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\jairheading{17}{2002}{450-478}{6/02}{12/02}
\ShortHeadings{Expert-Guided Subgroup Discovery}
{Gamberger \& Lavra\v{c}}
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\begin{figure*}
{\small
\begin{tabbing}
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{\bf Algorithm SD: Subgroup Discovery}  \\
{\bf Input:} \> \> $E=P \cup N$\  ($E$\  training set,  $|E|$ training set size, \\
 \> \> \> $P$\  positive (target class) examples, $N$\  negative (non-target class) examples) \\
 \> \>  $L$\  set of all defined features (attribute values), $l \in L$\  \\
{\bf Parameter:}\> \> \> $g$\  (generalization parameter, $0.1<g$, default value 1) \\
\> \> \> $min\_support$\  (minimal support for rule acceptance) \\
\> \> \> $beam\_width$\  (maximal number of rules in $Beam$\  and $New\_Beam$)\\
{\bf Output:} \> \> $S = \{TargetClass \leftarrow Cond\}$\   (set of
rules formed of $beam\_width$\  best conditions $Cond$) \\
(1)\> {\bf for} all rules in $Beam$\  and $New\_Beam$\  ($i=1$\  to $beam\_width$)  {\bf do} \\
\>\>  initialize condition part of the rule to be empty, $Cond(i) \leftarrow \{ \}$\  \\
\>\>  initialize rule quality, $q_g(i) \leftarrow 0$\  \\
(2)\> {\bf while} there are improvements in $Beam$\  {\bf do} \\
(3)\> \>{\bf for} all rules in $Beam$\  ($i=1$\  to $beam\_width$)  {\bf do} \\
(4)\> \> \>{\bf for} all $l \in L$\  {\bf do}\\
(5)\> \> \> \> form a new rule by forming a new condition as a
conjunction of the \\
\> \> \> \> \>  condition from  $Beam$\  and feature $l$,
                $Cond(i) \leftarrow Cond(i) \wedge l$\  \\
(6)\> \> \> \> compute  the quality of a new rule as $q_{g} = \frac{TP}{FP + g}$\\
(7)\> \> \> \> {\bf if} $\frac{TP}{|E|} \geq min\_support$\  {\bf and if } $q_{g}$\  is larger
              than any $q_g(i)$\  in $New\_Beam$\  \\
\> \> \> \> \> \> {\bf and if } the new rule is relevant {\bf do}\\
(8)\> \> \> \> \> replace the worst rule in $New\_Beam$\  with the new rule
and  \\
\> \> \> \> \> \> reorder the rules in $New\_Beam$\  with respect to their quality \\
(9)\> \> \> {\bf end for} features\\
(10)\> \> {\bf end for} rules from $Beam$\\
(11)\> \> $Beam \leftarrow New\_Beam$\  \\
(12)\> {\bf end while} \\
\end{tabbing}
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\begin{figure}
{\small
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{\bf Algorithm RSS:  Rule Subset Selection}  \\
{\bf Input:} \> \> $S$\  set of rules for
the target class \\
\> \>       $P$\  target class examples \\
{\bf Parameter:} \> \> \> $number$\  (required number of selected rules in output set $SS$) \\
{\bf Output:}\> \> $SS$\  set of relatively independent rules for the target class \\
(1)  \> {\bf initialize} $SS \leftarrow \{ \}$\  (empty set of selected rules) \\
(2)  \> {\bf for} every $e \in P$\  {\bf do} $c(e) \leftarrow 1$\  \\
(3)  \> {\bf repeat} $number$\  times \\
(4)  \> \> {\bf select} from $S$\  the rule with  the highest weight  $\sum 1/c(e)$\  where summation is \\
 \> \> \>   over the set $P' \subseteq P$\  of target class  examples covered by the rule \\
(5)  \> \> {\bf for} every $e \in P'$\  covered by the selected rule \\
 \> \> \> {\bf do} $c(e) \leftarrow c(e) + 1$\  \\
(6)  \> \> {\bf eliminate} the selected rule from $S$\  \\
(7)  \> \> {\bf add} the selected rule into set $SS$\\
(8)  \> {\bf end repeat} \\
\end{tabbing}
}

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\begin{figure}
{\small
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{\bf Algorithm DMS:  Data Mining Server subgroup construction}  \\
{\bf Input:}\> \> \> $E=P \cup N$\  ($E$\  training set,  $|E|$ training set size, \\
 \> \> \> \> \> \> \> $P$\  positive (target class) examples,\\
 \> \> \> \> \> \> \> $N$\  negative (non-target class) examples) \\
 \> \>  $L$\  set of all defined features (attribute values), $l \in L$\  \\
{\bf Parameter:} \> \> \> $number$\  (required number of selected rules \\
 \> \> \>  in output set $SS$) \\
\> \> \> $g$\  (generalization parameter, $0.1<g<100$, default value 1) \\
\> \> \> $min\_support$\  (minimal support for rule acceptance) \\
\> \> \> $beam\_width$\  (number of rules in the beam)\\
{\bf Output:}\> \> $SS$\  set of relatively independent rules for the target class \\
(1)  \> {\bf initialize} $SS \leftarrow \{ \}$\  (empty set of selected rules) \\
(2)  \> {\bf for} every $e \in P$\  {\bf do} $c(e) \leftarrow 1$\  \\
(3)  \> {\bf repeat} $number$\  times \\
(4)  \> \> call {\bf Algorithm SD} to construct a rule with maximal \\
 \> \> \> quality  \( q_g = \frac{\sum_{TP}\frac{1}{c(e)}}{FP + g} \)\\
(5)  \> \> {\bf for} every $e \in P'$\  covered by the constructed rule \\
 \> \> \> {\bf do} $c(e) \leftarrow c(e) + 1$\  \\
(6)  \> \> {\bf add} the constructed rule into set $SS$\\
(7)  \> {\bf end repeat} \\
\end{tabbing}
}

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