arules.rnw

本程序是基于linux系统下c++代码

transactions we can use the \func{size} and select very long
transactions (containing more than 20 items).

<<>>=
transactionInfo(Epub2003[size(Epub2003) > 20])
@

We found three long transactions and printed the corresponding
transaction information. Of course, size can be used in a similar
fashion to remove long or short transactions.

Transactions can be inspected using \func{inspect}. 
Since the long transactions identified above would result in
a very long printout, we will inspect 
the first 5 transactions in the subset for 2003.

<<>>=
inspect(Epub2003[1:5])
@

Most transactions contain one item. Only transaction 4 contains three items. 
For further inspection transactions can be converted into a list with:

<<>>=
as(Epub2003[1:5], "list")
@

Finally, transaction data in horizontal layout can be converted to
transaction ID lists in vertical layout using coercion.

<<>>=
EpubTidLists <- as(Epub, "tidLists")
EpubTidLists
@

For performance reasons the transaction ID list
is also stored in a sparse matrix. To get a list, coercion to \class{list}
can be used.

<<>>=
as(EpubTidLists[1:3], "list") 
@

In this representation each item has an entry
which is a vector of all transactions it occurs in.
\class{tidLists} can be directly used as input for mining algorithms which 
use such a vertical database layout to mine associations.

In the next example, we will see how a data set is created and
rules are mined.

\subsection{Example 2: Preparing and mining a 
questionnaire data set\label{sec:example-adult}}

As a second example, we prepare and mine questionnaire data.  We use the
Adult data set from the UCI machine learning repository
\citep{arules:Blake+Merz:1998} provided by package~\pkg{arules}.  This
data set is similar to the marketing data set used by
\cite{arules:Hastie+Tibshirani+Friedman:2001} in their chapter about
association rule mining.  The data originates from the U.S. census
bureau database and contains 48842 instances with 14 attributes like
age, work class, education, etc.  In the original applications of the
data, the attributes were used to predict the income level of
individuals.  We added the attribute \code{income} with levels
\code{small} and \code{large}, representing an income of
$\le$~USD~50,000 and $>$~USD~50,000, respectively.  This data is
included in \pkg{arules} as the data set \code{AdultUCI}.


<<data>>=
data("AdultUCI")
dim(AdultUCI)
AdultUCI[1:2,]
@


\code{AdultUCI} contains a mixture of categorical and metric attributes and
needs some preparations before it can be transformed into
transaction data suitable for association mining.
First, we remove the two attributes \code{fnlwgt} and
\code{education-num}. The first attribute is a weight calculated
by the creators of the data set from control data provided by
the Population Division of the U.S. census bureau. 
The second removed attribute is just a numeric representation of the
attribute \code{education} which is also part of the data set.

<<>>=
AdultUCI[["fnlwgt"]] <- NULL
AdultUCI[["education-num"]] <- NULL
@

Next, we need to map the four remaining metric attributes (\code{age},
\code{hours-per-week}, \code{capital-gain} and \code{capital-loss}) to ordinal
attributes by building suitable categories.
We divide the attributes \code{age} and \code{hours-per-week}
into suitable categories using knowledge about typical age groups 
and working hours. 
For the two capital related attributes,
we create a category called \code{None} 
for cases which have no gains/losses. 
Then we further divide the group with gains/losses
at their median into the two categories \code{Low} and \code{High}.


<<>>=
AdultUCI[[ "age"]] <- ordered(cut(AdultUCI[[ "age"]], c(15,25,45,65,100)),
    labels = c("Young", "Middle-aged", "Senior", "Old"))

AdultUCI[[ "hours-per-week"]] <- ordered(cut(AdultUCI[[ "hours-per-week"]],
      c(0,25,40,60,168)),
    labels = c("Part-time", "Full-time", "Over-time", "Workaholic"))
			    
AdultUCI[[ "capital-gain"]] <- ordered(cut(AdultUCI[[ "capital-gain"]],
      c(-Inf,0,median(AdultUCI[[ "capital-gain"]][AdultUCI[[ "capital-gain"]]>0]),Inf)),
    labels = c("None", "Low", "High"))

AdultUCI[[ "capital-loss"]] <- ordered(cut(AdultUCI[[ "capital-loss"]],
      c(-Inf,0,
	median(AdultUCI[[ "capital-loss"]][AdultUCI[[ "capital-loss"]]>0]),Inf)),
    labels = c("none", "low", "high"))
@

Now, the data can be automatically recoded as
a binary incidence matrix by coercing the data set to
\class{transactions}.

<<coerce>>=
Adult <- as(AdultUCI, "transactions")
Adult
@

The remaining \Sexpr{dim(Adult)[2]} categorical attributes were
automatically recoded into \Sexpr{dim(Adult)[2]}
binary items. During encoding the item labels were generated in the
form of 
\texttt{<\emph{variable name}>=<\emph{category label}>}. 
Note that for cases with missing values all items corresponding to the 
attributes with the missing values were set to zero.

<<summary>>=
summary(Adult)
@

The summary of the transaction data set gives a rough overview showing
the most frequent items, the length distribution of the transactions and
the extended item information which shows which variable and which value
were used to create each binary item. In the first example we see that
the item with label \code{age=Middle-aged} was generated by variable
\code{age} and level \code{middle-aged}.  

To see which items are important in the data set we can use the
\func{itemFrequencyPlot}. To reduce the number of items, we only plot
the item frequency for items with a support greater than 10\% (using the parameter \code{support}).  For
better readability of the labels, we reduce the label size with the
parameter \code{cex.names}. The plot is shown in Figure~\ref{fig:itemFrequencyPlot}.

<<itemFrequencyPlot, eval=FALSE>>=
itemFrequencyPlot(Adult, support = 0.1, cex.names=0.8)
@
\begin{figure}
\centering
<<echo=FALSE, fig=TRUE, width=8>>=
<<itemFrequencyPlot>>
@ %
\caption{Item frequencies of items in the Adult data set with support greater than 10\%.}
\label{fig:itemFrequencyPlot}
\end{figure}

Next, we call the function
\func{apriori} to find all rules (the default association type for
\func{apriori}) with a minimum support of 1\% and a confidence of 0.6.

<<apriori>>=
rules <- apriori(Adult, 
                 parameter = list(support = 0.01, confidence = 0.6))
rules
@

%The specified parameter values are validated and, for example,
%a support $> 1$ gives:
%
%<<error>>=
%error <- try(apriori(Adult, parameter = list(support = 1.3)))
%error
%@

First, the function prints the used parameters.  Apart from the
specified minimum support and minimum confidence, all parameters have
the default values. It is important to note that with parameter
\code{maxlen}, the maximum size of mined frequent itemsets, is by
default restricted to 5.  Longer association rules are only mined if
\code{maxlen} is set to a higher value.  After the parameter settings,
the output of the \proglang{C} implementation of the algorithm with timing
information is displayed.

The result of the mining algorithm is a set of \Sexpr{length(rules)}
rules.  For an overview of the mined rules \func{summary}
can be used.   It shows the number of rules, the most frequent items
contained in the left-hand-side and the right-hand-side and their
respective length distributions and summary statistics for the quality
measures returned by the mining algorithm.

<<summary>>=
summary(rules)
@

As typical for association rule mining, the number of rules found is
huge.  To analyze these rules, for example, \func{subset} can be used to
produce separate subsets of rules for each item which resulted form the
variable \code{income} in the right-hand-side of the rule. At the same
time we require that the \code{lift} measure exceeds $1.2$.

<<rules>>=
rulesIncomeSmall <- subset(rules, subset = rhs %in% "income=small" & lift > 1.2)
rulesIncomeLarge <- subset(rules, subset = rhs %in% "income=large" & lift > 1.2)
@

We now have a set with rules for persons with a small income and a set
for persons with a large income.  For comparison, we inspect for both
sets the three rules with the highest confidence (using \func{SORT}).

%%{\samepage\small
<<subset>>=
inspect(head(SORT(rulesIncomeSmall, by = "confidence"), n = 3))
inspect(head(SORT(rulesIncomeLarge, by = "confidence"), n = 3))
@
%%}

From the rules we see that workers in the private sector working part-time or
in the service industry tend to have a small income
while persons with high capital gain who are born in the US tend to have a
large income.
This example shows that using subset selection and sorting a
set of mined associations can be
analyzed even if it is huge.

Finally, the found rules can be written to disk to be shared 
with other applications. To save rules in plain text format 
the function \func{WRITE} is used. The 
following command saves a set of rules as the file named `data.csv' in 
comma separated value (CSV) format.

<<label = write_rules, eval = FALSE>>=
WRITE(rulesIncomeSmall, file = "data.csv", sep = ",", col.names = NA)
@

Alternatively, with package~\pkg{pmml}~\cite{arules:Williams:2008} the rules
can be saved in PMML (Predictive Modelling Markup Language), a standardized
XML-based representation used my many data mining tools. Note that \pkg{pmml}
requires the package~\pkg{XML} which might not be available for all operating
systems. 

<<label=pmml, eval=FALSE>>=
library("pmml")
rules_pmml <- pmml(rulesIncomeSmall)
saveXML(rules_pmml, file = "data.xml")
@

The saved data can now be easily shared and used by other applications. 
Itemsets (with \func{WRITE} also transactions) can be 
written to a file in the same way.

\subsection{Example 3: Extending arules with a new interest measure\label{sec:example-allconf}}

In this example, we show how easy it is to add a new interest measure,
using \emph{all-confidence} as introduced by
\cite{arules:Omiecinski:2003}.  The all-confidence of an itemset~$X$ is
defined as

\begin{equation}
\mbox{all-confidence}(X) = \frac{\mathrm{supp}(X)}
{\mathrm{max}_{I \subset X} \mathrm{supp}(I)}
\label{equ:all_conf}
\end{equation}

This measure has the property $\mathrm{conf}(I \Rightarrow X \setminus
I) \ge \mbox{all-confidence}(X)$ for all $I \subset X$.  This means that
all possible rules generated from itemset~$X$ must at least have a
confidence given by the itemset's all-confidence value.
\cite{arules:Omiecinski:2003} shows that the support in the denominator
of equation~\ref{equ:all_conf} must stem from a single item and thus can
be simplified to $\max_{i \in X} \mathrm{supp}(\{i\})$.

To obtain an itemset to calculate all-confidence for,