hierarchy: Support for Item Hierarchies

Description

Often an item hierarchy is available for datasets used for association rule mining. For example in a supermarket dataset items like "bread" and "beagle" might belong to the item group (category) "baked goods."

We provide support to use the item hierarchy to aggregate items to different group levels, to produce multi-level transactions and to filter spurious associations mined from multi-level transactions.

Usage

# S4 method for itemMatrix
aggregate(x, by)
# S4 method for itemsets
aggregate(x, by)
# S4 method for rules
aggregate(x, by)
addAggregate(x, by, postfix = "*")
filterAggregate(x)

Arguments

an transactions, itemsets or rules object.

name of a field (hierarchy level) available in itemInfo of x or a grouping vector of the same length as items in x by which should be aggregated. Items with the same group label in by will be aggregated into a single with that name. Note that the grouping vector will be coerced to factor before use.

postfix

characters added to mark group-level items.

Value

aggregate() returns an object of the same class as x encoded with a number of items equal to the number of unique values in by. Note that for associations (itemsets and rules) the number of associations in the returned set will most likely be reduced since several associations might map to the same aggregated association and aggregate returns a unique set. If several associations map to a single aggregated association then the quality measures of one of the original associations is randomly chosen.

addAggregate() returns a new transactions object with the original items and the group-items added. filterAggregateRules() returns a new rules object with the spurious rules remove.

Details

Transactions can store item hierarchies as additional columns in the itemInfo data.frame ("labels" is reserved for the item labels).

Aggregation: To perform analysis at a group level of the item hierarchy, aggregate() produces a new object with items aggregated to a given group level. A group-level item is present if one or more of the items in the group are present in the original object. If rules are aggregated, and the aggregation would lead to the same aggregated group item in the lhs and in the rhs, then that group item is removed from the lhs. Rules or itemsets, which are not unique after the aggregation, are also removed. Note also that the quality measures are not applicable to the new rules and thus are removed. If these measures are required, then aggregate the transactions before mining rules.

Multi-level analysis: To analyze relationships between individual items and item groups at the same time, addAggregate() can be used to create a new transactions object which contains both, the original items and group-level items (marked with a given postfix). In association rule mining, all items are handled the same, which means that we will produce a large number of rules of the type

$$item A => group of item A$$

with a confidence of 1. This will also happen if you mine itemsets. filterAggregate() can be used to filter these spurious rules or itemsets.

Examples

Run this code

# NOT RUN {
data("Groceries")
Groceries
  
## Groceries contains a hierarchy stored in itemInfo
head(itemInfo(Groceries))

## Example 1: Aggregate items using an existing hierarchy stored in itemInfo. 
## We aggregate to level2 stored in Groceries. All items with the same level2 label 
## will become a single item with that name.
## Note that the number of items is therefore reduced to 55
Groceries_level2 <- aggregate(Groceries, by = "level2")
Groceries_level2
head(itemInfo(Groceries_level2)) ## labels are alphabetically sorted!


## compare original and aggregated transactions
inspect(head(Groceries, 2))
inspect(head(Groceries_level2, 2))

## Example 2: Aggregate using a character vector.
## We create here labels manually to organize items by their first letter.
mylevels <- toupper(substr(itemLabels(Groceries), 1, 1))
head(mylevels)

Groceries_alpha <- aggregate(Groceries, by = mylevels)
Groceries_alpha
inspect(head(Groceries_alpha, 2))

## Example 3: Aggregate rules 
## Note: You could also directly mine rules from aggregated transactions to
## get support, lift and support
rules <- apriori(Groceries, parameter = list(supp = 0.005, conf = 0.5))
rules
inspect(rules[1])

rules_level2 <- aggregate(rules, by = "level2")
inspect(rules_level2[1])

## Example 4: Mine multi-level rules.
## (1) Add aggregate items. These items will have labels ending with a *
Groceries_multilevel <- addAggregate(Groceries, "level2")
summary(Groceries_multilevel)
inspect(head(Groceries_multilevel))

rules <- apriori(Groceries_multilevel, 
  parameter = list(support = 0.01, conf = .9))
inspect(head(rules, by = "lift"))
## Note that this contains many spurious rules of type 'item X => aggregate of item X'
## with a confidence of 1 and high lift. We can filter spurious rules resulting from 
## the aggregation 
rules <- filterAggregate(rules)
inspect(head(rules, by = "lift"))
# }