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< chromozone associated with all those types, what is the effect on the runtimes
---
> chromosome associated with all those types, what is the effect on the runtimes
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< learner. Since there are many steps in such a search ($N$
< features have $2^N$ subsets), WRAPPERs may be too slow.
---
> learner. Since there are many steps in such a search ($F$
> features have $2^F$ subsets), WRAPPERs may be too slow.
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< Another feature subset selector is RELIEF.  
< This is an instance based learning scheme \cite{Kir92,Kon94}
< that works by randomly sampling one instance within the data. It
< then locates the nearest neighbors for that instance from not
< only the same class but the opposite class as well. The values
< of the nearest neighbor features are  then compared to that of
< the sampled instance and the feature scores are maintained and
< updated based on this. This process is specified for some
< user-specified $M$ number of instances. RELIEF can handle noisy
< data and other data anomalies by averaging the values for $K$
< nearest neighbors of the same and opposite class for each
< instance \cite{Kon94}. For data sets with multiple classes, the
< nearest neighbors for each class that is different from that of the
< current sampled instance are selected and the contributions are 
< determined by using the class probabilities of the class in the dataset.
---
> Another feature subset selector is RELIEF \cite{Kir92,Kon94}.
> RELIEF assumes
> that the data is divided into $groups$\footnote{Technically, RELIEF assumes
> that instances have been classified using some ``class'' attribute. However,
> to avoid confusion with the concept of ``class'' discussed above, we will
> describe RELIEF in terms of ``groups''.} and tries to find the feature that
> serve to distinguish instances in one group from instances in other groups.  
> 
> RELIEF is a stochastic
> instance-based scheme 
> that works by randomly selects $N$ reference instances
> $R_1 .. R_N$; by default, $N=250$.
> For data sets with two groups, RELIEF can be implemented
> using the simple algorithm of \fig{relief2}. 
> The algorithm finds two other instances: the ``hit'' $H$ is the nearest instance 
> to $R$ in the same group while
> the ``miss'' $M$ is the nearest instance to $R$ in another group. RELIEF's core intuition is that
> features that change value between groups are more meritorious than features that change value
> within the same group.
> Accordingly,
> the merit of a feature (denoted $M_f$) is 
> {\em increased} for all features with a different  values in the ``miss'' and 
> {\em decreased} for all features with different values in the ``hit''.
> The $\Delta$ function of figure \fig{relief2} detects differences between feature values. 
> If a feature is discrete then the distance is one (if the
> symbols are different) or zero (if the symbols are the same). If a feature is numeric,
> the the feature is normalizes 0..1 for min..max then subtracted. If a feature has a
> missing value, then a Bayesian statistic is used to generate an estimate for the expected
> value (see ~\cite{Kir92} for details).
> \newcommand{\FOR}{{\sffamily \underline{for}}~}
> \newcommand{\TO}{{\sffamily \underline{to}}~}
> \newcommand{\DO}{{\sffamily \underline{do}}~}
> \newcommand{\DONE}{{\sffamily \underline{done}}~}
> \newcommand{\setuptabs}{
> \hspace*{.2in}\=\hspace*{.2in}\=\hspace*{1in}\=\hspace*{.2in}\=\hspace*{.1in}
> \hspace*{.2in}\=\hspace*{.2in}\=\hspace*{.2in}\=\hspace*{.2in}\=\hspace*{.2in}
> \hspace*{.2in}\=\hspace*{.2in}\=\hspace*{.2in}\=\hspace*{.2in}\=\hspace*{.2in}\kill
> }
> \begin{figure}
> {\footnotesize
>  \begin{tabbing}\setuptabs
> \FOR  $f \leftarrow 1$ \TO $|features|$ \DO \\
> \>$M_f =  0$ \>\> {\em // set to all merits are 0}\\
> \DONE\\
> \FOR i $\leftarrow$ 1 \TO $N$ \DO\\
> \>   randomly select instance $R$ from group $G$\\
> \>   find nearest hit $H$ \>\>{\em // closest thing in the same group}\\
> \>   find nearest miss $M$ \>\>{\em // closest thing in a  different group}\\
> \>   \FOR $f \leftarrow 1$ \TO $|features|$ \DO\\
> \>\>       $M_f \leftarrow M_f - \frac{\Delta(f,R,H)}{N} + \frac{\Delta(f,R,M)}{N}$\\
> \>	\DONE\\
> \DONE
> \end{tabbing}}
> \caption{Binary RELIEF (two group system) for $N$ instances
> for merit of different features. }\label{fig:relief2}
> \end{figure}
> 
> For complex data set with more than two groups, \fig{relief2} samples
> not one, but $k$ nearest misses and hits from the same or different group
> (respectively).
> The update function for 
> $M_f$ is modified accordingly:
> \[\footnotesize
> \begin{array}{r@{~}l}
> M_f \leftarrow M_f - &  \sum_i^k\frac{\Delta(f,R,H_i)}{N*k} \\
> 				   + &  \sum_{g \not= group(R)} \sum_i^k\left(\underbrace{\frac{P(g) }{  1 - P(group(R))}}_{normalization}  * \frac{\Delta(f,R,M_i(g))}{N*k}\right) \\ 
> \end{array} 
> \]
> $P(X)$ denotes the ratio of group $X$ in the entire data.
> When reasoning about rare 
> groups (i.e. when $P(X)$ is small), 
> there is less support for the inference that feature $f$ distinguishes
> one group from another. 
> Accordingly,
> when the  group of the reference instance $R$ or the group of the miss $M$ is rare,
> then the {\em normalization} term (shown above) demotes the influence of their difference.
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< stochastic nature of RELIEF makes it a natural choice.
---
> stochastic nature of RELIEF makes it a natural choice for our application.
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< we ran Nighthawk for 40 generations.  Each class therefore
---
> we ran Nighthawk for 40 generations.  Each group therefore
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< into three classes: bottom 10\%, next 25\%, remaining
---
> into three groups: bottom 10\%, next 25\%, remaining
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< the three regions.  
---
> the three groups.  
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< \begin{center}\includegraphics[width=2.5in]{Hashtable_rankedByMerit.pdf}
---
> \begin{center}\includegraphics[width=2.5in]{Hashtable_rankedByAvgMerit.pdf}
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< At the {\it metaheuristic level}, this work suggests that it may
< be useful to integrate FSS directly into metaheuristic
---
> At the {\it meta-heuristic level}, this work suggests that it may
> be useful to integrate FSS directly into meta-heuristic
438c499
< to metaheuristic algorithms that improve themselves
---
> to meta-heuristic algorithms that improve themselves
448c509
< metaheuristic algorithm, new strategies, heuristics, and
---
> meta-heuristic algorithm, new strategies, heuristics, and