Reglas de Asociación
Implementación con arules en R
Juan Manuel Fernandez
Contenidos
En esta clase vamos a trabajar con reglas de asociación en R:
- El objeto transactions: lectura, casteo y utilización.
- Generación de reglas de asociación.
- Inspección y evaluación de reglas.
- Filtrado de reglas.
Dataset para la demostración
Para los ejemplos de esta presentación vamos a utilizar el dataset Groceries del paquete arules:
library(arules)
data(Groceries)
Groceries
transactions in sparse format with
9835 transactions (rows) and
169 items (columns)
Como vemos, Groceries es de tipo transactions. La documentación de la clase está aquí:
El objeto transactions en R
La clase transactions representa transacciones utilizadas para el minado de itemsets o reglas (según documentación oficial).
inspect(head(Groceries, 3))
items
[1] {citrus fruit,
semi-finished bread,
margarine,
ready soups}
[2] {tropical fruit,
yogurt,
coffee}
[3] {whole milk}
El objeto transactions en R (++)
Podemos hacer un summary del objeto transactions:
resumen = summary(Groceries)
resumen
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 level2 level1
1 frankfurter sausage meat and sausage
2 sausage sausage meat and sausage
3 liver loaf sausage meat and sausage
El objeto transactions en R (+++)
Podemos acceder a las dimensiones del summary de a una con @:
resumen@Dim
[1] 9835 169
resumen@density
[1] 0.02609146
resumen@itemSummary
whole milk other vegetables rolls/buns soda
2513 1903 1809 1715
yogurt (Other)
1372 34055
El objeto transactions en R (+++)
Podemos acceder a las dimensiones del summary de a una con @:
resumen@lengths
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
resumen@lengthSummary
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.000 2.000 3.000 4.409 6.000 32.000
Transactions: Casteo de tipos
Podemos generar un objeto transactions a partir de una lista:
canasta <- list( c("cerveza","pañales","chocolate"),
c("cerveza","pañales"),
c("cerveza","pañales","pan"),
c("cerveza","pañales","pan","leche") )
## Equivalntee a canasta_tr = as(canasta, "transactions")
canasta_tr <- transactions(canasta)
canasta_tr
transactions in sparse format with
4 transactions (rows) and
5 items (columns)
Transactions: Casteo de tipos (++)
Resultado del casteo a partir de una lista (instrucción image(canasta_tr)):
Transactions: Casteo de tipos (+++)
Podemos generar un objeto transactions a partir de un dataframe:
a_df
age grade pass
1 6 A TRUE
2 8 C TRUE
3 <NA> F FALSE
4 9 <NA> TRUE
5 16 C TRUE
df_trans <- transactions(a_df)
Transactions: Casteo de tipos (++++)
Verificamos la transformación:
inspect(df_trans)
items transactionID
[1] {age=6,grade=A,pass} 1
[2] {age=8,grade=C,pass} 2
[3] {grade=F} 3
[4] {age=9,pass} 4
[5] {age=16,grade=C,pass} 5
También es posible generar transacciones a partir de otros tipos de datos, como por ejemplo matrices.
Transactions: Lectura de datos como transactions
La carga y casteo a transacciones para muchos datos puede volverse lento e ineficiente. Es posible cargar directamente transacciones con read.transactions().
Existen dos tipos: basket (cesta) y single (único).
Para el formato basket, cada línea del archivo representa una transacción donde cada item está separado por un caracter especificado en sep.
# Guardamos datos para formato basket
data <- paste(
"item1, item2",
"item1",
"item2, item3",
sep="\n")
write(data, file = "basket.txt")
Transactions: Formato basket
Cargamos los datos de tipo basket:
tr <- read.transactions("basket.txt", format = "basket", sep=",")
inspect(tr)
items
[1] {item1,item2}
[2] {item1}
[3] {item2,item3}
itemLabels(tr)
[1] "item1" "item2" "item3"
Transactions: Lectura de datos como transactions (single)
Para el formato single, cada línea del archivo corresponde a un item único, el cual contiene el id de la transacción.
# Guardamos datos para formato single
data <- paste(
"1;item1",
"1;item2",
"2;item1",
"3;item2",
"3;item3",
sep ="\n")
write(data, file = "single.txt")
Transactions: Formato single
Cargamos los datos de tipo single:
tr <- read.transactions("single.txt", format = "single", sep = ";", cols = c(1,2))
inspect(tr)
items transactionID
[1] {item1,item2} 1
[2] {item1} 2
[3] {item2,item3} 3
itemLabels(tr)
[1] "item1" "item2" "item3"
Generación de reglas con arules
Una vez que tenemos el objeto transactions, podemos generar las reglas:
# target vistos en clase: "frequent itemsets", "maximally frequent itemsets", "closed frequent itemsets", "rules"
reglas <- apriori(Groceries, parameter = list(support=0.01, confidence=0.01, target = "rules"))
Apriori
Parameter specification:
confidence minval smax arem aval originalSupport maxtime support minlen
0.01 0.1 1 none FALSE TRUE 5 0.01 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: 98
set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
sorting and recoding items ... [88 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 4 done [0.00s].
writing ... [610 rule(s)] done [0.00s].
creating S4 object ... done [0.00s].
Generación de reglas con arules (++)
Algunas instrucciones que podemos aplicar sobre reglas:
resumen = summary(reglas)
resumen@lengths
sizes
1 2 3
88 426 96
resumen@length
[1] 610
Generación de reglas con arules (+++)
resumen@quality
support confidence coverage lift
Min. :0.01007 Min. :0.01027 Min. :0.01729 Min. :0.7899
1st Qu.:0.01159 1st Qu.:0.08892 1st Qu.:0.05806 1st Qu.:1.1494
Median :0.01464 Median :0.15901 Median :0.10493 Median :1.4905
Mean :0.02138 Mean :0.19096 Mean :0.23668 Mean :1.5578
3rd Qu.:0.02227 3rd Qu.:0.26185 3rd Qu.:0.19349 3rd Qu.:1.8338
Max. :0.25552 Max. :0.58621 Max. :1.00000 Max. :3.3723
count
Min. : 99.0
1st Qu.: 114.0
Median : 144.0
Mean : 210.2
3rd Qu.: 219.0
Max. :2513.0
Generación de reglas con arules (++++)
resumen@info
$data
Groceries
$ntransactions
[1] 9835
$support
[1] 0.01
$confidence
[1] 0.01
Inspección de reglas generadas
Ahora debemos explotar y analizar las reglas:
inspect(reglas[1:2], )
lhs rhs support confidence coverage lift count
[1] {} => {liquor} 0.01108287 0.01108287 1 1 109
[2] {} => {condensed milk} 0.01026945 0.01026945 1 1 101
lhs: (left-hand-sides) es la parte izquierda de la regla, o antecedente.
rhs: ( right-hand-sides ) es la parte derecha de la regla, o resultado.
Support: es la frecuencia relativa de una regla sobre el total de transacciones.
Confidence: Mide cuantas veces sucede el rhs cuando se presenta el lhs, para cada regla.
Lift: es la confianza de la regla sobre el soporte del consecuente de la misma.
Filtrado de reglas generadas
También es posible ejecutar diferentes filtros sobre las reglas, por ejemplo ordenando por lift:
inspect(head(sort(reglas, by="lift", decreasing = TRUE), 3))
lhs rhs support
[1] {whole milk,yogurt} => {curd} 0.01006609
[2] {citrus fruit,other vegetables} => {root vegetables} 0.01037112
[3] {other vegetables,yogurt} => {whipped/sour cream} 0.01016777
confidence coverage lift count
[1] 0.1796733 0.05602440 3.372304 99
[2] 0.3591549 0.02887646 3.295045 102
[3] 0.2341920 0.04341637 3.267062 100
Filtrado de reglas generadas (++)
Con subset, podemos filtrar por cualquiera de los campos que aparecen en las reglas. Con %in% buscamos un producto en concreto.
Por ejemplo, buscamos las que poseen como antecedente -lhs- a la cerveza (bottled beer):
rules.sub <- subset(reglas, subset = lhs %in% "bottled beer")
inspect(rules.sub)
lhs rhs support confidence coverage
[1] {bottled beer} => {bottled water} 0.01576004 0.1957071 0.08052872
[2] {bottled beer} => {soda} 0.01698017 0.2108586 0.08052872
[3] {bottled beer} => {rolls/buns} 0.01362481 0.1691919 0.08052872
[4] {bottled beer} => {other vegetables} 0.01616675 0.2007576 0.08052872
[5] {bottled beer} => {whole milk} 0.02043721 0.2537879 0.08052872
lift count
[1] 1.7707259 155
[2] 1.2092094 167
[3] 0.9198466 134
[4] 1.0375464 159
[5] 0.9932367 201
Filtrado de reglas generadas (+++)
Además, con %pin% podemos buscar en el texto un producto que contenga determinado texto (beer):
rules.sub <- subset(reglas, subset = lhs %pin% "beer")
inspect(rules.sub)
lhs rhs support confidence coverage
[1] {canned beer} => {shopping bags} 0.01138790 0.1465969 0.07768175
[2] {canned beer} => {soda} 0.01382816 0.1780105 0.07768175
[3] {canned beer} => {rolls/buns} 0.01128622 0.1452880 0.07768175
[4] {bottled beer} => {bottled water} 0.01576004 0.1957071 0.08052872
[5] {bottled beer} => {soda} 0.01698017 0.2108586 0.08052872
[6] {bottled beer} => {rolls/buns} 0.01362481 0.1691919 0.08052872
[7] {bottled beer} => {other vegetables} 0.01616675 0.2007576 0.08052872
[8] {bottled beer} => {whole milk} 0.02043721 0.2537879 0.08052872
lift count
[1] 1.4879052 112
[2] 1.0208356 136
[3] 0.7898878 111
[4] 1.7707259 155
[5] 1.2092094 167
[6] 0.9198466 134
[7] 1.0375464 159
[8] 0.9932367 201
Filtrado de reglas generadas (++++)
También podríamos filtrar por el tamaño del antecedente::
rules.sub <- subset(reglas, subset = size(lhs)==1)
inspect(rules.sub)
lhs rhs support
[1] {hard cheese} => {whole milk} 0.01006609
[2] {whole milk} => {hard cheese} 0.01006609
[3] {butter milk} => {other vegetables} 0.01037112
[4] {other vegetables} => {butter milk} 0.01037112
[5] {butter milk} => {whole milk} 0.01159126
[6] {whole milk} => {butter milk} 0.01159126
[7] {ham} => {whole milk} 0.01148958
[8] {whole milk} => {ham} 0.01148958
[9] {sliced cheese} => {whole milk} 0.01077783
[10] {whole milk} => {sliced cheese} 0.01077783
[11] {oil} => {whole milk} 0.01128622
[12] {whole milk} => {oil} 0.01128622
[13] {onions} => {other vegetables} 0.01423488
[14] {other vegetables} => {onions} 0.01423488
[15] {onions} => {whole milk} 0.01209964
[16] {whole milk} => {onions} 0.01209964
[17] {berries} => {yogurt} 0.01057448
[18] {yogurt} => {berries} 0.01057448
[19] {berries} => {other vegetables} 0.01026945
[20] {other vegetables} => {berries} 0.01026945
[21] {berries} => {whole milk} 0.01179461
[22] {whole milk} => {berries} 0.01179461
[23] {hamburger meat} => {other vegetables} 0.01382816
[24] {other vegetables} => {hamburger meat} 0.01382816
[25] {hamburger meat} => {whole milk} 0.01474326
[26] {whole milk} => {hamburger meat} 0.01474326
[27] {hygiene articles} => {whole milk} 0.01281139
[28] {whole milk} => {hygiene articles} 0.01281139
[29] {salty snack} => {other vegetables} 0.01077783
[30] {other vegetables} => {salty snack} 0.01077783
[31] {salty snack} => {whole milk} 0.01118454
[32] {whole milk} => {salty snack} 0.01118454
[33] {sugar} => {other vegetables} 0.01077783
[34] {other vegetables} => {sugar} 0.01077783
[35] {sugar} => {whole milk} 0.01504830
[36] {whole milk} => {sugar} 0.01504830
[37] {waffles} => {other vegetables} 0.01006609
[38] {other vegetables} => {waffles} 0.01006609
[39] {waffles} => {whole milk} 0.01270971
[40] {whole milk} => {waffles} 0.01270971
[41] {long life bakery product} => {other vegetables} 0.01067616
[42] {other vegetables} => {long life bakery product} 0.01067616
[43] {long life bakery product} => {whole milk} 0.01352313
[44] {whole milk} => {long life bakery product} 0.01352313
[45] {dessert} => {other vegetables} 0.01159126
[46] {other vegetables} => {dessert} 0.01159126
[47] {dessert} => {whole milk} 0.01372649
[48] {whole milk} => {dessert} 0.01372649
[49] {canned beer} => {shopping bags} 0.01138790
[50] {shopping bags} => {canned beer} 0.01138790
[51] {canned beer} => {soda} 0.01382816
[52] {soda} => {canned beer} 0.01382816
[53] {canned beer} => {rolls/buns} 0.01128622
[54] {rolls/buns} => {canned beer} 0.01128622
[55] {cream cheese } => {yogurt} 0.01240468
[56] {yogurt} => {cream cheese } 0.01240468
[57] {cream cheese } => {other vegetables} 0.01372649
[58] {other vegetables} => {cream cheese } 0.01372649
[59] {cream cheese } => {whole milk} 0.01647178
[60] {whole milk} => {cream cheese } 0.01647178
[61] {chicken} => {root vegetables} 0.01087951
[62] {root vegetables} => {chicken} 0.01087951
[63] {chicken} => {other vegetables} 0.01789527
[64] {other vegetables} => {chicken} 0.01789527
[65] {chicken} => {whole milk} 0.01759024
[66] {whole milk} => {chicken} 0.01759024
[67] {white bread} => {soda} 0.01026945
[68] {soda} => {white bread} 0.01026945
[69] {white bread} => {other vegetables} 0.01372649
[70] {other vegetables} => {white bread} 0.01372649
[71] {white bread} => {whole milk} 0.01708185
[72] {whole milk} => {white bread} 0.01708185
[73] {chocolate} => {soda} 0.01352313
[74] {soda} => {chocolate} 0.01352313
[75] {chocolate} => {rolls/buns} 0.01179461
[76] {rolls/buns} => {chocolate} 0.01179461
[77] {chocolate} => {other vegetables} 0.01270971
[78] {other vegetables} => {chocolate} 0.01270971
[79] {chocolate} => {whole milk} 0.01667514
[80] {whole milk} => {chocolate} 0.01667514
[81] {coffee} => {rolls/buns} 0.01098119
[82] {rolls/buns} => {coffee} 0.01098119
[83] {coffee} => {other vegetables} 0.01342145
[84] {other vegetables} => {coffee} 0.01342145
[85] {coffee} => {whole milk} 0.01870869
[86] {whole milk} => {coffee} 0.01870869
[87] {frozen vegetables} => {root vegetables} 0.01159126
[88] {root vegetables} => {frozen vegetables} 0.01159126
[89] {frozen vegetables} => {yogurt} 0.01240468
[90] {yogurt} => {frozen vegetables} 0.01240468
[91] {frozen vegetables} => {rolls/buns} 0.01016777
[92] {rolls/buns} => {frozen vegetables} 0.01016777
[93] {frozen vegetables} => {other vegetables} 0.01779359
[94] {other vegetables} => {frozen vegetables} 0.01779359
[95] {frozen vegetables} => {whole milk} 0.02043721
[96] {whole milk} => {frozen vegetables} 0.02043721
[97] {beef} => {root vegetables} 0.01738688
[98] {root vegetables} => {beef} 0.01738688
[99] {beef} => {yogurt} 0.01169293
[100] {yogurt} => {beef} 0.01169293
[101] {beef} => {rolls/buns} 0.01362481
[102] {rolls/buns} => {beef} 0.01362481
[103] {beef} => {other vegetables} 0.01972547
[104] {other vegetables} => {beef} 0.01972547
[105] {beef} => {whole milk} 0.02125064
[106] {whole milk} => {beef} 0.02125064
[107] {curd} => {whipped/sour cream} 0.01047280
[108] {whipped/sour cream} => {curd} 0.01047280
[109] {curd} => {tropical fruit} 0.01026945
[110] {tropical fruit} => {curd} 0.01026945
[111] {curd} => {root vegetables} 0.01087951
[112] {root vegetables} => {curd} 0.01087951
[113] {curd} => {yogurt} 0.01728521
[114] {yogurt} => {curd} 0.01728521
[115] {curd} => {rolls/buns} 0.01006609
[116] {rolls/buns} => {curd} 0.01006609
[117] {curd} => {other vegetables} 0.01718353
[118] {other vegetables} => {curd} 0.01718353
[119] {curd} => {whole milk} 0.02613116
[120] {whole milk} => {curd} 0.02613116
[121] {napkins} => {tropical fruit} 0.01006609
[122] {tropical fruit} => {napkins} 0.01006609
[123] {napkins} => {soda} 0.01199797
[124] {soda} => {napkins} 0.01199797
[125] {napkins} => {yogurt} 0.01230300
[126] {yogurt} => {napkins} 0.01230300
[127] {napkins} => {rolls/buns} 0.01169293
[128] {rolls/buns} => {napkins} 0.01169293
[129] {napkins} => {other vegetables} 0.01443823
[130] {other vegetables} => {napkins} 0.01443823
[131] {napkins} => {whole milk} 0.01972547
[132] {whole milk} => {napkins} 0.01972547
[133] {pork} => {root vegetables} 0.01362481
[134] {root vegetables} => {pork} 0.01362481
[135] {pork} => {soda} 0.01189629
[136] {soda} => {pork} 0.01189629
[137] {pork} => {rolls/buns} 0.01128622
[138] {rolls/buns} => {pork} 0.01128622
[139] {pork} => {other vegetables} 0.02165735
[140] {other vegetables} => {pork} 0.02165735
[141] {pork} => {whole milk} 0.02216573
[142] {whole milk} => {pork} 0.02216573
[143] {frankfurter} => {sausage} 0.01006609
[144] {sausage} => {frankfurter} 0.01006609
[145] {frankfurter} => {root vegetables} 0.01016777
[146] {root vegetables} => {frankfurter} 0.01016777
[147] {frankfurter} => {soda} 0.01128622
[148] {soda} => {frankfurter} 0.01128622
[149] {frankfurter} => {yogurt} 0.01118454
[150] {yogurt} => {frankfurter} 0.01118454
[151] {frankfurter} => {rolls/buns} 0.01921708
[152] {rolls/buns} => {frankfurter} 0.01921708
[153] {frankfurter} => {other vegetables} 0.01647178
[154] {other vegetables} => {frankfurter} 0.01647178
[155] {frankfurter} => {whole milk} 0.02053889
[156] {whole milk} => {frankfurter} 0.02053889
[157] {bottled beer} => {bottled water} 0.01576004
[158] {bottled water} => {bottled beer} 0.01576004
[159] {bottled beer} => {soda} 0.01698017
[160] {soda} => {bottled beer} 0.01698017
[161] {bottled beer} => {rolls/buns} 0.01362481
[162] {rolls/buns} => {bottled beer} 0.01362481
[163] {bottled beer} => {other vegetables} 0.01616675
[164] {other vegetables} => {bottled beer} 0.01616675
[165] {bottled beer} => {whole milk} 0.02043721
[166] {whole milk} => {bottled beer} 0.02043721
[167] {brown bread} => {sausage} 0.01067616
[168] {sausage} => {brown bread} 0.01067616
[169] {brown bread} => {tropical fruit} 0.01067616
[170] {tropical fruit} => {brown bread} 0.01067616
[171] {brown bread} => {root vegetables} 0.01016777
[172] {root vegetables} => {brown bread} 0.01016777
[173] {brown bread} => {soda} 0.01260803
[174] {soda} => {brown bread} 0.01260803
[175] {brown bread} => {yogurt} 0.01453991
[176] {yogurt} => {brown bread} 0.01453991
[177] {brown bread} => {rolls/buns} 0.01260803
[178] {rolls/buns} => {brown bread} 0.01260803
[179] {brown bread} => {other vegetables} 0.01870869
[180] {other vegetables} => {brown bread} 0.01870869
[181] {brown bread} => {whole milk} 0.02521607
[182] {whole milk} => {brown bread} 0.02521607
[183] {margarine} => {bottled water} 0.01026945
[184] {bottled water} => {margarine} 0.01026945
[185] {margarine} => {root vegetables} 0.01108287
[186] {root vegetables} => {margarine} 0.01108287
[187] {margarine} => {soda} 0.01016777
[188] {soda} => {margarine} 0.01016777
[189] {margarine} => {yogurt} 0.01423488
[190] {yogurt} => {margarine} 0.01423488
[191] {margarine} => {rolls/buns} 0.01474326
[192] {rolls/buns} => {margarine} 0.01474326
[193] {margarine} => {other vegetables} 0.01972547
[194] {other vegetables} => {margarine} 0.01972547
[195] {margarine} => {whole milk} 0.02419929
[196] {whole milk} => {margarine} 0.02419929
[197] {butter} => {whipped/sour cream} 0.01016777
[198] {whipped/sour cream} => {butter} 0.01016777
[199] {butter} => {root vegetables} 0.01291307
[200] {root vegetables} => {butter} 0.01291307
[201] {butter} => {yogurt} 0.01464159
[202] {yogurt} => {butter} 0.01464159
[203] {butter} => {rolls/buns} 0.01342145
[204] {rolls/buns} => {butter} 0.01342145
[205] {butter} => {other vegetables} 0.02003050
[206] {other vegetables} => {butter} 0.02003050
[207] {butter} => {whole milk} 0.02755465
[208] {whole milk} => {butter} 0.02755465
[209] {newspapers} => {bottled water} 0.01128622
[210] {bottled water} => {newspapers} 0.01128622
[211] {newspapers} => {tropical fruit} 0.01179461
[212] {tropical fruit} => {newspapers} 0.01179461
[213] {newspapers} => {root vegetables} 0.01148958
[214] {root vegetables} => {newspapers} 0.01148958
[215] {newspapers} => {soda} 0.01464159
[216] {soda} => {newspapers} 0.01464159
[217] {newspapers} => {yogurt} 0.01535333
[218] {yogurt} => {newspapers} 0.01535333
[219] {newspapers} => {rolls/buns} 0.01972547
[220] {rolls/buns} => {newspapers} 0.01972547
[221] {newspapers} => {other vegetables} 0.01931876
[222] {other vegetables} => {newspapers} 0.01931876
[223] {newspapers} => {whole milk} 0.02735130
[224] {whole milk} => {newspapers} 0.02735130
[225] {domestic eggs} => {citrus fruit} 0.01037112
[226] {citrus fruit} => {domestic eggs} 0.01037112
[227] {domestic eggs} => {tropical fruit} 0.01138790
[228] {tropical fruit} => {domestic eggs} 0.01138790
[229] {domestic eggs} => {root vegetables} 0.01433655
[230] {root vegetables} => {domestic eggs} 0.01433655
[231] {domestic eggs} => {soda} 0.01240468
[232] {soda} => {domestic eggs} 0.01240468
[233] {domestic eggs} => {yogurt} 0.01433655
[234] {yogurt} => {domestic eggs} 0.01433655
[235] {domestic eggs} => {rolls/buns} 0.01565836
[236] {rolls/buns} => {domestic eggs} 0.01565836
[237] {domestic eggs} => {other vegetables} 0.02226741
[238] {other vegetables} => {domestic eggs} 0.02226741
[239] {domestic eggs} => {whole milk} 0.02999492
[240] {whole milk} => {domestic eggs} 0.02999492
[241] {fruit/vegetable juice} => {citrus fruit} 0.01037112
[242] {citrus fruit} => {fruit/vegetable juice} 0.01037112
[243] {fruit/vegetable juice} => {shopping bags} 0.01067616
[244] {shopping bags} => {fruit/vegetable juice} 0.01067616
[245] {fruit/vegetable juice} => {sausage} 0.01006609
[246] {sausage} => {fruit/vegetable juice} 0.01006609
[247] {fruit/vegetable juice} => {bottled water} 0.01423488
[248] {bottled water} => {fruit/vegetable juice} 0.01423488
[249] {fruit/vegetable juice} => {tropical fruit} 0.01372649
[250] {tropical fruit} => {fruit/vegetable juice} 0.01372649
[251] {fruit/vegetable juice} => {root vegetables} 0.01199797
[252] {root vegetables} => {fruit/vegetable juice} 0.01199797
[253] {fruit/vegetable juice} => {soda} 0.01840366
[254] {soda} => {fruit/vegetable juice} 0.01840366
[255] {fruit/vegetable juice} => {yogurt} 0.01870869
[256] {yogurt} => {fruit/vegetable juice} 0.01870869
[257] {fruit/vegetable juice} => {rolls/buns} 0.01453991
[258] {rolls/buns} => {fruit/vegetable juice} 0.01453991
[259] {fruit/vegetable juice} => {other vegetables} 0.02104728
[260] {other vegetables} => {fruit/vegetable juice} 0.02104728
[261] {fruit/vegetable juice} => {whole milk} 0.02663955
[262] {whole milk} => {fruit/vegetable juice} 0.02663955
[263] {whipped/sour cream} => {citrus fruit} 0.01087951
[264] {citrus fruit} => {whipped/sour cream} 0.01087951
[265] {whipped/sour cream} => {tropical fruit} 0.01382816
[266] {tropical fruit} => {whipped/sour cream} 0.01382816
[267] {whipped/sour cream} => {root vegetables} 0.01708185
[268] {root vegetables} => {whipped/sour cream} 0.01708185
[269] {whipped/sour cream} => {soda} 0.01159126
[270] {soda} => {whipped/sour cream} 0.01159126
[271] {whipped/sour cream} => {yogurt} 0.02074225
[272] {yogurt} => {whipped/sour cream} 0.02074225
[273] {whipped/sour cream} => {rolls/buns} 0.01464159
[274] {rolls/buns} => {whipped/sour cream} 0.01464159
[275] {whipped/sour cream} => {other vegetables} 0.02887646
[276] {other vegetables} => {whipped/sour cream} 0.02887646
[277] {whipped/sour cream} => {whole milk} 0.03223183
[278] {whole milk} => {whipped/sour cream} 0.03223183
[279] {pip fruit} => {pastry} 0.01067616
[280] {pastry} => {pip fruit} 0.01067616
[281] {pip fruit} => {citrus fruit} 0.01382816
[282] {citrus fruit} => {pip fruit} 0.01382816
[283] {pip fruit} => {sausage} 0.01077783
[284] {sausage} => {pip fruit} 0.01077783
[285] {pip fruit} => {bottled water} 0.01057448
[286] {bottled water} => {pip fruit} 0.01057448
[287] {pip fruit} => {tropical fruit} 0.02043721
[288] {tropical fruit} => {pip fruit} 0.02043721
[289] {pip fruit} => {root vegetables} 0.01555669
[290] {root vegetables} => {pip fruit} 0.01555669
[291] {pip fruit} => {soda} 0.01331978
[292] {soda} => {pip fruit} 0.01331978
[293] {pip fruit} => {yogurt} 0.01799695
[294] {yogurt} => {pip fruit} 0.01799695
[295] {pip fruit} => {rolls/buns} 0.01392984
[296] {rolls/buns} => {pip fruit} 0.01392984
[297] {pip fruit} => {other vegetables} 0.02613116
[298] {other vegetables} => {pip fruit} 0.02613116
[299] {pip fruit} => {whole milk} 0.03009659
[300] {whole milk} => {pip fruit} 0.03009659
[301] {pastry} => {shopping bags} 0.01189629
[302] {shopping bags} => {pastry} 0.01189629
[303] {pastry} => {sausage} 0.01250635
[304] {sausage} => {pastry} 0.01250635
[305] {pastry} => {tropical fruit} 0.01321810
[306] {tropical fruit} => {pastry} 0.01321810
[307] {pastry} => {root vegetables} 0.01098119
[308] {root vegetables} => {pastry} 0.01098119
[309] {pastry} => {soda} 0.02104728
[310] {soda} => {pastry} 0.02104728
[311] {pastry} => {yogurt} 0.01769192
[312] {yogurt} => {pastry} 0.01769192
[313] {pastry} => {rolls/buns} 0.02094560
[314] {rolls/buns} => {pastry} 0.02094560
[315] {pastry} => {other vegetables} 0.02257245
[316] {other vegetables} => {pastry} 0.02257245
[317] {pastry} => {whole milk} 0.03324860
[318] {whole milk} => {pastry} 0.03324860
[319] {citrus fruit} => {sausage} 0.01128622
[320] {sausage} => {citrus fruit} 0.01128622
[321] {citrus fruit} => {bottled water} 0.01352313
[322] {bottled water} => {citrus fruit} 0.01352313
[323] {citrus fruit} => {tropical fruit} 0.01992883
[324] {tropical fruit} => {citrus fruit} 0.01992883
[325] {citrus fruit} => {root vegetables} 0.01769192
[326] {root vegetables} => {citrus fruit} 0.01769192
[327] {citrus fruit} => {soda} 0.01281139
[328] {soda} => {citrus fruit} 0.01281139
[329] {citrus fruit} => {yogurt} 0.02165735
[330] {yogurt} => {citrus fruit} 0.02165735
[331] {citrus fruit} => {rolls/buns} 0.01677682
[332] {rolls/buns} => {citrus fruit} 0.01677682
[333] {citrus fruit} => {other vegetables} 0.02887646
[334] {other vegetables} => {citrus fruit} 0.02887646
[335] {citrus fruit} => {whole milk} 0.03050330
[336] {whole milk} => {citrus fruit} 0.03050330
[337] {shopping bags} => {sausage} 0.01565836
[338] {sausage} => {shopping bags} 0.01565836
[339] {shopping bags} => {bottled water} 0.01098119
[340] {bottled water} => {shopping bags} 0.01098119
[341] {shopping bags} => {tropical fruit} 0.01352313
[342] {tropical fruit} => {shopping bags} 0.01352313
[343] {shopping bags} => {root vegetables} 0.01281139
[344] {root vegetables} => {shopping bags} 0.01281139
[345] {shopping bags} => {soda} 0.02460600
[346] {soda} => {shopping bags} 0.02460600
[347] {shopping bags} => {yogurt} 0.01525165
[348] {yogurt} => {shopping bags} 0.01525165
[349] {shopping bags} => {rolls/buns} 0.01952211
[350] {rolls/buns} => {shopping bags} 0.01952211
[351] {shopping bags} => {other vegetables} 0.02318251
[352] {other vegetables} => {shopping bags} 0.02318251
[353] {shopping bags} => {whole milk} 0.02450432
[354] {whole milk} => {shopping bags} 0.02450432
[355] {sausage} => {bottled water} 0.01199797
[356] {bottled water} => {sausage} 0.01199797
[357] {sausage} => {tropical fruit} 0.01392984
[358] {tropical fruit} => {sausage} 0.01392984
[359] {sausage} => {root vegetables} 0.01494662
[360] {root vegetables} => {sausage} 0.01494662
[361] {sausage} => {soda} 0.02430097
[362] {soda} => {sausage} 0.02430097
[363] {sausage} => {yogurt} 0.01962379
[364] {yogurt} => {sausage} 0.01962379
[365] {sausage} => {rolls/buns} 0.03060498
[366] {rolls/buns} => {sausage} 0.03060498
[367] {sausage} => {other vegetables} 0.02694459
[368] {other vegetables} => {sausage} 0.02694459
[369] {sausage} => {whole milk} 0.02989324
[370] {whole milk} => {sausage} 0.02989324
[371] {bottled water} => {tropical fruit} 0.01850534
[372] {tropical fruit} => {bottled water} 0.01850534
[373] {bottled water} => {root vegetables} 0.01565836
[374] {root vegetables} => {bottled water} 0.01565836
[375] {bottled water} => {soda} 0.02897814
[376] {soda} => {bottled water} 0.02897814
[377] {bottled water} => {yogurt} 0.02297916
[378] {yogurt} => {bottled water} 0.02297916
[379] {bottled water} => {rolls/buns} 0.02419929
[380] {rolls/buns} => {bottled water} 0.02419929
[381] {bottled water} => {other vegetables} 0.02480935
[382] {other vegetables} => {bottled water} 0.02480935
[383] {bottled water} => {whole milk} 0.03436706
[384] {whole milk} => {bottled water} 0.03436706
[385] {tropical fruit} => {root vegetables} 0.02104728
[386] {root vegetables} => {tropical fruit} 0.02104728
[387] {tropical fruit} => {soda} 0.02084392
[388] {soda} => {tropical fruit} 0.02084392
[389] {tropical fruit} => {yogurt} 0.02928317
[390] {yogurt} => {tropical fruit} 0.02928317
[391] {tropical fruit} => {rolls/buns} 0.02460600
[392] {rolls/buns} => {tropical fruit} 0.02460600
[393] {tropical fruit} => {other vegetables} 0.03589222
[394] {other vegetables} => {tropical fruit} 0.03589222
[395] {tropical fruit} => {whole milk} 0.04229792
[396] {whole milk} => {tropical fruit} 0.04229792
[397] {root vegetables} => {soda} 0.01860702
[398] {soda} => {root vegetables} 0.01860702
[399] {root vegetables} => {yogurt} 0.02582613
[400] {yogurt} => {root vegetables} 0.02582613
[401] {root vegetables} => {rolls/buns} 0.02430097
[402] {rolls/buns} => {root vegetables} 0.02430097
[403] {root vegetables} => {other vegetables} 0.04738180
[404] {other vegetables} => {root vegetables} 0.04738180
[405] {root vegetables} => {whole milk} 0.04890696
[406] {whole milk} => {root vegetables} 0.04890696
[407] {soda} => {yogurt} 0.02735130
[408] {yogurt} => {soda} 0.02735130
[409] {soda} => {rolls/buns} 0.03833249
[410] {rolls/buns} => {soda} 0.03833249
[411] {soda} => {other vegetables} 0.03274021
[412] {other vegetables} => {soda} 0.03274021
[413] {soda} => {whole milk} 0.04006101
[414] {whole milk} => {soda} 0.04006101
[415] {yogurt} => {rolls/buns} 0.03436706
[416] {rolls/buns} => {yogurt} 0.03436706
[417] {yogurt} => {other vegetables} 0.04341637
[418] {other vegetables} => {yogurt} 0.04341637
[419] {yogurt} => {whole milk} 0.05602440
[420] {whole milk} => {yogurt} 0.05602440
[421] {rolls/buns} => {other vegetables} 0.04260295
[422] {other vegetables} => {rolls/buns} 0.04260295
[423] {rolls/buns} => {whole milk} 0.05663447
[424] {whole milk} => {rolls/buns} 0.05663447
[425] {other vegetables} => {whole milk} 0.07483477
[426] {whole milk} => {other vegetables} 0.07483477
confidence coverage lift count
[1] 0.41078838 0.02450432 1.6076815 99
[2] 0.03939515 0.25551601 1.6076815 99
[3] 0.37090909 0.02796136 1.9169159 102
[4] 0.05359958 0.19349263 1.9169159 102
[5] 0.41454545 0.02796136 1.6223854 114
[6] 0.04536411 0.25551601 1.6223854 114
[7] 0.44140625 0.02602949 1.7275091 113
[8] 0.04496618 0.25551601 1.7275091 113
[9] 0.43983402 0.02450432 1.7213560 106
[10] 0.04218066 0.25551601 1.7213560 106
[11] 0.40217391 0.02806304 1.5739675 111
[12] 0.04417031 0.25551601 1.5739675 111
[13] 0.45901639 0.03101169 2.3722681 140
[14] 0.07356805 0.19349263 2.3722681 140
[15] 0.39016393 0.03101169 1.5269647 119
[16] 0.04735376 0.25551601 1.5269647 119
[17] 0.31804281 0.03324860 2.2798477 104
[18] 0.07580175 0.13950178 2.2798477 104
[19] 0.30886850 0.03324860 1.5962805 101
[20] 0.05307409 0.19349263 1.5962805 101
[21] 0.35474006 0.03324860 1.3883281 116
[22] 0.04615997 0.25551601 1.3883281 116
[23] 0.41590214 0.03324860 2.1494470 136
[24] 0.07146611 0.19349263 2.1494470 136
[25] 0.44342508 0.03324860 1.7354101 145
[26] 0.05769996 0.25551601 1.7354101 145
[27] 0.38888889 0.03294357 1.5219746 126
[28] 0.05013928 0.25551601 1.5219746 126
[29] 0.28494624 0.03782410 1.4726465 106
[30] 0.05570152 0.19349263 1.4726465 106
[31] 0.29569892 0.03782410 1.1572618 110
[32] 0.04377238 0.25551601 1.1572618 110
[33] 0.31831832 0.03385867 1.6451186 106
[34] 0.05570152 0.19349263 1.6451186 106
[35] 0.44444444 0.03385867 1.7393996 148
[36] 0.05889375 0.25551601 1.7393996 148
[37] 0.26190476 0.03843416 1.3535645 99
[38] 0.05202312 0.19349263 1.3535645 99
[39] 0.33068783 0.03843416 1.2941961 125
[40] 0.04974135 0.25551601 1.2941961 125
[41] 0.28532609 0.03741739 1.4746096 105
[42] 0.05517604 0.19349263 1.4746096 105
[43] 0.36141304 0.03741739 1.4144438 133
[44] 0.05292479 0.25551601 1.4144438 133
[45] 0.31232877 0.03711235 1.6141636 114
[46] 0.05990541 0.19349263 1.6141636 114
[47] 0.36986301 0.03711235 1.4475140 135
[48] 0.05372065 0.25551601 1.4475140 135
[49] 0.14659686 0.07768175 1.4879052 112
[50] 0.11558308 0.09852567 1.4879052 112
[51] 0.17801047 0.07768175 1.0208356 136
[52] 0.07930029 0.17437722 1.0208356 136
[53] 0.14528796 0.07768175 0.7898878 111
[54] 0.06135987 0.18393493 0.7898878 111
[55] 0.31282051 0.03965430 2.2424123 122
[56] 0.08892128 0.13950178 2.2424123 122
[57] 0.34615385 0.03965430 1.7889769 135
[58] 0.07094062 0.19349263 1.7889769 135
[59] 0.41538462 0.03965430 1.6256696 162
[60] 0.06446478 0.25551601 1.6256696 162
[61] 0.25355450 0.04290798 2.3262206 107
[62] 0.09981343 0.10899847 2.3262206 107
[63] 0.41706161 0.04290798 2.1554393 176
[64] 0.09248555 0.19349263 2.1554393 176
[65] 0.40995261 0.04290798 1.6044106 173
[66] 0.06884202 0.25551601 1.6044106 173
[67] 0.24396135 0.04209456 1.3990437 101
[68] 0.05889213 0.17437722 1.3990437 101
[69] 0.32608696 0.04209456 1.6852681 135
[70] 0.07094062 0.19349263 1.6852681 135
[71] 0.40579710 0.04209456 1.5881474 168
[72] 0.06685237 0.25551601 1.5881474 168
[73] 0.27254098 0.04961871 1.5629391 133
[74] 0.07755102 0.17437722 1.5629391 133
[75] 0.23770492 0.04961871 1.2923316 116
[76] 0.06412383 0.18393493 1.2923316 116
[77] 0.25614754 0.04961871 1.3238103 125
[78] 0.06568576 0.19349263 1.3238103 125
[79] 0.33606557 0.04961871 1.3152427 164
[80] 0.06526064 0.25551601 1.3152427 164
[81] 0.18914186 0.05805796 1.0283085 108
[82] 0.05970149 0.18393493 1.0283085 108
[83] 0.23117338 0.05805796 1.1947400 132
[84] 0.06936416 0.19349263 1.1947400 132
[85] 0.32224168 0.05805796 1.2611408 184
[86] 0.07321926 0.25551601 1.2611408 184
[87] 0.24101480 0.04809354 2.2111759 114
[88] 0.10634328 0.10899847 2.2111759 114
[89] 0.25792812 0.04809354 1.8489235 122
[90] 0.08892128 0.13950178 1.8489235 122
[91] 0.21141649 0.04809354 1.1494092 100
[92] 0.05527916 0.18393493 1.1494092 100
[93] 0.36997886 0.04809354 1.9121083 175
[94] 0.09196006 0.19349263 1.9121083 175
[95] 0.42494715 0.04809354 1.6630940 201
[96] 0.07998408 0.25551601 1.6630940 201
[97] 0.33139535 0.05246568 3.0403668 171
[98] 0.15951493 0.10899847 3.0403668 171
[99] 0.22286822 0.05246568 1.5976012 115
[100] 0.08381924 0.13950178 1.5976012 115
[101] 0.25968992 0.05246568 1.4118576 134
[102] 0.07407407 0.18393493 1.4118576 134
[103] 0.37596899 0.05246568 1.9430662 194
[104] 0.10194430 0.19349263 1.9430662 194
[105] 0.40503876 0.05246568 1.5851795 209
[106] 0.08316753 0.25551601 1.5851795 209
[107] 0.19656489 0.05327911 2.7421499 103
[108] 0.14609929 0.07168277 2.7421499 103
[109] 0.19274809 0.05327911 1.8368968 101
[110] 0.09786822 0.10493137 1.8368968 101
[111] 0.20419847 0.05327911 1.8734067 107
[112] 0.09981343 0.10899847 1.8734067 107
[113] 0.32442748 0.05327911 2.3256154 170
[114] 0.12390671 0.13950178 2.3256154 170
[115] 0.18893130 0.05327911 1.0271638 99
[116] 0.05472637 0.18393493 1.0271638 99
[117] 0.32251908 0.05327911 1.6668288 169
[118] 0.08880715 0.19349263 1.6668288 169
[119] 0.49045802 0.05327911 1.9194805 257
[120] 0.10226821 0.25551601 1.9194805 257
[121] 0.19223301 0.05236401 1.8319880 99
[122] 0.09593023 0.10493137 1.8319880 99
[123] 0.22912621 0.05236401 1.3139687 118
[124] 0.06880466 0.17437722 1.3139687 118
[125] 0.23495146 0.05236401 1.6842183 121
[126] 0.08819242 0.13950178 1.6842183 121
[127] 0.22330097 0.05236401 1.2140216 115
[128] 0.06357103 0.18393493 1.2140216 115
[129] 0.27572816 0.05236401 1.4250060 142
[130] 0.07461902 0.19349263 1.4250060 142
[131] 0.37669903 0.05236401 1.4742678 194
[132] 0.07719857 0.25551601 1.4742678 194
[133] 0.23633157 0.05765125 2.1682099 134
[134] 0.12500000 0.10899847 2.1682099 134
[135] 0.20634921 0.05765125 1.1833495 117
[136] 0.06822157 0.17437722 1.1833495 117
[137] 0.19576720 0.05765125 1.0643286 111
[138] 0.06135987 0.18393493 1.0643286 111
[139] 0.37566138 0.05765125 1.9414764 213
[140] 0.11192853 0.19349263 1.9414764 213
[141] 0.38447972 0.05765125 1.5047187 218
[142] 0.08674891 0.25551601 1.5047187 218
[143] 0.17068966 0.05897306 1.8168103 99
[144] 0.10714286 0.09395018 1.8168103 99
[145] 0.17241379 0.05897306 1.5818001 100
[146] 0.09328358 0.10899847 1.5818001 100
[147] 0.19137931 0.05897306 1.0975018 111
[148] 0.06472303 0.17437722 1.0975018 111
[149] 0.18965517 0.05897306 1.3595179 110
[150] 0.08017493 0.13950178 1.3595179 110
[151] 0.32586207 0.05897306 1.7716161 189
[152] 0.10447761 0.18393493 1.7716161 189
[153] 0.27931034 0.05897306 1.4435193 162
[154] 0.08512874 0.19349263 1.4435193 162
[155] 0.34827586 0.05897306 1.3630295 202
[156] 0.08038201 0.25551601 1.3630295 202
[157] 0.19570707 0.08052872 1.7707259 155
[158] 0.14259430 0.11052364 1.7707259 155
[159] 0.21085859 0.08052872 1.2092094 167
[160] 0.09737609 0.17437722 1.2092094 167
[161] 0.16919192 0.08052872 0.9198466 134
[162] 0.07407407 0.18393493 0.9198466 134
[163] 0.20075758 0.08052872 1.0375464 159
[164] 0.08355229 0.19349263 1.0375464 159
[165] 0.25378788 0.08052872 0.9932367 201
[166] 0.07998408 0.25551601 0.9932367 201
[167] 0.16457680 0.06487036 1.7517455 105
[168] 0.11363636 0.09395018 1.7517455 105
[169] 0.16457680 0.06487036 1.5684233 105
[170] 0.10174419 0.10493137 1.5684233 105
[171] 0.15673981 0.06487036 1.4380000 100
[172] 0.09328358 0.10899847 1.4380000 100
[173] 0.19435737 0.06487036 1.1145800 124
[174] 0.07230321 0.17437722 1.1145800 124
[175] 0.22413793 0.06487036 1.6067030 143
[176] 0.10422741 0.13950178 1.6067030 143
[177] 0.19435737 0.06487036 1.0566637 124
[178] 0.06854616 0.18393493 1.0566637 124
[179] 0.28840125 0.06487036 1.4905025 184
[180] 0.09668944 0.19349263 1.4905025 184
[181] 0.38871473 0.06487036 1.5212930 248
[182] 0.09868683 0.25551601 1.5212930 248
[183] 0.17534722 0.05856634 1.5865133 101
[184] 0.09291628 0.11052364 1.5865133 101
[185] 0.18923611 0.05856634 1.7361354 109
[186] 0.10167910 0.10899847 1.7361354 109
[187] 0.17361111 0.05856634 0.9956066 100
[188] 0.05830904 0.17437722 0.9956066 100
[189] 0.24305556 0.05856634 1.7423115 140
[190] 0.10204082 0.13950178 1.7423115 140
[191] 0.25173611 0.05856634 1.3686151 145
[192] 0.08015478 0.18393493 1.3686151 145
[193] 0.33680556 0.05856634 1.7406635 194
[194] 0.10194430 0.19349263 1.7406635 194
[195] 0.41319444 0.05856634 1.6170980 238
[196] 0.09470752 0.25551601 1.6170980 238
[197] 0.18348624 0.05541434 2.5596981 100
[198] 0.14184397 0.07168277 2.5596981 100
[199] 0.23302752 0.05541434 2.1378971 127
[200] 0.11847015 0.10899847 2.1378971 127
[201] 0.26422018 0.05541434 1.8940273 144
[202] 0.10495627 0.13950178 1.8940273 144
[203] 0.24220183 0.05541434 1.3167800 132
[204] 0.07296849 0.18393493 1.3167800 132
[205] 0.36146789 0.05541434 1.8681223 197
[206] 0.10352076 0.19349263 1.8681223 197
[207] 0.49724771 0.05541434 1.9460530 271
[208] 0.10783924 0.25551601 1.9460530 271
[209] 0.14140127 0.07981698 1.2793758 111
[210] 0.10211592 0.11052364 1.2793758 111
[211] 0.14777070 0.07981698 1.4082605 116
[212] 0.11240310 0.10493137 1.4082605 116
[213] 0.14394904 0.07981698 1.3206519 113
[214] 0.10541045 0.10899847 1.3206519 113
[215] 0.18343949 0.07981698 1.0519693 144
[216] 0.08396501 0.17437722 1.0519693 144
[217] 0.19235669 0.07981698 1.3788834 151
[218] 0.11005831 0.13950178 1.3788834 151
[219] 0.24713376 0.07981698 1.3435934 194
[220] 0.10724157 0.18393493 1.3435934 194
[221] 0.24203822 0.07981698 1.2508912 190
[222] 0.09984235 0.19349263 1.2508912 190
[223] 0.34267516 0.07981698 1.3411103 269
[224] 0.10704337 0.25551601 1.3411103 269
[225] 0.16346154 0.06344687 1.9749929 102
[226] 0.12530713 0.08276563 1.9749929 102
[227] 0.17948718 0.06344687 1.7105198 112
[228] 0.10852713 0.10493137 1.7105198 112
[229] 0.22596154 0.06344687 2.0730706 141
[230] 0.13152985 0.10899847 2.0730706 141
[231] 0.19551282 0.06344687 1.1212062 122
[232] 0.07113703 0.17437722 1.1212062 122
[233] 0.22596154 0.06344687 1.6197753 141
[234] 0.10276968 0.13950178 1.6197753 141
[235] 0.24679487 0.06344687 1.3417510 154
[236] 0.08512991 0.18393493 1.3417510 154
[237] 0.35096154 0.06344687 1.8138238 219
[238] 0.11508145 0.19349263 1.8138238 219
[239] 0.47275641 0.06344687 1.8502027 295
[240] 0.11738957 0.25551601 1.8502027 295
[241] 0.14345992 0.07229283 1.7333271 102
[242] 0.12530713 0.08276563 1.7333271 102
[243] 0.14767932 0.07229283 1.4988918 105
[244] 0.10835913 0.09852567 1.4988918 105
[245] 0.13924051 0.07229283 1.4820675 99
[246] 0.10714286 0.09395018 1.4820675 99
[247] 0.19690577 0.07229283 1.7815715 140
[248] 0.12879485 0.11052364 1.7815715 140
[249] 0.18987342 0.07229283 1.8095010 135
[250] 0.13081395 0.10493137 1.8095010 135
[251] 0.16596343 0.07229283 1.5226216 118
[252] 0.11007463 0.10899847 1.5226216 118
[253] 0.25457103 0.07229283 1.4598869 181
[254] 0.10553936 0.17437722 1.4598869 181
[255] 0.25879044 0.07229283 1.8551049 184
[256] 0.13411079 0.13950178 1.8551049 184
[257] 0.20112518 0.07229283 1.0934583 143
[258] 0.07904920 0.18393493 1.0934583 143
[259] 0.29113924 0.07229283 1.5046529 207
[260] 0.10877562 0.19349263 1.5046529 207
[261] 0.36849508 0.07229283 1.4421604 262
[262] 0.10425786 0.25551601 1.4421604 262
[263] 0.15177305 0.07168277 1.8337690 107
[264] 0.13144963 0.08276563 1.8337690 107
[265] 0.19290780 0.07168277 1.8384188 136
[266] 0.13178295 0.10493137 1.8384188 136
[267] 0.23829787 0.07168277 2.1862496 168
[268] 0.15671642 0.10899847 2.1862496 168
[269] 0.16170213 0.07168277 0.9273122 114
[270] 0.06647230 0.17437722 0.9273122 114
[271] 0.28936170 0.07168277 2.0742510 204
[272] 0.14868805 0.13950178 2.0742510 204
[273] 0.20425532 0.07168277 1.1104760 144
[274] 0.07960199 0.18393493 1.1104760 144
[275] 0.40283688 0.07168277 2.0819237 284
[276] 0.14923805 0.19349263 2.0819237 284
[277] 0.44964539 0.07168277 1.7597542 317
[278] 0.12614405 0.25551601 1.7597542 317
[279] 0.14112903 0.07564820 1.5862903 105
[280] 0.12000000 0.08896797 1.5862903 105
[281] 0.18279570 0.07564820 2.2085942 136
[282] 0.16707617 0.08276563 2.2085942 136
[283] 0.14247312 0.07564820 1.5164752 106
[284] 0.11471861 0.09395018 1.5164752 106
[285] 0.13978495 0.07564820 1.2647516 104
[286] 0.09567617 0.11052364 1.2647516 104
[287] 0.27016129 0.07564820 2.5746476 201
[288] 0.19476744 0.10493137 2.5746476 201
[289] 0.20564516 0.07564820 1.8866793 153
[290] 0.14272388 0.10899847 1.8866793 153
[291] 0.17607527 0.07564820 1.0097378 131
[292] 0.07638484 0.17437722 1.0097378 131
[293] 0.23790323 0.07564820 1.7053777 177
[294] 0.12900875 0.13950178 1.7053777 177
[295] 0.18413978 0.07564820 1.0011138 137
[296] 0.07573245 0.18393493 1.0011138 137
[297] 0.34543011 0.07564820 1.7852365 257
[298] 0.13504992 0.19349263 1.7852365 257
[299] 0.39784946 0.07564820 1.5570432 296
[300] 0.11778750 0.25551601 1.5570432 296
[301] 0.13371429 0.08896797 1.3571517 117
[302] 0.12074303 0.09852567 1.3571517 117
[303] 0.14057143 0.08896797 1.4962338 123
[304] 0.13311688 0.09395018 1.4962338 123
[305] 0.14857143 0.08896797 1.4158915 130
[306] 0.12596899 0.10493137 1.4158915 130
[307] 0.12342857 0.08896797 1.1323881 108
[308] 0.10074627 0.10899847 1.1323881 108
[309] 0.23657143 0.08896797 1.3566647 207
[310] 0.12069971 0.17437722 1.3566647 207
[311] 0.19885714 0.08896797 1.4254810 174
[312] 0.12682216 0.13950178 1.4254810 174
[313] 0.23542857 0.08896797 1.2799558 206
[314] 0.11387507 0.18393493 1.2799558 206
[315] 0.25371429 0.08896797 1.3112349 222
[316] 0.11665791 0.19349263 1.3112349 222
[317] 0.37371429 0.08896797 1.4625865 327
[318] 0.13012336 0.25551601 1.4625865 327
[319] 0.13636364 0.08276563 1.4514463 111
[320] 0.12012987 0.09395018 1.4514463 111
[321] 0.16339066 0.08276563 1.4783323 133
[322] 0.12235511 0.11052364 1.4783323 133
[323] 0.24078624 0.08276563 2.2947022 196
[324] 0.18992248 0.10493137 2.2947022 196
[325] 0.21375921 0.08276563 1.9611211 174
[326] 0.16231343 0.10899847 1.9611211 174
[327] 0.15479115 0.08276563 0.8876799 126
[328] 0.07346939 0.17437722 0.8876799 126
[329] 0.26167076 0.08276563 1.8757521 213
[330] 0.15524781 0.13950178 1.8757521 213
[331] 0.20270270 0.08276563 1.1020349 165
[332] 0.09121061 0.18393493 1.1020349 165
[333] 0.34889435 0.08276563 1.8031403 284
[334] 0.14923805 0.19349263 1.8031403 284
[335] 0.36855037 0.08276563 1.4423768 300
[336] 0.11937923 0.25551601 1.4423768 300
[337] 0.15892673 0.09852567 1.6916065 154
[338] 0.16666667 0.09395018 1.6916065 154
[339] 0.11145511 0.09852567 1.0084278 108
[340] 0.09935603 0.11052364 1.0084278 108
[341] 0.13725490 0.09852567 1.3080445 133
[342] 0.12887597 0.10493137 1.3080445 133
[343] 0.13003096 0.09852567 1.1929613 126
[344] 0.11753731 0.10899847 1.1929613 126
[345] 0.24974200 0.09852567 1.4321939 242
[346] 0.14110787 0.17437722 1.4321939 242
[347] 0.15479876 0.09852567 1.1096544 150
[348] 0.10932945 0.13950178 1.1096544 150
[349] 0.19814241 0.09852567 1.0772419 192
[350] 0.10613599 0.18393493 1.0772419 192
[351] 0.23529412 0.09852567 1.2160366 228
[352] 0.11981083 0.19349263 1.2160366 228
[353] 0.24871001 0.09852567 0.9733637 241
[354] 0.09590131 0.25551601 0.9733637 241
[355] 0.12770563 0.09395018 1.1554598 118
[356] 0.10855566 0.11052364 1.1554598 118
[357] 0.14826840 0.09395018 1.4130036 137
[358] 0.13275194 0.10493137 1.4130036 137
[359] 0.15909091 0.09395018 1.4595700 147
[360] 0.13712687 0.10899847 1.4595700 147
[361] 0.25865801 0.09395018 1.4833245 239
[362] 0.13935860 0.17437722 1.4833245 239
[363] 0.20887446 0.09395018 1.4972889 193
[364] 0.14067055 0.13950178 1.4972889 193
[365] 0.32575758 0.09395018 1.7710480 301
[366] 0.16639027 0.18393493 1.7710480 301
[367] 0.28679654 0.09395018 1.4822091 265
[368] 0.13925381 0.19349263 1.4822091 265
[369] 0.31818182 0.09395018 1.2452520 294
[370] 0.11699164 0.25551601 1.2452520 294
[371] 0.16743330 0.11052364 1.5956459 182
[372] 0.17635659 0.10493137 1.5956459 182
[373] 0.14167433 0.11052364 1.2997827 154
[374] 0.14365672 0.10899847 1.2997827 154
[375] 0.26218951 0.11052364 1.5035766 285
[376] 0.16618076 0.17437722 1.5035766 285
[377] 0.20791168 0.11052364 1.4903873 226
[378] 0.16472303 0.13950178 1.4903873 226
[379] 0.21895124 0.11052364 1.1903734 238
[380] 0.13156440 0.18393493 1.1903734 238
[381] 0.22447102 0.11052364 1.1601012 244
[382] 0.12821860 0.19349263 1.1601012 244
[383] 0.31094756 0.11052364 1.2169396 338
[384] 0.13450060 0.25551601 1.2169396 338
[385] 0.20058140 0.10493137 1.8402220 207
[386] 0.19309701 0.10899847 1.8402220 207
[387] 0.19864341 0.10493137 1.1391592 205
[388] 0.11953353 0.17437722 1.1391592 205
[389] 0.27906977 0.10493137 2.0004746 288
[390] 0.20991254 0.13950178 2.0004746 288
[391] 0.23449612 0.10493137 1.2748863 242
[392] 0.13377557 0.18393493 1.2748863 242
[393] 0.34205426 0.10493137 1.7677896 353
[394] 0.18549658 0.19349263 1.7677896 353
[395] 0.40310078 0.10493137 1.5775950 416
[396] 0.16553920 0.25551601 1.5775950 416
[397] 0.17070896 0.10899847 0.9789636 183
[398] 0.10670554 0.17437722 0.9789636 183
[399] 0.23694030 0.10899847 1.6984751 254
[400] 0.18513120 0.13950178 1.6984751 254
[401] 0.22294776 0.10899847 1.2121013 239
[402] 0.13211719 0.18393493 1.2121013 239
[403] 0.43470149 0.10899847 2.2466049 466
[404] 0.24487651 0.19349263 2.2466049 466
[405] 0.44869403 0.10899847 1.7560310 481
[406] 0.19140470 0.25551601 1.7560310 481
[407] 0.15685131 0.17437722 1.1243678 269
[408] 0.19606414 0.13950178 1.1243678 269
[409] 0.21982507 0.17437722 1.1951242 377
[410] 0.20840243 0.18393493 1.1951242 377
[411] 0.18775510 0.17437722 0.9703476 322
[412] 0.16920652 0.19349263 0.9703476 322
[413] 0.22973761 0.17437722 0.8991124 394
[414] 0.15678472 0.25551601 0.8991124 394
[415] 0.24635569 0.13950178 1.3393633 338
[416] 0.18684356 0.18393493 1.3393633 338
[417] 0.31122449 0.13950178 1.6084566 427
[418] 0.22438255 0.19349263 1.6084566 427
[419] 0.40160350 0.13950178 1.5717351 551
[420] 0.21925985 0.25551601 1.5717351 551
[421] 0.23161968 0.18393493 1.1970465 419
[422] 0.22017867 0.19349263 1.1970465 419
[423] 0.30790492 0.18393493 1.2050318 557
[424] 0.22164743 0.25551601 1.2050318 557
[425] 0.38675775 0.19349263 1.5136341 736
[426] 0.29287704 0.25551601 1.5136341 736
Filtrado de reglas generadas (+++++)
A su vez, podemos filtrar por más de una de las condiciones antes vistas:
soda = subset(reglas, subset = rhs %in% "soda" & lift > 1.2)
inspect(head(sort(soda, by="lift", decreasing = TRUE), 3))
lhs rhs support confidence coverage lift count
[1] {chocolate} => {soda} 0.01352313 0.2725410 0.04961871 1.562939 133
[2] {bottled water} => {soda} 0.02897814 0.2621895 0.11052364 1.503577 285
[3] {sausage} => {soda} 0.02430097 0.2586580 0.09395018 1.483324 239