Building on the arules Infrastructure for
Analyzing Transaction Data with R
Michael Hahsler1 and Kurt Hornik2
1 Department of Information Systems and Operations,
Wirtschaftsuniversita¨t, A-1090 Wien, Austria
2 Department of Statistics and Mathematics,
Wirtschaftsuniversita¨t, A-1090 Wien, Austria
Abstract. The free and extensible statistical computing environment R with its
enormous number of extension packages already provides many state-of-the-art tech-
niques for data analysis. Support for association rule mining, a popular exploratory
method which can be used, among other purposes, for uncovering cross-selling op-
portunities in market baskets, has become available recently with the R extension
package arules. After a brief introduction to transaction data and association rules,
we present the formal framework implemented in arules and demonstrate how clus-
tering and association rule mining can be applied together using a market basket
data set from a typical retailer. This paper shows that implementing a basic in-
frastructure with formal classes in R provides an extensible basis which can very
efficiently be employed for developing new applications (such as clustering transac-
tions) in addition to association rule mining.
1 Introduction
An aim of analyzing transaction data is to discover interesting patterns (e.g.,
association rules) in large databases containing transaction data. Transaction
data can originate from various sources. For example, POS systems collect
large quantities of records (i.e., transactions, market baskets) containing prod-
ucts purchased during a shopping trip. Analyzing market basket data is called
Market Basket Analysis (Russell et al. (1997), Berry and Linoff (1997)) and
is used to uncover unexploited selling opportunities. Table 1 depicts a simple
example for transaction data. Formally, let I = {i1, i2, . . . , in} be a set of n
binary attributes called items. Let D = {t1, t2, . . . , tm} be a set of transactions
called the database. Each transaction in D has a unique transaction ID and
contains a subset of the items in I.
Categorical and/or metric attributes from other data sources (e.g., in sur-
vey data) can be mapped to binary attributes and thus be treated in the same
way as transaction data (Piatetsky-Shapiro (1991), Hastie et al. (2001)). Here
interesting relationships between values of the attributes can be discovered.

2 Michael Hahsler and Kurt Hornik
transaction ID items
1 milk, bread
2 bread, butter
3 beer
4 milk, bread, butter
5 bread, butter
(a)
items
trans. ID milk bread butter beer
1 1 1 0 0
2 0 1 1 0
3 0 0 0 1
4 1 1 1 0
5 0 1 1 0
(b)
Table 1. Example of market basket data represented as (a) shopping lists and as
(b) a binary purchase incidence matrix where ones indicate that an item is contained
in a transaction.
Agrawal et al. (1993) stated the problem of mining association rules from
transaction data (e.g., database of market baskets) as follows:
A rule is defined as an implication of the form X ⇒ Y where X,Y ⊆ I
and X ∩ Y = ∅. The sets of items (for short itemsets) X and Y are called
antecedent (left-hand-side or lhs) and consequent (right-hand-side or rhs) of
the rule. To select interesting rules from the set of all possible rules, constraints
on various measures of strength and interestingness can be used. The best-
known constraints are minimum thresholds on support and confidence. The
support supp(X) of an itemset X is defined as the proportion of transactions
in the data set which contain the itemset. The confidence of a rule is defined
conf(X ⇒ Y ) = supp(X ∪ Y )/supp(X). Association rules are required to
satisfy both a minimum support and a minimum confidence constraint at the
same time.
An infrastructure for mining transaction data for the free statistical com-
puting environment R (R Development Team (2005)) is provided by the ex-
tension package arules (Hahsler et al. (2005, 2006)). In this paper we discuss
this infrastructure and indicate how it can conveniently be enhanced (by pro-
viding functionality to compute proximities between transactions) to create
application frameworks with new data analysis capabilities.
In Section 2 we give a very brief overview of the infrastructure provided by
arules and discuss calculating similarities between transactions. In Section 3
we demonstrate how the arules infrastructure can be used in combination with
clustering algorithms (as provided by a multitude of R extension packages)
to group transactions representing similar purchasing behavior and then to
discover association rules for interesting transaction groups. All necessary R
code is provided in the paper.
2 Building on the arules Infrastructure
The arules infrastructure implements the formal framework presented by the
S4 class structure (Chambers (1998)) in Figure 1. For transaction data the

Analyzing Transaction Data with R 3
associations
quality : data.frame
itemsetsrules
itemMatrix
itemInfo : data.frame
tidList
Matrix
dgCMatrix
transactions
transactionInfo : data.frame
Fig. 1. Simplified UML class diagram (see Fowler (2004)) of the arules package.
classes transactions and tidLists (transaction ID lists, an alternative way to rep-
resent transaction data) are provided. When needed, data formats commonly
used in R to represent transaction data (e.g., data frames and matrices) are
automatically transformed into transactions.
For mining patterns, the popular mining algorithm implementations of
Apriori and Eclat (Borgelt (2003)) are used in arules. Patterns are stored
as itemsets and rules representing sets of itemsets or rules, respectively. Both
classes directly extend a common virtual class called associations which pro-
vides a common interface. In this structure it is easy to add a new type of
associations by adding a new class that extends associations.
For efficiently handling the typically very sparse transaction data, items in
associations and transactions are implemented by the itemMatrix class which
provides a facade for the sparse matrix implementation dgCMatrix from the
R package Matrix (Bates and Maechler (2005)). To use sparse data (e.g.
transactions or associations) for computations which need dense matrices or
are implemented in packages which do not support sparse representations,
transformation into dense matrices is provided. For all classes standard ma-
nipulation methods as well as special methods for analyzing the data are
implemented. A full reference of the capabilities of arules can be found in the
package documentation (Hahsler et al. (2005)).
With the availability of such a conceptual and computational infrastruc-
ture providing fundamental data structures and algorithms, powerful applica-
tion frameworks can be developed by taking advantage of the vast data min-
ing and analysis capabilities of R. Typically, this only requires providing some
application-specific “glue” and customization. In what follows, we illustrate
this approach for finding interesting groups of market baskets, one of the core
value-adding tasks in the analysis of purchase decisions. As grouping (clus-
tering) is based on notions of proximity (similarity or dissimilarity), the glue
needed is functionality to compute proximities between transactions, which
can be done by using the asymmetric Jaccard dissimilarity (Sneath (1957))
often used for binary data where only ones (corresponding to purchases in our
application) carry information. Alternatively, more domain specific proximity

4 Michael Hahsler and Kurt Hornik
measures like Affinity (Aggarwal et al. (2002)) are possible. Extensions to
proximity measures for associations are straightforward.
In a recent version of arules, we added the necessary extensions for cluster-
ing. In the following example, we illustrate how conveniently this now allows
for combining clustering and association rule mining.
3 Example: Clustering and Mining Retail Data
We use 1 month (30 days) of real-world point-of-sale transaction data from a
typical local grocery outlet for the example. The items are product categories
(e.g., popcorn) instead of the individual brands. In the available 9835 trans-
actions we found 169 different categories for which articles were purchased.
The data set is included in package arules under the name Groceries. First,
we load the package and the data set.
R> library("arules")
R> data("Groceries")
Suppose the store manager wants to promote the purchases of beef and
thus is interested in associations which include the category beef. A direct
approach would be to mine association rules on the complete data set and
filter the rules which include this category. However, since the store manager
knows that there are several different types of shopping behavior (e.g., small
baskets at lunch time and rather large baskets on Fridays), we first cluster the
transactions to find promising groups of transactions which represent similar
shopping behavior. From the distance-based clustering algorithms available in
R, we choose partitioning around medoids (PAM; Kaufman and Rousseeuw
(1990)) which takes a dissimilarity matrix between the objects (transactions)
and a predefined number of clusters (k) as inputs and returns cluster labels
for the objects. PAM is similar to the well-known k-means algorithm, with the
main differences that is uses medoids instead of centroids to represent cluster
centers and that it works on arbitrary dissimilarity matrices. PAM is available
in the recommended R extension package cluster (Maechler (2005)).
To keep the dissimilarity matrix at a manageable size, we take a sam-
ple of size 2000 from the transaction database (Note that we first set the
random number generator’s seed for reasons of reproducibility). For the sam-
ple, we calculate the dissimilarity matrix using the function dissimilarity()
with the method "Jaccard" which implements the Jaccard dissimilarity. Both
dissimilarity() and sample() are recent “glue” additions to arules. With
this dissimilarity matrix and the number of clusters pre-set to k = 8 (using
expert judgment by the store manager), we apply PAM to the sample.
R> set.seed(1234)
R> s <- sample(Groceries, 2000)
R> d <- dissimilarity(s, method = "Jaccard")

Analyzing Transaction Data with R 5
Silhouette width si
−0.2 0.0 0.2 0.4 0.6 0.8 1.0
Silhouette plot of pam(x = d, k = 8)
Average silhouette width : 0.07
n = 2000 8 clusters Cj
j : nj | avei∈Cj si
1 : 540 | −0.006
2 : 192 | 0.14
3 : 421 | −0.005
4 : 143 | 0.17
5 : 74 | 0.30
6 : 182 | 0.09
7 : 337 | −0.004
8 : 111 | 0.54
Fig. 2. Silhouette plot of the clustering.
R> library("cluster")
R> clustering <- pam(d, k = 8)
R> plot(clustering)
Visualization is employed to assess the obtained clustering. The silhou-
ette plot (Kaufman and Rousseeuw (1990)) in Figure 2 displays the silhouette
widths for each object (transaction) ordered by cluster as horizontal bars. The
silhouette width is a measure of how well an object belongs to its assigned
cluster. Compact clusters exclusively consist of objects with high silhouette
widths. In the plot we see, that cluster 8 is by far the most compact clus-
ter. Several other clusters have objects with negative silhouette widths which
indicates dispersed clusters. However, this is typical for clustering in high-
dimensional space.
To predict labels for the whole data set based on the clustered sample,
we use the nearest neighbor approach. Package arules provides now a new
“glue” predict() method which can be used to find the labels for all trans-
actions in the Groceries database given the cluster medoids. With labels for
all transactions, we can generate a list of transaction data sets, one for each
cluster.
R> allLabels <- predict(s[clustering$medoids], Groceries,
+ method = "Jaccard")
R> cluster <- split(Groceries, allLabels)

6 Michael Hahsler and Kurt Hornik
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Fig. 4. Item frequencies in the cluster 3.
The transaction data set for each cluster can now be analyzed and used
independently. We will demonstrate this by choosing two different clus-
ters, clusters number 8 and 3. For visualization of the clusters, we use
itemFrequencyPlot() from arules which produces a cluster profile where
bars are used to represent the relative frequency of product categories in the
cluster and a line is used for the relative frequency of the categories in the
whole data set. Large differences between the data set and the cluster are
interesting since they indicate strong cluster-specific behavior. For better vis-
ibility, we only show the categories with a support greater than 5%.
R> itemFrequencyPlot(cluster[[8]], population = s, support = 0.05)
R> itemFrequencyPlot(cluster[[3]], population = s, support = 0.05)
The cluster profile of the compact cluster 8 (Figure 3) shows a group of
transactions which almost entirely consists of canned beer.
Cluster 3 consists of many transactions containing a large number of items.
The cluster’s profile in Figure 4 shows that almost all product categories are

Analyzing Transaction Data with R 7
on average bought more often in the transactions in this group than in the
whole data set. This cluster is interesting for association rule mining since the
transactions contain many items and thus represent high sales volume.
As mentioned above, we suppose that the store manager is interested in
promoting beef. Because beef is not present in cluster 8, we will concentrate
on cluster 3 for mining association rules. We choose relatively small values for
support and confidence and, in a second step, we filter only rules which have
the product category beef in the right-hand-side.
R> rules <- apriori(cluster[[3]], parameter = list(support = 0.005,
+ confidence = 0.2), control = list(verbose = FALSE))
R> beefRules <- subset(rules, subset = rhs %in% "beef")
Now the store manager can use a wide array of methods provided by arules
to analyze the found 181 rules. As an example, we show the 3 rules with the
highest confidence values.
R> inspect(head(SORT(beefRules, by = "confidence"), n = 3))
lhs rhs support confidence lift
1 {tropical fruit,
root vegetables,
whole milk,
rolls/buns} => {beef} 0.006189 0.3889 2.327
2 {tropical fruit,
other vegetables,
whole milk,
rolls/buns} => {beef} 0.006631 0.3846 2.302
3 {tropical fruit,
root vegetables,
other vegetables,
rolls/buns} => {beef} 0.005747 0.3824 2.288
4 Conclusion
In this contribution, we showed how the formal framework implemented in the
R package arules can be extended for transaction clustering by simply provid-
ing methods to calculate proximities between transactions and corresponding
nearest neighbor classifications. Analogously, proximities between associations
can be defined and used for clustering itemsets or rules (Gupta et al. (1999)).
Provided that item ontologies or transaction-level covariates are available,
these can be employed for interpreting and validating obtained clusterings.
In addition, stability of the “interesting” groups found can be assessed us-
ing resampling methods, as e.g. made available via the R extension pack-
age clue (Hornik (2005, 2006)).

8 Michael Hahsler and Kurt Hornik
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