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% �s�b�`�������p�������k�ގ��x�ɂ������̎�������
% Automatic classification of Japanese dialects using compression similarity distance assisted by pitch information
% g-2009 SAITO / YAMAMOTO / SHIGIHARA
%
% ./tani_resume_last.syt
% ./assyuku.tex
% ./�g�p����摜�F�ȉ��摜���X�g
%   [ nj.eps upgma.eps quartet.eps consistent.eps ]
%   [ mae1-nj-bz2.eps mae1-upgma-bz2.eps mae1-quartet-bz2.eps]
%   [ mae2-nj-bz2.eps mae2-upgma-bz2.eps mae2-quartet-bz2.eps]
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\documentclass[a4paper]{jarticle}

\usepackage{tani_resume_last}

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

\jptitle{�s�b�`�������p�������k�ގ��x�ɂ������̎�������}
\etitle{Automatic classification of Japanese dialects using compression similarity distance assisted by pitch information}
\jpauthor{�V�� �x�ہA�R�{ �s�A���� ���K}
\eauthor{Takemaru Saito , Satoshi Yamamoto , Katsuyuki Shigihara}
\course{�J�@������}
\year{20}
\abstract{%
���k�ɂ��f�[�^�Ԃ̗ގ��x�Ɋւ��鋗������`����ADNA�̗ގ��x�⌾��̗ގ��x�A���y�̗ގ��x����ɗL�p���Ƃ����������ʂ������Ă���B��N�A�r�x�A���c���������k�ގ��x��p���������̗ގ��x���͂ɑ΂��āA�������̓f�[�^�̂̎����e�L�X�g����؂̕]�����@�A���k���@�̈Ⴂ�ɂ�錤�����s�������A�{�����ł͉������̓f�[�^�̃e�L�X�g���Ƀs�b�`�f�[�^���܂ނ��Ƃɂ��Ă̒ǉ��������s���B}

% �ŏI�X�V�����̑}��
%\compheading

\begin{document}

% �^�C�g����\��������
\maketitle

\begin{multicols}{2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% (1/8)�͂��߂�
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{�͂��߂�}
���ݗl�X�Ȏ������f�[�^������Ă���B�������A���y�╶�͂��u�f�[�^�v�Ƃ��Ĉ�����悤�ɂȂ��Ă��Ă���B�ߔNMing Li�炪���k�ގ��x�Ɋ�Â��f�[�^�Ԃ̗ގ��x�Ɋւ��鋗����\��similarity metric�𔭈āi����DNA�̗ގ��x�⌾��̗ގ��x�A���y�̗ގ��x����ɗL�p���Ƃ������Ƃ��������Ă���j�����B\\
�@��N�A�r�x���A���c�������k�ގ��x��p���������̗ގ��x���͂ɑ΂��āA�������̓f�[�^���h���S���X�s�[�`�Ƃ��������F���\�t�g�ŉ����f�[�^���e�L�X�g���������̂�p���Ď������s�����B�{�����ł͉������̓f�[�^�������^�����Ƃ����\�t�g�E�F�A�ɂ��s�b�`���𒊏o���A���̏����e�L�X�g�ɕt�������f�[�^��p���A���N�̃f�[�^�Ƃ̔�r���s���ǉ������Ƃ���B\\
�@��Q�͂ł�Kolmogorov�L�q�ʂɂ��āA��R�͂ł͈��k�ގ��x�ɂ��āA��S�͂ł͉����̃s�b�`���̐������A��T�͂ł̓N���X�^�����O�̐����A��U�͂ł͎g�p�����N���X�^�����O�̊T�v�ɂ��ďq�ׁA��V�͂Ŏ����̊T�v�ƌ��ʂɂ��Đ��������A��W�͂Ŗ{�����ł̍l�@�����q�ׂ�B\\

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%
% (2/8)Kolmogorov�L�q�ʂ̒�`
%
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\section{Kolmogorov�L�q�ʂ̒�`}
   \subsection{Kolmogorov�L�q��}
����^����ꂽ�L���̑Ώ�(�Ⴆ�Ε�����)�Ɋ܂܂����ʂ�,���̑Ώۂ𐶐�
   ����v���O�����̃T�C�Y�i���Ȃ킿�r�b�g���j�ƒ�`����B������,�����Ō�
   ���f��������v���O�����f�Ƃ͑S�Ẵ���������̏�����Ԃ���X�^�[�g��,����
   �Ώۂ��o�͂��Ē�~����v���O�����̂��Ƃł���B���̏ꍇ,�ǂ�ȃv���O��
   �~���O�����I��ł�,���ꂪ�Ó��ł���΂��̏��ʂ̍�,���Ȃ킿�e�v��
   �O�����̃T�C�Y�̍��͒萔���̍������Ȃ����Ƃ��ؖ�����Ă���B���̂悤��
   ��`�������̗ʂ̂��Ƃ�kolmogorov�L�q�ʂƂ����B\\
   $S$���v���O��������A$|p|$���v���O�����T�C�Y�Ƃ���ƁA�Ώ�$x$��Kolmogorov�L�q��$K_s(x)$�́A�ȉ��̂悤�ɒ�`�����B
\begin{displaymath}
K_s(x)=min\{|p|:S(p)=x\}
\end{displaymath}
�@���Ȃ킿$K_s(x)$�́A�h�v���O��������$S$�ɂ�����$x$�𐶐�����ŏ��̃v���O�����̒����h�ƍl���Ă������낤�B\\
�@���ɕ⏕���$y$���^�����Ă���Ƃ��̑Ώ�$x$�ɂ��Ă̋L�q�ʁi���΋L�q�ʁj�ɂ��čl����B������$x$���A�v�Z�\�֐��i�C���^�v���^�֐��j$f$�A����ɕ�����$p$��$y$�ɂ��$f(p,x)=x$�ƋL�q���邱�Ƃ��l����B�C���^�v���^�֐�$f$�̂��ƂŁA�⏕�֐�$y$�ɑ΂���$x$�̋L�q��$K_f$�����̂悤�ɒ�`����B
\begin{displaymath}
K_f(x|y)=min\{|p|:P\in\{0,1\}*f(p,y)=x\}
\end{displaymath}
�⏕���$y$�͂��炩���ߗ^�����Ă������,���̏�񂪐����������Ώ�$x$
�̏����܂�ł���ΑΏۂ��o�͂���v���O�����͗e�ՂɂȂ�B\\
�@�܂��A$x$��$y$����ʂł���`�ŏo�͂�����ŒZ�̃v���O�����̒���$K(xy)$�Ƃ���킷�B$O(logK(xy))$�̌덷�͈͂ł́A
\begin{displaymath}
K(xy)=K(x)+K(y|x)
\end{displaymath}
�ƂȂ邱�Ƃ��ؖ�����Ă���B
   \subsection{����}
���΋L�q��$K(x|y)$����΋L�q��$K(x)$��肩�Ȃ菬�����ꍇ�A�u$y$��$x$�ɂ�
���Ă̏������Ȃ�܂�ł���v�Ɖ��߂��邱�Ƃ��o����B���������āA�萔���̍��ق𖳎�����΁A \\
 \begin{displaymath}
I(x:y)=K(y)-K(y|x)
\end{displaymath}
�́h$y$�Ɋ܂܂��$x$�̏��ʁh�Ƃ��邱�Ƃ��o����B�܂��A$K(x|x)$�ƂȂ�$x$��I�ׂ΁A
\begin{displaymath}
I(x:x)=K(x)
\end{displaymath}
�ƂȂ�B\\
�����ŏ��̑Ώې��Ƃ������Ƃ��l����B��q���$O(logK(xy))$�̌덷�͈͂ł́A
 \begin{displaymath}
K(xy)=K(x)+K(y|x)
\end{displaymath}
�ł���B����������
 \begin{displaymath}
I(x:y)=I(y:x)
\end{displaymath}
����������B
\\
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%
% (3/8)���k�ގ��x
%
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\section{���k�ގ��x}
���w�ɂ����ċ�����ԂƂ́C�C�ӂ�2�_�Ԃŋ�������߂�ꂽ��Ԃ̂��Ƃ������B\\
\fbox{��`}\\
����W��$X$��̋����Ƃ́C�����l�֐�$d:X\times X\rightarrow R$�ŔC�ӂ�$x,y,z\in X$�ɑ΂��Ď��̂悤�Ȑ����𖞂����B\\
\begin{eqnarray}
&&d(x,y)\geq 0
\nonumber \\
&&d(x,y)=0\Leftrightarrow x=y
\nonumber \\
&&d(x,y)=d(y,x)
\nonumber \\
&&d(x,y)\leq d(x,z)+d(z,y) :�O�p�s����
\nonumber
\end{eqnarray}
\\
��������ƂɁC��񋗗��ɂ��čl����B

Ming Li,Xin Chen��̌����ł́C���Ɋւ��鋗����W�������Ă���,�C�ӂ̕�����$x,y$
�ɂ��āC�ȉ��̂悤�Ɍ��߂Ă���B\\
\begin{eqnarray}
d(x,y)=\frac{max\{ K(x|y),K(y|x)\} }{max\{ K(x),K(y)\} }
\nonumber 
\end{eqnarray}
�܂��C$K(y)\geq K(x)$�Ƃ����Ƃ��C\\
\\
\begin{eqnarray}
d(x,y)&=&\frac{K(y|x)}{K(y)}
\nonumber 
\end{eqnarray}\\
����ɑ΂��Đ�ɏq�ׂ����ʂ̌�����p����ƁC\\
\begin{eqnarray}
d(x,y)&=&\frac{K(y)-I(x:y)}{K(y)}
\nonumber 
\end{eqnarray}\\
�ƂȂ�B�܂�2�߂Ŏ������ʂ�C$O(\log K(xy))$�͈̔͂ł�$K(xy)=K(x)+K(y|x)$�����藧�̂ŁC\\
\begin{eqnarray}
d(x,y)=\frac{K(xy)-K(x)}{K(y)}
\nonumber 
\end{eqnarray}\\
�ƕ\�����Ƃ��ł���B

\renewcommand{\labelenumi}{(\arabic{enumi})}
kolmogorov�L�q�ʂ͌v�Z�ł��̒l���Z�o���邱�Ƃ��s�\�ł��邽��,���k�v���O������p���Ēl���ߎ��I�ɋ��߂邱�ƂɂȂ�B
$bz2(x)$�𕶎���$x$��bzip2�ň��k�����Ƃ��̃t�@�C���T�C�Y�Ƃ���Ə�񋗗�$d(x,y)$�͈ȉ��̂悤�ɋߎ������B\\
\begin{eqnarray}
d(x,y)\fallingdotseq \frac{b2(xy)-bz(x)}{bz2(y)}
\nonumber
\end{eqnarray}
\\
�@�܂����k���@$C$���ȉ��𖞂����Ƃ�$O(\log n)$�̌덷�͈̔͂Ŗ��\�ł���Əؖ�����Ă���B\\
1.�C�ӂ̕�����$x$�ɑ΂���$C(xx)$=$C(x)$�ł���A�󕶎���ɂɑ΂��āA$C(��)$=0�ł���B\\
2.�C�ӂ̕�����$x,y$�ɑ΂���$C(xy)$��$C(x)$�B\\
3.�C�ӂ̕�����$x,y$�ɑ΂���$C(xy)$��$C(yx)$�B\\
4.�C�ӂ̕�����$x,y,z$�ɑ΂���$C(xy)+$C(z)$��$C(xz)$+$C(yz)$�B\\
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%
% (4/8)�����̃s�b�`���
%
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\section{�����̃s�b�`���}
�l�Ԃ̔������鉹���́A���т��U�����邱�Ƃɂ���Ĕ������鉹�����ɍ\������A�l�X�Ȏ��g���������܂ށB\\
�@���ɕꉹ����������鎞�ɐ��т��U�����A���̎��g�����s�b�`���g���Ƃ����B\\
\begin{center}
\includegraphics[width=9cm,height=6cm]{a.eps}
��ԉ��̐��i�ԁj���s�b�`���\\
\end{center}
�@���̎��g���ɕ����ɂ��������o��ƍl������B\\
�@����͉����^�����Ƃ����\�t�g�E�F�A���g�p���A�����̃s�b�`���𒊏o���A������f�[�^�̈ꕔ�Ƃ��ė��p����B\\
�@���̃f�[�^�͉����P�b�Ԃ�200�ɋ�؂�A���̉ӏ����̉ӏ��̃s�b�`���g���̒l�𓾂���B\\
\begin{center}
\includegraphics[width=8cm,height=7cm]{data.eps}
�s�b�`�̒��o
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% (5/8)�N���X�^�����O
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{�N���X�^�����O}
�����NJ�@�AUPGMA�Aquartet-method�̎O�̃N���X�^�����O��@���̗p�����B\\
�@�����͂ǂꂾ�����Ă��邩�������ړx�Ƃ��ċ�����p����Ƃ������������邱�ƂƁA��N�Ƃ̔�r���s�����߂Ɏg�p�����B
%%%%%%%%%%%
% NJ�@
\subsection{NJ�@}
�ߗ׌����@�ƌĂ΂�A�S�Ă̎}�̒����̑��a���ŏ��ɂȂ�悤�Ɍn�������쐬���Ă��������n�����B\\
�@�������ǂ��A���̕��@�ł͈����Ȃ��悤�ȑ�ʂ̃f�[�^���������Ƃ��ł��邪�A�o�͂��ꂽ�؂��œK�Ƃ͌���Ȃ��B
%%%%%%%%%%%
% UPGMA
\subsection{UPGMA}
���ϋ����@�ƌĂ΂��P���Ȍn��������@�ŁA�ł��߉��ȃN���X�^�Ԃ̋����̕��ς����߂Ȃ���n�������쐬����B
�@�t���猈�܂�A�Ō�̍��̈ʒu�����܂�L���n�����B
%%%%%%%%%%%
% ����Ă���
\subsection{Quartet Method}
�؂������\�ɂǂ̒��x�����Ă��邩�]������������A
�����_���ɖ؂�ύX���]���l���X�V���Ă����q���[���X�e�B�b�N�i���s����j�A���S���Y���ł���B\\
�@NJ�@�AUPGMA�@�Ɣ�r����Ƒ啝�ɏ������Ԃ�v����B

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% (6/8)�O����
%
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\section{�O����}
\subsection{�O�����̖ړI}

\subsection*{��s�����ł̑O�����̖ړI}

��s�����ł͕������ł̔�r���s���Ă����B�������͈�ʓI�ɂ�SJIS,EUC,UTF-8���̕����R�[�h�Ƃ��ĕ\������邪�A
���k�ގ��x���Z�o����ꍇ�ɂ͖��ʂȏ����܂�ł���͍̂D�܂����Ȃ��ׁA���Ȍ��Ƀf�[�^��\���ׂ��ł���B\\
�����ŁA�����𐔒l�ɒu�������ĒP�������Ă���B\\


\subsection*{�{�����ł̑O�����̖ړI}

�����𐔒l�ɒu�������ĒP�������Ă���̂͐�s�����Ɠ��������A�{�����ł͕������Ƀs�b�`����g�ݍ��ޕK�v������B\\
�@��s�����������G�����@�������ɍl�����邽�߁A�{�����̗v�_�Ƃ�������B\\
�@����͑O�������Q��ތ������A�������s�����B\\

\subsection{�������̒P����}
�������̒P�����̋�̓I�Ȏ�@�ɂ��ďq�ׂ�B\\
�@���\�́u���v�u���v�u���v�Ƃ��������̊e�����R�[�h�ł̕\���ƁA�P�����ϊ����s������̕\���ł���B\\
�@SJIS,EUC�͂P������2byte(UTF-8��3byte)�ŕ\�����邪�A�擪��1byte(UTF-8��2byte)�͋��ʂ̒l�������Ă���B\\
�@���k�ގ��x�����߂�ꍇ�͂��̂悤�ȏ��͕s�v�Ȃ��̂Ȃ��߁A�Ђ炪�Ȃɑ΂��ĕ����R�[�h���ɔԍ������蓖�āA�P����1byte�̏��ɕϊ����s���B\\
\\
�P������\\
\begin{tabular}{|c|c|c|c|c|}
\hline
���� & SJIS & EUC & UTF-8 & �P���� \\
\hline
�� & 0x82A0 & 0xA4A2 & 0xE38182 & 0x02 \\
\hline
�� & 0x82A9 & 0xA4AB & 0xE3818B & 0x0B \\
\hline
�� & 0x82B3 & 0xA4B5 & 0xE38195 & 0x15 \\
\hline
\end{tabular}
\\
\subsection{�O�����P}

�s�b�`���(Hz)�̒l�͘b�҂ɂ���č������邪�A�T��300Hz�O��܂ł̒l�ō\������Ă��邽�߁A2byte�ŕ\�����Ƃɂ���B\\
�@�������͐�̒P�����ɏ]���ϊ����s�����A�s�b�`���Ƃ̃f�[�^�̒����𑵂��邽�߂�2byte�ŕ\�����Ƃɂ���B\\
�@���̏������݂ɕ��ׁA�����f�[�^�Ƃ���B\\
�@���̎����f�[�^�́A�������Ƀs�b�`�������̂܂ܕt�����邱�Ƃ�ړI�Ƃ��Ă���B
\\
\\
�O�����P��\\
\begin{tabular}{|c|c|c|}
\hline
���� & ����(�P������) & �s�b�`(Hz)\\
\hline
�� & 10�F0x000A & 116�F0x0074\\
\hline
�� & 48�F0x0030 & 155�F0x009B\\
\hline
�� & 2�F0x0002 & 145�F0x0091\\
\hline
�� & 21�F0x0015 & 98�F0x0062\\
\hline
�� & 83�F0x0053 & 130�F0x0082\\
\hline
�� & 12�F0x000C & 140�F0x008C\\
\hline
\end{tabular}
\\
�������f�[�^(16�i���\��)\\
000A 0074 0030 009B 0002 0091 0015 0062 0053 0082 000C 008C\\

\subsection{�O�����Q}
����̘b�҂̃s�b�`���(Hz)�̕��ϒl���Ƃ�A���̒l��128(1byte�����Ȃ������\��0�`255�̒����l)�̍����I�t�Z�b�g�l�Ƃ���B\\
�@���鎞�_�̃s�b�`���(Hz)����I�t�Z�b�g�l�������A���̒l���s�b�`���Ƃ��Ďg�p���A1byte�ŕ\���B\\
�@�������͐�̒P�����ɏ]���ϊ����s���A1byte�ŕ\���B\\
�@���̏������݂ɕ��ׁA�����f�[�^�Ƃ���B\\
�@���̎����f�[�^�́A�������Ƀs�b�`����t������̂͑O�����P�Ɠ��������A
�s�b�`���̘b�҂̒j�������̌l���𕽋ω����邱�Ƃ�ړI�Ƃ��Ă���B\\
\\
�O�����Q��\\
�s�b�`��񕽋ϒl�F147\\
�I�t�Z�b�g�l�F19\\
\begin{tabular}{|c|c|c|}
\hline
���� & ����(�P������) & �s�b�`(Hz)\\
\hline
�� & 10�F0x0A & 116 - 19 = 97�F0x61\\
\hline
�� & 48�F0x30 & 155 - 19 = 136�F0x88\\
\hline
�� & 2�F0x02 & 145 - 19 = 126�F0x7E\\
\hline
�� & 21�F0x15 & 98  - 19 = 79�F0x4F\\
\hline
�� & 83�F0x53 & 130 - 19 = 111�F0x6F\\
\hline
�� & 12�F0x0C & 140 - 19 = 121�F0x79\\
\hline
\end{tabular}
\\
�������f�[�^(16�i���\��)\\
0A61 3088 027E 154F 536F 0C79\\
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%
% (7/8)����
%
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\section{����}
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\begin{center}
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\section{�Q�l����}
\begin{enumerate}
\item�@�J ����@��񐔊w���ʍu�`�i2008�j
\item�@Ming Li and Paul M.B.Vitanyi. �n�ӎ��|��
Kolmogorov Complexity and its Applications. �@
�R���s���[�^��b���_�n���h�u�b�N(1994)Ming Li and Paul M.B.Vitanyi. �n�ӎ��|��
Kolmogorov Complexity and its Applications. �@
�R���s���[�^��b���_�n���h�u�b�N(1994)
\item�@���� ���v�@������������i2005�j
\item�@���� �_���@Kolmogorov�L�q�ʂɊ�Â��ގ��x��p���������̎������ށ@(2007)
\item�@�x�� �K�i�@Kolmogorov�L�q�ʂɊ�Â��ގ��x��p���������̎������ށ@(2007)
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\end{document}
