arules.tex

本程序是基于linux系统下c++代码

\end{figure}

The plot is a direct visualization of the binary incidence matrix where
the the dark dots represent the ones in the matrix.  From the plot we
see that the items in the data set are not evenly distributed.  In fact,
the white area to the top right side suggests, that in the beginning of
2003 only very few items were available (less than 50) and then during
the year more items were added until it reached a number of around 300
items. Also, we can see that there are some transactions in the data set
which contain a very high number of items (denser horizontal lines).
These transactions need further investigation since they could originate
from data collection problems (e.g., a web robot downloading many
documents from the publication site).  To find the very long
transactions we can use the \func{size} and select very long
transactions (containing more than 20 items).

\begin{Schunk}
\begin{Sinput}
> transactionInfo(Epub2003[size(Epub2003) > 20])
\end{Sinput}
\begin{Soutput}
    transactionID           TimeStamp
301  session_56e2 2003-04-29 12:30:38
580  session_6308 2003-08-17 17:16:12
896  session_72dc 2003-12-29 19:35:35
\end{Soutput}
\end{Schunk}

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.

\begin{Schunk}
\begin{Sinput}
> inspect(Epub2003[1:5])
\end{Sinput}
\begin{Soutput}
  items     transactionID           TimeStamp
1 {doc_154}  session_4795 2003-01-01 19:59:00
2 {doc_3d6}  session_4797 2003-01-02 06:46:01
3 {doc_16f}  session_479a 2003-01-02 09:50:38
4 {doc_f4,                                   
   doc_11d,                                  
   doc_1a7}  session_47b7 2003-01-02 17:55:50
5 {doc_83}   session_47bb 2003-01-02 20:27:44
\end{Soutput}
\end{Schunk}

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

\begin{Schunk}
\begin{Sinput}
> as(Epub2003[1:5], "list")
\end{Sinput}
\begin{Soutput}
$session_4795
[1] "doc_154"

$session_4797
[1] "doc_3d6"

$session_479a
[1] "doc_16f"

$session_47b7
[1] "doc_f4"  "doc_11d" "doc_1a7"

$session_47bb
[1] "doc_83"
\end{Soutput}
\end{Schunk}

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

\begin{Schunk}
\begin{Sinput}
> EpubTidLists <- as(Epub, "tidLists")
> EpubTidLists
\end{Sinput}
\begin{Soutput}
tidLists in sparse format with
 465 items/itemsets (rows) and
 3975 transactions (columns)
\end{Soutput}
\end{Schunk}

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.

\begin{Schunk}
\begin{Sinput}
> as(EpubTidLists[1:3], "list")
\end{Sinput}
\begin{Soutput}
$doc_154
 [1] "session_4795" "session_6082" "session_60dd" "session_67db"
 [5] "session_769c" "session_7ee3" "session_bd9d" "session_c591"
 [9] "session_ce9f" "session_cf4b" "session_e019"

$doc_3d6
 [1] "session_4797"    "session_4893"    "session_48f4"   
 [4] "session_4ca3"    "session_wu4450a" "session_52c6"   
 [7] "session_5712"    "session_58e3"    "session_5984"   
[10] "session_5b20"    "session_5c20"    "session_5dc0"   
[13] "session_5eac"    "session_wu4a129" "session_6599"   
[16] "session_673d"    "session_683e"    "session_wu4d25a"
[19] "session_6f2f"    "session_708a"    "session_7a0c"   
[22] "session_7de5"    "session_89db"    "session_9227"   
[25] "session_9941"    "session_a4d7"    "session_a8c0"   
[28] "session_c3c4"    "session_c546"    "session_ca44"   
[31] "session_d328"    "session_d5b4"   

$doc_16f
[1] "session_479a" "session_56e2" "session_630c" "session_72dc"
[5] "session_8b3e" "session_91ab" "session_a202" "session_a7b9"
\end{Soutput}
\end{Schunk}

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}.


\begin{Schunk}
\begin{Sinput}
> data("AdultUCI")
> dim(AdultUCI)
\end{Sinput}
\begin{Soutput}
[1] 48842    15
\end{Soutput}
\begin{Sinput}
> AdultUCI[1:2, ]
\end{Sinput}
\begin{Soutput}
  age        workclass fnlwgt education education-num     marital-status
1  39        State-gov  77516 Bachelors            13      Never-married
2  50 Self-emp-not-inc  83311 Bachelors            13 Married-civ-spouse
       occupation  relationship  race  sex capital-gain capital-loss
1    Adm-clerical Not-in-family White Male         2174            0
2 Exec-managerial       Husband White Male            0            0
  hours-per-week native-country income
1             40  United-States  small
2             13  United-States  small
\end{Soutput}
\end{Schunk}


\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.

\begin{Schunk}
\begin{Sinput}
> AdultUCI[["fnlwgt"]] <- NULL
> AdultUCI[["education-num"]] <- NULL
\end{Sinput}
\end{Schunk}

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}.


\begin{Schunk}
\begin{Sinput}
> 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"))
\end{Sinput}
\end{Schunk}

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

\begin{Schunk}
\begin{Sinput}
> Adult <- as(AdultUCI, "transactions")
> Adult
\end{Sinput}
\begin{Soutput}
transactions in sparse format with
 48842 transactions (rows) and
 115 items (columns)
\end{Soutput}
\end{Schunk}

The remaining 115 categorical attributes were
automatically recoded into 115
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.

\begin{Schunk}
\begin{Sinput}
> summary(Adult)
\end{Sinput}
\begin{Soutput}
transactions as itemMatrix in sparse format with
 48842 rows (elements/itemsets/transactions) and
 115 columns (items) and a density of 0.1089939 

most frequent items:
           capital-loss=none            capital-gain=None 
                       46560                        44807 
native-country=United-States                   race=White 
                       43832                        41762 
           workclass=Private                      (Other) 
                       33906                       401333 

element (itemset/transaction) length distribution:
sizes
    9    10    11    12    13 
   19   971  2067 15623 30162 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   9.00   12.00   13.00   12.53   13.00   13.00 

includes extended item information - examples:
           labels variables      levels
1       age=Young       age       Young
2 age=Middle-aged       age Middle-aged
3      age=Senior       age      Senior

includes extended transaction information - examples:
  transactionID
1             1
2             2
3             3
\end{Soutput}
\end{Schunk}

The summary of the transaction data set gives a rough overview showing
the most frequent items, the length distribution of the transactions and