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\noindent
{\bf Data Mining 2: Frequent Pattern Mining} \hfill Summer 2018 \\
Christian Borgelt \hfill from 26.04.2018

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\vskip3ex
\centerline{\bf Organisational Rules for Exam Admission}

\medskip\noindent
The lecture is accompanied by exercise sheets.
At the beginning of each exercise lesson, the exercises are
{\em voted for}. By voting for an exercise, one expresses one's
willingness to present something about it. (Suggestions for a
solution will be discussed, they need not be correct right away.)
To the exam will be admitted, who
\begin{enumerate}\itemsep0pt\parskip2pt
\item voted for {\em at least\/} half of the exercises {\em and}
\item presented something for {\em at least\/} two exercises.
\end{enumerate}

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\vskip3ex
\centerline{\bf Exercise Sheet 1}

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\subsubsection*{Exercise 1 \quad\rm Use of Frequent Patterns}

\begin{enumerate}\itemsep0pt
\item[a)\hfill]
     What does the term ``market basket analysis'' mean?
\item[b)\hfill]
     How could information in the form of frequent item sets
     or association rules \\ be used for marketing purposes etc.?
\item[c)\hfill]
     What are potential applications of frequent item set mining? \\
     Try to find others than those mentioned on the motivation slide
     of the lecture!
\item[d)\hfill]
     Does its frequency already make a pattern
     or a rule interesting? \\
     If not, why not? Try to find counterexamples!
\item[e)\hfill]
     What are advantages of representing frequent patterns as
     association rules compared to representing them as
     frequent item sets? What are disadvantages?
\end{enumerate}

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\subsubsection*{Exercise 2 \quad\rm Basic Notions}

\begin{enumerate}\itemsep0pt
\item[a)\hfill]
     Why are transactions databases represented as vectors/arrays? \\
     Why can't we use simple sets?
     What are alternative representations? \\
     What are advantages/disadvantages of alternative representations?
\item[b)\hfill]
     Why is the item base often not given explicitly?
     How can it be obtained?
\item[c)\hfill]
     How can absolute and relative (minimum) support
     be translated into each other? \\
     What additional information is needed for the transformation?
\item[d)\hfill]
     In frequent item set mining we consider only whether an item
     is present in or absent from a transaction. However, in market
     basket data, items have multiplicities (a customer buys 3 cartons
     of milk, 5 apples, 2 cans of soup etc.). \\
     How can this be handled?
     Can it be handled by preprocessing? If yes, how?
\end{enumerate}

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\subsubsection*{Exercise 3 \quad\rm Properties of Support}

\begin{enumerate}\itemsep0pt
\item[a)\hfill]
     What is the {\em cover\/} of an item or item set? \\
     How is it related to the {\em support\/} of an item or item set?
\item[b)\hfill]
     What does it mean that support
     is anti-monotone or downward closed? \\
     How can this be expressed as a formula?
\item[c)\hfill]
     What relation of item set covers corresponds
     to the anti-monotonicity of support?
\item[d)\hfill]
     What is the {\em apriori property\/}?
     How is it stated formally? How does it follow? \\
     What does the contraposition of the apriori property say?
     What does it suggest?
\end{enumerate}

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\subsubsection*{Exercise 4 \quad\rm Properties of Support}

\begin{enumerate}\itemsep0pt
\item[a)\hfill]
     Demonstrate that the support of an item set
     and one of its supersets can \\ be equal!
     (That is, the support of the superset need
     not be actually smaller.) \\
     How can one describe the condition under which this holds? \\
     Can there be multiple different supersets
     that have the same support?
\item[b)\hfill]
     Let $I$ be an item set and $a$ and $b$ two items
     that are not in $I$. \\
     Let $s(I) = s(I \cup \{a\}) = s(I \cup \{b\})$.
     What is the support of $I \cup \{a,b\}$?
\item[c)\hfill]
     Find an example where one can determine from the support of
     (several) item sets $I_k$ that $\bigcup_k I_k$ must be frequent
     w.r.t. $s_{\min} \ge 3$ without accessing the transaction database
     (you may, however, use the size~$n$ of the transaction
     database). \\
     Do {\em not\/} use the solution/assumptions of part~b)!
\end{enumerate}

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