snack} 0.001220132
## [4] {salty snack, soda} => {popcorn} 0.001220132
## [5] {Instant food products, soda} => {hamburger meat} 0.001220132
## [6] {hamburger meat, soda} => {Instant food products} 0.001220132
## [7] {Instant food products, whole milk} => {hamburger meat} 0.001525165
## [8] {ham, processed cheese} => {white bread} 0.001931876
## [9] {processed cheese, white bread} => {ham} 0.001931876
## [10] {ham, white bread} => {processed cheese} 0.001931876
## [11] {fruit/vegetable juice, ham} => {processed cheese} 0.001118454
## [12] {baking powder, flour} => {sugar} 0.001016777
## [13] {baking powder, sugar} => {flour} 0.001016777
## [14] {sugar, whipped/sour cream} => {baking powder} 0.001321810
## [15] {curd, sugar} => {flour} 0.001118454
## [16] {margarine, sugar} => {flour} 0.001626843
## confidence coverage lift count
## [1] 0.4130435 0.004677173 21.49356 19
## [2] 0.3958333 0.004880529 35.71579 19
## [3] 0.6315789 0.001931876 16.69779 12
## [4] 0.1304348 0.009354347 18.06797 12
## [5] 0.6315789 0.001931876 18.99565 12
## [6] 0.2105263 0.005795628 26.20919 12
## [7] 0.5000000 0.003050330 15.03823 15
## [8] 0.6333333 0.003050330 15.04549 19
## [9] 0.4634146 0.004168785 17.80345 19
## [10] 0.3800000 0.005083884 22.92822 19
## [11] 0.2894737 0.003863752 17.46610 11
## [12] 0.5555556 0.001830198 16.40807 10
## [13] 0.3125000 0.003253686 17.97332 10
## [14] 0.2708333 0.004880529 15.30831 13
## [15] 0.3235294 0.003457041 18.60767 11
## [16] 0.2962963 0.005490595 17.04137 16
{bottled beer, liquor} => {red/blush wine}: Customers who buy both “bottled beer” and “liquor” are highly likely to also purchase “red/blush wine.” The high lift value of 21.49 indicates a strong association between these alcohol items.
{bottled beer, red/blush wine} => {liquor}: Similarly, customers who purchase “bottled beer” and “red/blush wine” are likely to buy “liquor,” with a lift value of 35.71.
{baking powder, flour} => {sugar}: Customers purchasing “baking powder” and “flour” are likely to buy “sugar.” The lift of 16.41 suggests a connection between these baking ingredients.
inspect(subset(top_20_rules, subset=confidence > 0.3))## lhs rhs support confidence
## [1] {honey} => {whole milk} 0.001118454 0.7333333
## [2] {soap} => {whole milk} 0.001118454 0.4230769
## [3] {tidbits} => {soda} 0.001016777 0.4347826
## [4] {tidbits} => {rolls/buns} 0.001220132 0.5217391
## [5] {cocoa drinks} => {whole milk} 0.001321810 0.5909091
## [6] {snack products} => {soda} 0.001118454 0.3666667
## [7] {snack products} => {rolls/buns} 0.001118454 0.3666667
## [8] {pudding powder} => {whole milk} 0.001321810 0.5652174
## [9] {cooking chocolate} => {whole milk} 0.001321810 0.5200000
## [10] {bathroom cleaner} => {soda} 0.001016777 0.3703704
## [11] {bathroom cleaner} => {other vegetables} 0.001016777 0.3703704
## [12] {nuts/prunes} => {rolls/buns} 0.001016777 0.3030303
## coverage lift count
## [1] 0.001525165 2.870009 11
## [2] 0.002643620 1.655775 11
## [3] 0.002338587 2.493345 10
## [4] 0.002338587 2.836542 12
## [5] 0.002236909 2.312611 13
## [6] 0.003050330 2.102721 11
## [7] 0.003050330 1.993459 11
## [8] 0.002338587 2.212062 13
## [9] 0.002541942 2.035097 13
## [10] 0.002745297 2.123961 10
## [11] 0.002745297 1.914132 10
## [12] 0.003355363 1.647486 10
**{tidbits} => {rolls/buns}:**Similarly, customers who buy “tidbits” have a confidence of 52.17% to buy “rolls/buns.” These associations might be due to snack preferences or consumption patterns.
**{pudding powder} => {whole milk}:**Customers who buy “pudding powder” are likely to purchase “whole milk” with a confidence of 56.52%. This could be due to the use of milk in preparing pudding.
inspect(subset(rules, subset=lift > 10 & confidence > 0.5))## lhs rhs support
## [1] {liquor, red/blush wine} => {bottled beer} 0.001931876
## [2] {popcorn, soda} => {salty snack} 0.001220132
## [3] {Instant food products, soda} => {hamburger meat} 0.001220132
## [4] {ham, processed cheese} => {white bread} 0.001931876
## [5] {domestic eggs, processed cheese} => {white bread} 0.001118454
## [6] {baking powder, flour} => {sugar} 0.001016777
## confidence coverage lift count
## [1] 0.9047619 0.002135231 11.23527 19
## [2] 0.6315789 0.001931876 16.69779 12
## [3] 0.6315789 0.001931876 18.99565 12
## [4] 0.6333333 0.003050330 15.04549 19
## [5] 0.5238095 0.002135231 12.44364 11
## [6] 0.5555556 0.001830198 16.40807 10
**{liquor, red/blush wine} => {bottled beer}:**This rule has a confidence of 90.48% and a lift of 11.24. Customers who buy “liquor” and “red/blush wine” are highly likely to buy “bottled beer” as well. This might suggest that customers who purchase alcoholic beverages tend to buy a variety of them.
{popcorn, soda} => {salty snack}: With a confidence of 63.16% and a lift of 16.70, customers who buy “popcorn” and “soda” are likely to purchase “salty snack” as well. This rule could represent common snacking patterns.
{ham, processed cheese} => {white bread}: With a confidence of 63.33% and a lift of 15.05, customers who buy “ham” and “processed cheese” are likely to purchase “white bread” as well. This might indicate a preference for making sandwiches or similar items
**{domestic eggs, processed cheese} => {white bread}:**This rule has a confidence of 52.38% and a lift of 12.44. Customers who buy “domestic eggs” and “processed cheese” are likely to purchase “white bread.” Similar to the previous rule, this could suggest a preference for breakfast items or sandwiches.
plot(rules, jitter =0)
It can be observed that high lift rules tend to have low support. High lift rules with low support can provide valuable insights about specific interactions between items that might not be immediately obvious from looking at high-support items.
Swapping the axes and color scales:
plot(rules, jitter = 0, measure = c("support", "lift"), shading = "confidence")
“Two key” plot: coloring is by size (order) of item set
plot(rules, method='two-key plot', jitter =0)
Pick your own thresholds for lift and confidence; just be clear what these thresholds are and say why you picked them
-
support > 0.05 : The chosen support threshold of 0.05 captures relatively common associations while allowing for more general patterns to be uncovered. This presents associations among frequently bought items, showcasing moderate associations between items that are commonly purchased together. This type of analysis provides insights into customer behavior and potential marketing opportunities.
-
confidence > 0.5 : The high-confidence association rules reveal strong buying patterns that can be leveraged for marketing and sales strategies. The chosen threshold(confidence = 50%) emphasizes confident and meaningful associations, making it easier to make informed business decisions.
-
lift > 25 : The rules in this subset have exceptionally high lift values, exceeding 25. High lift values indicate that the presence of the items on the left-hand side (LHS) significantly increases the likelihood of the items on the right-hand side (RHS) being bought.
Do your discovered item sets make sense? Present your discoveries in an interesting and visually appealing way.
inspect(subset(rules, support > 0.05))## lhs rhs support confidence coverage
## [1] {} => {bottled water} 0.11052364 0.1105236 1.0000000
## [2] {} => {tropical fruit} 0.10493137 0.1049314 1.0000000
## [3] {} => {root vegetables} 0.10899847 0.1089985 1.0000000
## [4] {} => {soda} 0.17437722 0.1743772 1.0000000
## [5] {} => {yogurt} 0.13950178 0.1395018 1.0000000
## [6] {} => {rolls/buns} 0.18393493 0.1839349 1.0000000
## [7] {} => {other vegetables} 0.19349263 0.1934926 1.0000000
## [8] {} => {whole milk} 0.25551601 0.2555160 1.0000000
## [9] {yogurt} => {whole milk} 0.05602440 0.4016035 0.1395018
## [10] {whole milk} => {yogurt} 0.05602440 0.2192598 0.2555160
## [11] {rolls/buns} => {whole milk} 0.05663447 0.3079049 0.1839349
## [12] {whole milk} => {rolls/buns} 0.05663447 0.2216474 0.2555160
## [13] {other vegetables} => {whole milk} 0.07483477 0.3867578 0.1934926
## [14] {whole milk} => {other vegetables} 0.07483477 0.2928770 0.2555160
## lift count
## [1] 1.000000 1087
## [2] 1.000000 1032
## [3] 1.000000 1072
## [4] 1.000000 1715
## [5] 1.000000 1372
## [6] 1.000000 1809
## [7] 1.000000 1903
## [8] 1.000000 2513
## [9] 1.571735 551
## [10] 1.571735 551
## [11] 1.205032 557
## [12] 1.205032 557
## [13] 1.513634 736
## [14] 1.513634 736
If a customer buys rolls/buns, there’s a moderate chance they’ll also buy whole milk. This insight can inform product placement or promotional strategies.
The confidence values in this subset of rules generally range from around 0.2 to 0.4, indicating moderate confidence in these associations
The rule {yogurt} => {whole milk} suggests that customers who buy yogurt are likely to buy whole milk as well, and vice-versa.
inspect(subset(top_20_rules, confidence > 0.5))## lhs rhs support confidence coverage
## [1] {honey} => {whole milk} 0.001118454 0.7333333 0.001525165
## [2] {tidbits} => {rolls/buns} 0.001220132 0.5217391 0.002338587
## [3] {cocoa drinks} => {whole milk} 0.001321810 0.5909091 0.002236909
## [4] {pudding powder} => {whole milk} 0.001321810 0.5652174 0.002338587
## [5] {cooking chocolate} => {whole milk} 0.001321810 0.5200000 0.002541942
## lift count
## [1] 2.870009 11
## [2] 2.836542 12
## [3] 2.312611 13
## [4] 2.212062 13
## [5] 2.035097 13
The rule {honey} => {whole milk} has a confidence of approximately 0.73. This implies that when a customer buys honey, there’s a high likelihood (73%) they will also buy whole milk. So, if honey and whole milk are placed close to each other, it might encourage more customers to buy both items.
The other rules also show strong associations. For instance, items like tidbits are often associated with rolls/buns, cocoa drinks are linked with whole milk, and cooking chocolate is connected to whole milk.
In this subset, lift values are above 2 for all rules, indicating significant association.
inspect(subset(rules, lift > 25))## lhs rhs support
## [1] {bottled beer, red/blush wine} => {liquor} 0.001931876
## [2] {hamburger meat, soda} => {Instant food products} 0.001220132
## confidence coverage lift count
## [1] 0.3958333 0.004880529 35.71579 19
## [2] 0.2105263 0.005795628 26.20919 12
The rule {bottled beer, red/blush wine} => {liquor} has a lift of approximately 35.72. This suggests that when customers buy bottled beer and red/blush wine together, they are significantly more likely to also purchase liquor.
In retail settings, placing related items in close proximity can encourage customers to buy complementary products, leading to increased sales.
While these rules have high lift, they might be based on a smaller number of transactions, and therefore their applicability could be limited.