%C-c tj
%C-c tp

\documentclass[a4paper]{jsarticle}

\usepackage{tani_resume, graphics}%$B%9%?%$%k%U%!%$%k$NFI$_9~$_(B

\alignbeforeskip -5mm
\alignafterskip -5mm
\eqnarraybeforeskip -5mm
\eqnarrayafterskip -5mm

%jp$B$OF|K\8l(B
%e$B$O1Q8l(B
%title$B$H(Bauthor$B$O<+J,MQ$K=q$-49$($F$/$@$5$$!#(B

\jptitle{$B8rM'4X78%G!<%?$HG>GH%G!<%?$+$i$N4XO"@-<+F0Cj=P(B}
\etitle{
%The relative automatic formation from friends and acquaintances data
%and electroencephalographic data
%
}
\jpauthor{$B>.NS!!:L(B}
\eauthor{Aya Kobayashi}
\course{$BC+!!8&5f<<(B}
\year{23}
\abstract{%$B35MW(B(2009$B%a%s%P!<$O=q$$$F$$$^$9!#(B)
%$B$3$3$+$i(B
$BK\8&5f$G$O!$>.3X@8$rBP>]$K9T$C$?G>GH4J0WB,Dj5Z$S!$M'?M4X78$d(B
$B%3%s%T%e!<%?%2!<%`$N%W%l%$;~4VEy$K4X$9$k%"%s%1!<%H$K$h$j<}=8$5$l$?%G!<%?$KBP$7$F!$%G!<%?%^%$(B
$B%K%s%0<jK!$rMQ$$$F!$G>GH%G!<%?%Q%?!<%s$H%W%l%$;~4V(B
$B$N4X78@-$NCj=P$r;n$_$k!%(B
%$B$3$3$^$G35MW(B
}

\setcounter{page}{9}

\begin{document}%$B%I%-%e%a%s%H$N;O$a(B

\maketitle

\begin{multicols}{2}%$BJ8>O$r(B2$BCJMn$KJ,$1$k!uJ8>O$N;O$a(B

\section{$B$O$8$a$K(B}

%$BGX7J!&F05!!&@h9T8&5f!&L\E*!&:#2s$d$k$3$H!!$r$3$N2<$K!#(B
$B%G!<%?%^%$%K%s%0(B
%$B!J1Q8l(B:Data Mining$B!K(B
$B$H$O!$B?NL$N%G!<%?$+$iM-MQ$JCN<1$rH/7!$9$k%G!<%?=hM}5;=Q$NAm>N$G$"$k!%(B
%$B$3$l$K$h$j!$BgNL$N%G!<%?C_@Q$,2DG=$H$J$C$?!%(B
$B8\5R4IM}>pJs!$Gd$j>e$2%G!<%?Ey$N4IM}$K$bMQ$$$i$l$k!%(B
$BBeI=E*$J2r@O<jK!$H$7$FIQ=P%Q%?!<%sCj=P!$%/%i%9J,N`!$2s5"J,@O!$%/%i%9%?%j(B
$B%s%0$,CN$i$l$F$$$k(B\cite{fukuda,motoda}$B!%(B

$B6aG/!$%3%s%T%e!<%?!$7HBSEEOC!$%9%^!<%H%U%)%s!$%3%s%T%e!<%?%2!<%`5!$NIa5Z(B
$B$KH<$$!$%3%s%T%e!<%?%2!<%`$d%3%s%T%e!<%?A`:nEy$,?M4V$NG>$KM?$($k1F6A$K$D(B
$B$$$F5DO@$5$l$F$*$j!$(B
$B1F6A$,$J$$$H$$$&<gD%$H!$1F6A$,$"$k$H$$$&<gD%$NAPJ}$,B8:_$9$k!%(B
$BKt!$1F6A$,$"$k$H$$$&<gD%$NCf$K$b!$9%1F6A$,$"$k$H$$$&<gD%(B\cite{nouchi}$B!$0-1F6A$,$"(B
$B$k$H$$$&<gD%(B\cite{mori}$B$,B8:_$9$k!%(B

%2002$BG/(B7$B7n$K!$F|K\Bg3XJ8M}3XItBN0i3X2J?9><M:65<x$,!$(B
%$BCx=q!V%2!<%`G>$N62I]!W(B\cite{mori}$B$K$*$$$F!$(B
%$B%3%s%T%e!<%?%2!<%`$,?M4V$NG>$K0-1F6A$rM?$($k$H<gD%$7!$(B
%$B$=$NMM$J>uBV$JG>$r%2!<%`G>$HDj5A$7$?$,!$??56$ODj$+$G$O$J$$!%(B

$BK\8&5f$G$O!$F|K\Bg3XJ8M}3XIt$N%W%m%8%'%/%H%A!<%`$,(B2007$BG/(B9$B7n$K:k6L8)Fb$N(B
$B>.3X@8(B5,6$BG/@8(B103$B?M$rBP>]$K9T$C$?G>GH4J0WB,Dj$*$h$SM'?M4X78$d(B
$B%3%s%T%e!<%?%2!<%`$N%W%l%$;~4VEy$N%G!<%?$KBP$7$F!$%G!<%?%^%$%K%s%0<jK!$r(B
$BMQ$$$F!$(B
$BG>GH%G!<%?%Q%?!<%s$H%W%l%$;~4V$N4X78@-$NCj=P$r;n$_$k!%(B

%$B$3$3$^$G!!$O$8$a$K(B

\section{$B%/%i%9%?%j%s%0(B}
%$B$=$N$?$a$N=`Hw!JFI$`?M!?J9$/?M$N$?$a!K!!$r$3$N2<$K(B
$BK\8&5f$G$O!$:GC;5wN%K!!$:G1sE@5wN%K!!$(B$k$--medoids$BK!(B\cite{fukuda,motoda}$B$N(B
3$B$D$N%/%i%9%?%j%s%0<jK!$r:NMQ$7$?!%(B
$B:GC;5wN%K!!$:G1sE@5wN%K!$O%/%i%9%?%j%s%0<jK!$NCf$G$b3,AXE*<jK!$N6E=87?$K(B
$BJ,N`$5$l$k!%(B
$B$^$?!$(B$k$--medoids$BK!$OJ,3d:GE,2=<jK!$KJ,N`$5$l$k!%(B
$B3F%/%i%9%?$O%G!<%?$N=89g$G$"$j!$%G!<%?(B$d$, $d'$$B$N5wN%$r(B
$\mathrm{dis}(d,d')$$B$H$9$k!%(B
$B%/%i%9%?(B$C$, $C'$$B$N:GC;5wN%$r(B$\min_{d\in C,d'\in C'}\mathrm{dis}(d,d')$
$B$H$9$k!%(B
$B%/%i%9%?4V$N5wN%$H$7$F!$:GC;5wN%K!$G$O:GC;5wN%$rMQ$$$k!%(B
$B0J2<$G!$:GC;5wN%K!!$:G1sE@5wN%K!!$(B$k$--medoids$BK!$=$l$>$l$N%"%k%4%j%:%`35(B
$BMW$r=R$Y$k!%(B
\\

$\diamondsuit$$B:GC;5wN%K!!%(B
\begin{enumerate}
 \item $BF~NO$N(B$n$$B8D$N%G!<%?=89g(B$D=\{d_1,\ldots,d_n\}$$B$KBP$7$F!$(B
       $n$$B8D$N%/%i%9%?(B$C_1=\{d_1\}$, $\ldots$ , $C_n=\{d_n\}$$B$r:n@.$7!$(B
       $C=\{C_1,\ldots,C_n\}$$B$H$9$k!%(B
 \item $B%/%i%9%?$N3F%Z%"$N5wN%$r5a$a:G$b5wN%$N>.$5$$%/%i%9%?$N%Z%"(B$C_i$,
       $C_j$$B$rA*Br!%(B
 \item $C$$B$+$i(B$C_i$, $C_j$$B$r:o=|$7!$(B$C$$B$K(B$C_i\cup C_j$$B$rDI2C!%(B
 \item $|C|$$B$,F~NO$5$l$?%/%i%9%??t$K$J$k$^$G(B2.$B$+$i(B4.$B$r7+$jJV$9!%(B
\end{enumerate}

$\diamondsuit$$B:G1sE@K!!%(B
\begin{enumerate}
 \item $BF~NO$N(B$n$$B8D$N%G!<%?=89g(B$D=\{d_1,\ldots,d_n\}$$B$+$iG$0U$N(B1$BE@(B$d_i$$B$r$H$j!$(B
       $C=\{d_i\}$$B$H$9$k!%(B
 \item $\max_{d\in D-C,d'\in C}\mathrm{dis}(d,d')$$B$H$J$k(B$d$$B$r(B$C$$B$K2C$($k!%(B
 \item $C$$B$N%5%$%:$,(B$k$$BL$K~$J$i(B2.$B$KLa$k!%(B
 \item $C$$B$NE@$KBP1~$7$?(B$k$$B8D$N%/%i%9%?$r:n$k!%(B
       $B$3$N$H$-!$(B$D$$B$N3FE@$O!$:G$b6a$$(B$C$$B$NE@$KBP1~$7$?%/%i%9%?$KJ,N`$5(B
       $B$l$k!%(B
\end{enumerate}

$\diamondsuit$ $k$--medoids$BK!(B.
\begin{enumerate}
 \item $BF~NO$N(B$n$$B8D$N%G!<%?=89g(B$D=\{d_1,\ldots,d_n\}$$B$N3FMWAG(B$d$$B$KBP$7(B
       $B$F%/%i%9%?(B$C_1,\ldots,C_k$$B$r%i%s%@%`$KA*$S(B$d$$B$r$=$N%/%i%9%?$NMW(B
       $BAG$H$9$k!%(B
 \item $B3F%/%i%9%?(B$C_i$$B$KBP$7$F(B
       $\min_{d\in C_i}\sum_{d'\in C_i-{d}}\mathrm{dis}(d,d')$$B$H$J$k(B
       $BMWAG$r(B1$B$DA*$S(Bmedoid $m_i$$B$H$9$k!%(B
 \item $D=\{d_1,\ldots,d_n\}$$B$N3FMWAG(B$d$$B$KBP$7$F(B
       $\min_{i\in\{1,\ldots,k\}}\mathrm{dis}(d,m_i)$$B$H$J$k(B
       $BMWAG$r(B1$B$DA*$S(B$d$$B$r%/%i%9%?(B$C_i$$B$NMWAG$H$9$k!%(B
 \item $BB0$9$k%/%i%9%?$,JQ$o$C$?MWAG$,(B$D=\{d_1,\ldots,d_n\}$$B$KB8:_$9$l$P(B
       2.$B$KLa$k!%(B
\end{enumerate}

%$B$3$3$^$G!!%/%i%9%?%j%s%0(B

\section{$B<B8335MW(B}
%$B<B8335MW(B
$B>.3X@8$N%2!<%`$N%W%l%$;~4V$HG>GH%G!<%?%Q%?!<%s$r%/%i%9%??t(B3, 5, 10$B$G(B
$B:GC;5wN%K!!$(B$k$--medoids$BK!!$:G1sE@K!$rMQ$$$F%/%i%9%?%j%s%0$r9T$&!%(B

\subsection{$B%^%$%K%s%0BP>]%G!<%?(B}
$BF|K\Bg3XJ8M}3XIt$N%W%m%8%'%/%H%A!<%`$,(B2007$BG/(B9$B7n$K(B
$B:k6L8)Fb$N>.3X@8(B5,6$BG/@8(B103$B?M$rBP>]$K!$G>GH4J0WB,Dj!$(B
$B$*$h$S!$%3%s%T%e!<%?%2!<%`$N%W%l%$;~4VEy$N%"%s%1!<%HD4::$r<B;\$7$?!%(B
$B%3%s%T%e!<%?%2!<%`$N%W%l%$;~4V$K4X$9$k<ALd9`L\$O!$(B1$BF|$"$?$j$N7HBS7?%2!<%`5!$NJ?6Q%W%l%$(B
$B;~4V!$?x$(CV$-7?%2!<%`5!$NJ?6Q%W%l%$;~4V!$(B1$BF|$N:GD9%W%l%$;~4V$G$"$k!%(B
%$B>.3X@8$K(B1$BF|$K$I$l$/$i$$%2!<%`$rM7$V$+$rD4$Y$?%"%s%1!<%H%G!<%?(B,
$B$^$?!$F|K\Bg3XJ8M}3XIt$N%W%m%8%'%/%H(B
$B%A!<%`$O!$4J0WG>GHB,Dj$GF@$i$l$?%G!<%?$r(B3$B$D$NG>GH%Q%?!<%s(B$P_1$$B!$(B$P_2$$B!$(B$P_3$$B$KJ,N`$7$?!%(B
$B$3$3$G!$(B$i<j$$B$J$i$P!$G>GH%Q%?!<%s(B$P_i$$B$OG>GH%G!<%?(B$P_j$$B$h$j0-1F6A$,>/$J(B
$B$$!%(B
%$B$3$3$^$G!!<B8335MW(B

\section{$B<B837k2L(B}
$B3FI=$K$*$$$F!$(B1$BNsL\$r%/%i%9%?!$(B2$BNsL\$r%/%i%9%?$KB0$9$k%G!<%?$N?t!$(B
3$BNsL\$+$i(B5$BNsL\$r%/%i%9%?$KB0$9$k3FG>GH%Q%?!<%s(B$P_1$, $P_2$, $P_3$$B$N%G!<(B
$B%?$N?t!J>eCJ!K$H3d9g$NI4J,N(!J2<CJ!K$H$9$k!%(B
$B$?$@$7!$(B$i<j$$B$J$i$P!$%/%i%9%?(B$C_i$$B$NJ?6Q%W%l%$;~4V$O%/%i%9%?(B$C_i$$B$NJ?6Q(B
$B%W%l%$;~4V0J>e$H$9$k!%(B

%\begin{center}
% $
% \begin{array}{|c|r|r|r|}\hline
%  & C_1 & C_2 & C_3\\\hline
%   \mbox{$B?t(B} & 2 & 3 & 80\\\hline
%   P_1 & 0 & 0 & 39\\
%  & 0 & 0 & 31\\\hline
%   P_2 & 100 & 33 & 48\\
%  & 2 & 1 & 38\\\hline
%   P_3 & 0 & 67 & 13\\
%  & 0 & 2 & 11\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B1: $k=3$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $\begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 2 & 0 & 100 & 0\\
  & & 0 & 2 & 0\\\hline
   C_2 & 3 & 0 & 33 & 67\\
  & & 0 & 1 & 2\\\hline
   C_3 & 80 & 39 & 48 & 13\\
  & & 31 & 38 & 11\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B1: $B:G1sE@K!(B $k=3$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \begin{array}{|c|r|r|r|r|r|}\hline
%  & C_1 & C_2 & C_3 & C_4 & C_5\\\hline
%   \mbox{$B?t(B} & 2 & 3 & 17 & 5 & 58\\\hline
%   P_1 & 0 & 0 & 29 & 60 & 40\\
%  & 0 & 0 & 5 & 3 & 23\\\hline
%   P_2 & 100 & 33 & 47 & 40 & 48\\
%  & 2 & 1 & 8 & 2 & 28\\\hline
%   P_3 & 0 & 67 & 24 & 0 & 12\\
%  & 0 & 2 & 4 & 0 & 12\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B2: $k=5$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $
 \begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 2 & 0 & 100 & 0\\
  & & 0 & 2 & 0\\\hline
   C_2 & 3 & 0 & 33 & 67\\
  & & 0 & 1 & 2\\\hline
   C_3 & 17 & 29 & 47 & 24\\
  & & 5 & 8 & 4\\\hline
   C_4 & 5 & 60 & 40 & 0\\
  & & 3 & 2 & 0\\\hline
   C_5 & 58 & 40 & 48 & 12\\
  & & 23 & 28 & 12\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B2: $B:G1sE@K!(B $k=5$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \begin{array}{|c|r|r|r|r|r|r|r|r|r|r|}\hline
%  & C_1 & C_2 & C_3 & C_4 & C_5 & C_6 & C_7 & C_8 & C_9 & C_{10}\\\hline
%   \mbox{$B?t(B} & 2 & 2 & 14 & 5 & 3 & 4 & 7 & 1 & 29 & 18 \\\hline
%   P_1 & 0 & 0 & 21 & 60 & 67 & 75 & 57 & 0 & 31  & 39\\
%  & 0 & 0 & 3 & 3 & 2 & 3 & 4 & 0 & 9 & 7\\\hline
%   P_2 & 100 & 50 & 50 & 40 & 33 & 25 & 29 & 0 & 55 & 50\\
%  & 2 & 1 & 7 & 2 & 1 & 1 & 2 & 0 & 16 & 9\\\hline
%   P_3 & 0 & 50 & 29 & 0 & 0 & 0 & 14 & 100 & 14 & 11\\
%  & 0 & 1 & 4 & 0 & 0 & 0 & 1 & 1 & 4 & 2\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B3: $k=10$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $
 \begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 2 & 0 & 100 & 0\\
  & & 0 & 2 & 0\\\hline
   C_2 & 2 & 0 & 50 & 50\\
  & & 0 & 1 & 1\\\hline
   C_3 & 14 & 21 & 50 & 29\\
  & & 3 & 7 & 4\\\hline
   C_4 & 5 & 60 & 40 & 0\\
  & & 3 & 2 & 0\\\hline
   C_5 & 3 & 67 & 33 & 0\\
  & & 2 & 1 & 0\\\hline
   C_6 & 4 & 75 & 25 & 0\\
  & & 3 & 1 & 0\\\hline
   C_7 & 7 & 57 & 29 & 14\\
  & & 4 & 2 & 1\\\hline
   C_8 & 1 & 0 & 0 & 100\\
  & & 0 & 0 & 1\\\hline
   C_9 & 29 & 31 & 55 & 14\\
  & & 9 & 16 & 4\\\hline
   C_{10} & 18 & 39 & 50 & 11\\
  & & 7 & 9 & 2\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B3: $B:G1sE@K!(B $k=10$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \begin{array}{|c|r|r|r|}\hline
%  & C_1 & C_2 & C_3\\\hline
%   \mbox{$B?t(B} & 1 & 7 & 77\\\hline
%   P_1 & 0 & 29 & 14\\
%  & 0 & 2 & 11\\\hline
%   P_2 & 100 & 42 & 48\\
%  & 1 & 3 & 37\\\hline
%   P_3 & 0 & 29 & 38\\
%  & 0 & 2 & 29\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B4: $k=3$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $\begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 1 & 0 & 100 & 0\\
  & & 0 & 1 & 0\\\hline
   C_2 & 7 & 29 & 42 & 29\\
  & & 2 & 3 & 2\\\hline
   C_3 & 77 & 14 & 48 & 38\\
  & & 11 & 37 & 29\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B4: $B:GC;5wN%K!(B $k=3$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \hspace{-10ex}
% \begin{array}{|c|r|r|r|r|r|}\hline
%  & C_1 & C_2 & C_3 & C_4 & C_5\\\hline
%   \mbox{$B?t(B} & 1 & 1 & 5 & 1 & 77\\\hline
%   P_1 & 0 & 0 & 40 & 0 & 37\\
%  & 0 & 0 & 2 & 0 & 29\\\hline
%   P_2 & 100 & 100 & 20 & 100 & 48\\
%  & 1 & 1 & 1 & 1 & 37\\\hline
%   P_3 & 0 & 0 & 40 & 0 & 14\\
%  & 0 & 0 & 2 & 0 & 11\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B5: $k=5$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $
 \begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 1 & 0 & 100 & 0\\
  & & 0 & 1 & 0\\\hline
   C_2 & 1 & 0 & 100 & 0\\
  & & 0 & 1 & 0\\\hline
   C_3 & 5 & 40 & 20 & 40\\
  & & 2 & 1 & 2\\\hline
   C_4 & 1 & 0 & 100 & 0\\
  & & 0 & 1 & 0\\\hline
   C_5 & 77 & 37 & 48 & 14\\
  & & 29 & 37 & 11\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B5: $B:GC;5wN%K!(B $k=5$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \begin{array}{|c|r|r|r|r|r|r|r|r|r|r|}\hline
%  & C_1 & C_2 & C_3 & C_4 & C_5 & C_6 & C_7 & C_8 & C_9 & C_{10}\\\hline
%   \mbox{$B?t(B} & 1 & 1 & 1 & 3 & 1 & 1 & 2 & 25 & 3 & 47 \\\hline
%   P_1 & 100 & 0 & 100 & 0 & 0 & 0 & 50 & 44 & 33  & 34\\
%  & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 11 & 1 & 16\\\hline
%   P_2 & 0 & 100 & 0 & 67 & 100 & 100 & 50 & 44 & 0 & 51\\
%  & 0 & 1 & 0 & 2 & 1 & 1 & 1 & 11 & 0 & 24\\\hline
%   P_3 & 0 & 0 & 0 & 33 & 0 & 0 & 0 & 12 & 67 & 14\\
%  & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 3 & 2 & 7\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B6: $k=10$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $
 \begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 1 & 100 & 0 & 0\\
  & & 1 & 0 & 0\\\hline
   C_2 & 1 & 0 & 100 & 0\\
  & & 0 & 1 & 0\\\hline
   C_3 & 1 & 100 & 0 & 0\\
  & & 1 & 0 & 0\\\hline
   C_4 & 3 & 0 & 67 &33\\
  & & 0 & 2 & 1\\\hline
   C_5 & 1 & 0 & 100 & 0\\
  & & 0 & 1 & 0\\\hline
   C_6 & 1 & 0 & 100 & 0\\
  & & 0 & 1 & 0\\\hline
   C_7 & 2 & 50 & 50 & 0\\
  & & 1 & 1 & 0\\\hline
   C_8 & 25 & 44 & 44 & 12\\
  & & 11 & 11 & 3\\\hline
   C_9 & 3 & 33 & 0 & 67\\
  & & 1 & 0 & 2\\\hline
   C_{10} & 47 & 34 & 51 & 14\\
  & & 16 & 24 & 7\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B6: $B:GC;5wN%K!(B $k=10$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \begin{array}{|c|r|r|r|}\hline
%  & C_1 & C_2 & C_3\\\hline
%   \mbox{$B?t(B} & 21 & 30 & 34\\\hline
%   P_1 & 33 & 37 & 38\\
%  & 7 & 11 & 13\\\hline
%   P_2 & 48 & 43 & 53\\
%  & 10 & 13 & 18\\\hline
%   P_3 & 19 & 20 & 9\\
%  & 4 & 6 & 3\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B7: $k=3$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $\begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 21 & 33 & 48 & 19\\
  & & 7 & 10 & 4\\\hline
   C_2 & 30 & 37 & 43 & 20\\
  & & 11 & 13 & 6\\\hline
   C_3 & 34 & 38 & 53 & 9\\
  & & 13 & 18 & 3\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B7: $k$--medoids$BK!(B $k=3$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \begin{array}{|c|r|r|r|r|r|}\hline
%  & C_1 & C_2 & C_3 & C_4 & C_5\\\hline
%   \mbox{$B?t(B} & 19 & 18 & 11 & 5 & 32\\\hline
%   P_1 & 26 & 33 & 36 & 60 & 41\\
%  & 5 & 6 & 4 & 3 & 13\\\hline
%   P_2 & 53 & 50 & 36 & 40 & 50\\
%  & 10 & 9 & 4 & 2 & 16\\\hline
%  P_3 & 21 & 17 & 28 & 0 & 9\\
%  & 4 & 3 & 3 & 0 & 3\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B8: $k=5$
% \\\vspace{2ex}
%\end{center}


\begin{center}
 $
 \begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 19 & 26 & 53 & 21\\
  & & 5 & 10 & 4\\\hline
   C_2 & 18 & 33 & 50 & 17\\
  & & 6 & 9 & 3\\\hline
   C_3 & 11 & 36 & 36 & 28\\
  & & 4 & 4 & 3\\\hline
   C_4 & 5 & 60 & 40 & 0\\
  & & 3 & 2 & 0\\\hline
   C_5 & 32 & 41 & 50 & 9\\
  & & 13 & 16 & 3\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B8: $k$--medoids$BK!(B $k=5$
 \\\vspace{2ex}
\end{center}

%\begin{center}
% $
% \begin{array}{|c|r|r|r|r|r|r|r|r|r|r|}\hline
%  & C_1 & C_2 & C_3 & C_4 & C_5 & C_6 & C_7 & C_8 & C_9 & C_{10}\\\hline
%   \mbox{$B?t(B} & 5 & 11 & 11 & 10 & 6 & 2 & 8 & 5 & 13 & 14 \\\hline
%   P_1 & 40 & 9 & 27 & 40 & 33 & 50 & 75 & 40 & 23  & 50\\
%  & 2 & 1 & 3 & 4 & 2 & 1 & 6 & 2 & 3 & 7\\\hline
%   P_2 & 60 & 64 & 55 & 30 & 33 & 50 & 25 & 60 & 62 & 43\\
%  & 3 & 7 & 6 & 3 & 2 & 1 & 2 & 3 & 8 & 6\\\hline
%   P_3 & 0 & 27 & 18 & 30 & 33 & 0 & 0 & 0 & 15 & 7\\
%  & 0 & 3 & 2 & 3 & 2 & 0 & 0 & 0 & 2 & 1\\\hline
% \end{array}
% $\\
% \vspace{1ex}
% $BI=(B9: $k=10$
% \\\vspace{2ex}
%\end{center}

\begin{center}
 $
 \begin{array}{|c|c|r|r|r|}\hline
  & \mbox{$B?t(B} & P_1 & P_2 & P_3\\\hline
   C_1 & 5 & 40 & 60 & 0\\
  & & 2 & 3 & 0\\\hline
   C_2 & 11 & 9 & 64 & 27\\
  & & 1 & 7 & 3\\\hline
   C_3 & 11 & 27 & 55 & 18\\
  & & 3 & 6 & 2\\\hline
   C_4 & 10 & 40 & 30 &30\\
  & & 4 & 3 & 3\\\hline
   C_5 & 6 & 33 & 33 & 33\\
  & & 2 & 2 & 2\\\hline
   C_6 & 2 & 50 & 50 & 0\\
  & & 1 & 1 & 0\\\hline
   C_7 & 8 & 75 & 25 & 0\\
  & & 6 & 2 & 0\\\hline
   C_8 & 5 & 40 & 60 & 0\\
  & & 2 & 3 & 0\\\hline
   C_9 & 13 & 23 & 62 & 15\\
  & & 3 & 8 & 2\\\hline
   C_{10} & 14 & 50 & 43 & 7\\
  & & 7 & 6 & 1\\\hline
 \end{array}
 $\\
 \vspace{1ex}
 $BI=(B9: $k$--medoids$BK!(B $k=10$
 \\\vspace{2ex}
\end{center}

\columnbreak

%$B<B837k2L(B
%$B%f!<%/%j%C%I5wN%(B

%\scalebox{0.6}{\includegraphics{ma4_gr1.eps}}

%$BJ?J}%f!<%/%j%C%I5wN%(B

%\scalebox{0.6}{\includegraphics{ma4_gr2.eps}}

%$B%^%s%O%C%?%s5wN%(B

%\scalebox{0.6}{\includegraphics{ma4_gr3.eps}}

%$B%A%'%9HW$"$k$$$O%A%'%S%7%'%U5wN%(B

%\scalebox{0.6}{\includegraphics{ma4_gr4.eps}}

%$B%-%c%s%Y%i5wN%(B

%\scalebox{0.6}{\includegraphics{ma4_gr5.eps}}

%$BM>895wN%(B

%\scalebox{0.6}{\includegraphics{ma4_gr6.eps}}
%$B$3$3$^$G!!<B837k2L(B


\section{$B9M;!(B}
%$B9M;!(B

$B:G1sE@K!$K$*$$$F$O!$(B$k=3$$B$H(B$k=5$$B$N>l9g$O%/%i%9%?$4$H$N%5%$%:$KJP$j$,8+$i(B
$B$l$?$,!$(B$k=10$$B$N>l9g$N%/%i%9%?$4$H$N%5%$%:$KJP$j$,$"$^$j8+$i$l$J$+$C$?!%(B
$B$^$?%/%i%9%?$HG>GH%Q%?!<%s$N4XO"@-$O8+$i$l$J$+$C$?!JI=(B1, 2, 3$B;2>H!K!%(B

$B:GC;5wN%K!$K$*$$$F$O!$(B$k=3$, $k=5$, $k=10$$B$N>l9g$K%/%i%9%?$4$H$N%5%$%:$K(B
$BJP$j$,8+$i$l$?!%(B
$B$^$?%/%i%9%?$HG>GH%Q%?!<%s$N4XO"@-$O8+$i$l$J$+$C$?!JI=(B4, 5, 6$B;2>H!K!%(B

$k$--medoids$BK!$K$*$$$F$O!$(B$k=3$$B$H(B$k=5$$B$N(B$k=10$$B>l9g$O%/%i%9%?$4$H$N%5%$%:(B
$B$KJP$j$,$"$^$j8+$i$l$J$+$C$?!%(B
$B$^$?%/%i%9%?$HG>GH%Q%?!<%s$N4XO"@-$O8+$i$l$J$+$C$?!JI=(B7, 8, 9$B;2>H!K!%(B

$B$h$C$F!$(B3$B$D$N<jK!$rMQ$$$F9T$C$?K\8&5f$K$*$1$k!$%W%l%$;~4V$ND9$5$K$h$k%/(B
$B%i%9%?%j%s%07k2L$+$i$O!$(B
$B%W%l%$;~4V$HG>GH%Q%?!<%s$N4XO"@-$OG'$a$i$l$J$+$C$?!%:#8e$NB><jK!$rMQ$$(B
$B$?$5$i$J$k8!>Z$,BT$?$l$k!%(B

%$B$3$3$^$G!!9M;!(B

\end{multicols}%2$BCJMn$NJ8>O$N=*$o$j(B

\begin{thebibliography}{4}%$B;29MJ88%(B({2}$B!'(B2$B$D;29MJ88%$,$"$k$H$$$&0UL#(B)
 \bibitem{nouchi}
	 Rui Nouchi, Yasuyuki Taki, Hikaru Takeuchi, Hiroshi Hashizume,
	 Yuko Akitsuki, Yayoi Shigemune, Atsushi Sekiguchi, Yuka
	 Kotozaki, Takashi Tsukiura, Yukihito Yomogida, Ryuta Kawashima,
	 Brain Training Game Improves Executive Functions and Processing
	 Speed in the Elderly: A Randomized Controlled Trial.	 
 \bibitem{fukuda}
	 $BJ!ED(B $B9d;V!$FA;3(B $B9k!$?9K\(B $B9/I'!$%G!<%?%^%$%K%s%0!$6&N)=PHG!$(B2001$BG/!%(B
 \bibitem{motoda}
	 $B85ED(B $B9@!$;38}(B $B9bJ?!$DEK\(B $B<~:n!$>BHx(B $B@59T!$%G!<%?%^%$%K%s%0$N4pAC!$(B
	 $B%*!<%`<R!$(B2006$BG/!%(B
 \bibitem{mori}
	 $B?9(B $B><M:!$%2!<%`G>$N62I]!$(BNHK$B=PHG!$(B2007$BG/!%(B
 \bibitem{wolfram}
	 Wolfram Research, Partitioning Data into Clusters,\\	 
	 http://reference.wolfram.com/mathematica/tutorial/PartitioningDataIntoClusters.en.html
	 
\end{thebibliography}%$B;29MJ88%=*$o$j(B

\end{document}%$B%I%-%e%a%s%H$N=*$o$j(B
