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$B%Q!<%;%W%H%m%s$N3X=,(B

$B%Q%?!<%s(B c $B$KBP$9$k65;U?.9f$r(B tc $B$H=q$/$3$H$K$9$k$H(B $B%Q!<%;%W%H%m%s$N3X=,!"$9$J$o$A7k9g6/EY$N99?7<0$O(B

 \begin{displaymath}\Delta w_{ji} = \eta\delta x_{c,j} = \eta \Brc{t_{c,j} - y_{c,j}}x_{c,j}.
\end{displaymath} (1)

$B$HI=$9$3$H$,$G$-$k!#$"$k$$$O!"(Bwji $B$N99?7<0$H$7$F(B

 \begin{displaymath}w_{ji}(n+1) = w_{ji}(n) + \eta\Delta w_{ji}(n)
= w_{ji}(n) + \eta\Brc{t_{c,j} - y_{c,j}}x_{c,j}.
\end{displaymath} (2)

$B$G$bF1$80UL#!#%Y%/%H%kI=8=$9$l$P(B

 \begin{displaymath}\mb{w}(n+1) = \mb{w}(n) + \eta\Brc{\mb{t}_c - \mb{y}_c}\,\mb{x}_c.
\end{displaymath} (3)

$B$3$3$G!"(B$\mb{w}(n)$ $B$O(B n $B2sL\$N3X=,=*N;;~E@$G$N7k9g6/EY$rF~NOAX$N(B $B%K%e!<%m%s$@$1JB$Y$F(B $\Brc{w_1,w_2,\ldots,w_{N}}$ $B$H$7$?$b$N$G$"$k!#(B $\mb{t}_c$ $B$O%Q%?!<%s(B c $B$KBP1~$9$k65;U?.9f$rI=$7!"(B $\mb{y}_c$ $B$O%Q%?!<%s(B c $B$KBP$9$k%Q!<%;%W%H%m%s$N=PNO$rI=$9!#(B $\mb{x}_c$ $B$OF~NO?.9f$G$"$k!#(B

$BF~NO(B 2 $B=PNO(B 1 $B$N%M%C%H%o!<%/$r9M$($l$P!"$3$N%M%C%H%o!<%/$X$NF~NOA4BN$O(B 2 $B
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\begin{center}
\resizebox{0.4\textwidt...
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\end{FigHere}

$B$3$NJ?LL(B($B$3$N>l9g$OF~NOAX$N%K%e!<%m%s?t$,(B 2 $B$@$C$?$+$iJ?LL$G$"$C$?$,(B) $B$N$3$H$rF~NO6u4V$H8F$V$3$H$,$"$k!#(B $B%Q!<%;%W%H%m%s$K$*$1$k3X=,$H$O$3$N6u4V$r(B 2 $BJ,3d$9$k$h$&$JNN0h$KJ,$1$k$3$H$G$"$k!#(B

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\begin{displaymath}\Brc{\mb{w},\mb{x}} = w_1x_1 + w_2x_2 = \vert\mb{w}\vert\,\vert\mb{x}\vert \cos\theta
\end{displaymath} (4)

$B$@$+$i$G$"$k!#(B $B>e<0$N:G1&JU$N@5Ii$O(B 2 $B$D$N%Y%/%H%k$N$J$93Q(B $\cos\theta$ $B$N$_$K$h$C$F7h$^$k!#(B $B$9$J$o$A(B


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\begin{center}
\resizebox{0.4\textwidt...
...$BNNN0h$G@5$K$J$k$H$O!

Figure.2 $B$N$h$&$K@~$NK!@~%Y%/%H%k$H$NFb@Q$,@5$G$"$k!#$D$^$j(B $\cos\theta$ $B$O(B $-\displaystyle\frac{\pi}{2}<\theta<\displaystyle\frac{\pi}{2} \rightarrow
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$B$3$N%Q!<%;%W%H%m%s$K3X=,$9$Y$-%G!<%?$,0l$DF~$C$FMh$?$H2>Dj$7$h$&!#(B
 \begin{FigHere}% latex2html id marker 70
\begin{center}
\resizebox{0.4\textwidt...
...phics{perceptron-supp3.eps}} \end{center}\caption{$B3X=,$9$Y$-%G!<%?(B}\end{FigHere}
Figure 3 $B$O(B 1 $B$H=PNO$9$Y$-(B(y=1 $B$9$J$o$AK!@~%Y%/%H%k$H$NFb@Q$,@5$G$"$k$Y$-(B)$B%G!<%?$r!"8m$C$F(B 0 $B$H=PNO$7$F$7$^$C$?$H$$$&;vBV$G$"$k!#(B $B$3$N$H$-!"<0(B(3) $BFb$N(B $\Brc{\mb{t}-\mb{y}}$ $B$O(B 1 - 0 = 1 $B$K$J$k$N$G(B $B7k9g2Y=E$N99?7<0!"$9$J$o$AK!@~%Y%/%H%k$N99?7<0$O(B

 \begin{displaymath}\mb{w}(n) + \eta\Brc{\mb{t}_c - \mb{y}_c}\,\mb{x}_c =
\mb{w}(n) + \eta\mb{x}_c.
\end{displaymath} (5)

$B$H$J$C$F%Y%/%H%k$NB-$7;;$K$J$k!#(B


\begin{FigHere}\begin{center}
\resizebox{0.4\textwidth}{!}{\includegraphics{perceptron-supp4.eps}} \end{center}\end{FigHere}

$B$3$l$K$h$C$FH=JLD>@~$,2sE>$7(B


\begin{FigHere}\begin{center}
\resizebox{0.4\textwidth}{!}{\includegraphics{perceptron-supp5.eps}} \end{center}\end{FigHere}

$B:#EY$OK!@~%Y%/%H%k$H%G!<%?(B $\mb{x}$ $B$H$N$J$93Q$,(B 90 $BEY0JFb$K$J$k!#(B 0 $B$H=PNO$9$Y$-%G!<%?$r!"8m$C$F(B 1 $B$H=PNO$7$F$7$^$C$?>l9g$O(B $B%Y%/%H%k$N0z$-;;$K$J$k!#(B

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\begin{FigHere}\begin{center}
\resizebox{0.4\textwidth}{!}{\includegraphics{perceptron-supp7.eps}} \end{center}\end{FigHere}

$B$3$N>l9g$O!"86E@$rDL$kD>@~$rJB9T0\F0$7$?$3$H$K$J$k$N$G!"(B $B86E@$rDL$kH=JLD>@~$G$O(B 1 $B$HEz$($k$Y$-$NNN0h(B($B?^Cf$NGr%^%k(B)$B$KF~$C$F$7$^$C$F$$$k(B $BE@$rDl%"%2$7$F(B 0 $B$HEz$($k$Y$-NN0h(B($B?^Cf$N9u%^%k(B) $B$NNN0h$K$9$k$?$a$K(B $B9T$o$l$k$H9M$($k$3$H$,$G$-$k!#(B



Shinichi ASAKAWA
1999-10-29