images.pl

高斯混合模型算法

 WIDTH="135" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.gif"
 ALT="$ X=\{x_1, x_2,\cdots,x_N\}$">|; 

$key = q/ensuremathboldsymbol{Sigma}_k;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.gif"
 ALT="$ \ensuremath\boldsymbol{\Sigma}_k$">|; 

$key = q/f_k(ensuremathmathbf{x}_i)=logp(ensuremathmathbf{x}_i|q_k,ensuremathboldsymbol{Theta})+logP(q_k|ensuremathboldsymbol{Theta});MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.gif"
 ALT="$ f_k(\ensuremath\mathbf{x}_i) = \log
p(\ensuremath\mathbf{x}_i\vert q_k,\ensuremath\boldsymbol{\Theta}) + \log P(q_k\vert\ensuremath\boldsymbol{\Theta})$">|; 

$key = q/displaystylelogP(q_k|X,Theta)simeqlogp(X|q_k,Theta)+logP(q_k|Theta);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.gif"
 ALT="$\displaystyle \log P(q_k\vert X,\Theta) \simeq \log p(X\vert q_k,\Theta) + \log P(q_k\vert\Theta)
$">|; 

$key = q/displaystylexinq_k;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.gif"
 ALT="$\displaystyle x \in q_k$">|; 

$key = q/P(q_k|ensuremathboldsymbol{Theta});MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.gif"
 ALT="$ P(q_k\vert\ensuremath\boldsymbol{\Theta})$">|; 

$key = q/F_2;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.gif"
 ALT="$ F_2$">|; 

$key = q/displaystyle=sum_{k=1}^{K}sum_{n=1}^{N}P(q_k|x_n,Theta)logp(x_n|Theta);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.gif"
 ALT="$\displaystyle = \sum_{k=1}^{K} \sum_{n=1}^{N} P(q_k\vert x_n,\Theta) \log p(x_n\vert\Theta)$">|; 

$key = q/hat{ensuremathboldsymbol{Sigma}}_{(10000)}=;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.gif"
 ALT="$ \hat{\ensuremath\boldsymbol{\Sigma}}_{(10000)} =$">|; 

$key = q/hat{ensuremathboldsymbol{Sigma}};MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img51.gif"
 ALT="$ \hat{\ensuremath\boldsymbol{\Sigma}}$">|; 

$key = q/includegraphics[height=0.98textheight]{iso};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="748" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img118.gif"
 ALT="\includegraphics[height=0.98\textheight]{iso}">|; 

$key = q/hat{ensuremathboldsymbol{mu}}_{(1000)}=;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.gif"
 ALT="$ \hat{\ensuremath\boldsymbol{\mu}}_{(1000)}
=$">|; 

$key = q/x_j;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.gif"
 ALT="$ x_j$">|; 

$key = q/displaystylep(X|Theta)=prod_{i=1}^{N}p(x_i|Theta);;;Leftrightarrow;;;logp(X|Theta)=sum_{i=1}^{N}logp(x_i|Theta);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.gif"
 ALT="$\displaystyle p(X\vert\Theta) = \prod_{i=1}^{N} p(x_i\vert\Theta)
\;\;\; \Leftrightarrow \;\;\;
\log p(X\vert\Theta) = \sum_{i=1}^{N} \log p(x_i\vert\Theta)
$">|; 

$key = q/kin{;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.gif"
 ALT="$ k \in
\{$">|; 

$key = q/P(q_k^{(i)}|ensuremathmathbf{x}_n,ensuremathboldsymbol{Theta}^{(i)});MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.gif"
 ALT="$ P(q_k^{(i)}\vert\ensuremath\mathbf{x}_n,\ensuremath\boldsymbol{\Theta}^{(i)})$">|; 

$key = q/displaystylehat{mu}=frac{1}{N}sum_{i=1}^{N}x_i;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.gif"
 ALT="$ \displaystyle \hat{\mu} = \frac{1}{N}
\sum_{i=1}^{N} x_i$">|; 

$key = q/logp(X|q_k,ensuremathboldsymbol{Theta});MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.gif"
 ALT="$ \log p(X\vert q_k,\ensuremath\boldsymbol{\Theta})$">|; 

$key = q/displaystylelogp(x|Theta);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.gif"
 ALT="$\displaystyle \log p(x\vert\Theta)$">|; 

$key = q/displaystyle;logp(X_3|Theta_4).;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.gif"
 ALT="$\displaystyle \; \log p(X_3\vert\Theta_4).
$">|; 

$key = q/Sigma_k;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.gif"
 ALT="$ \Sigma_k$">|; 

$key = q/mu_k;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.gif"
 ALT="$ \mu_k$">|; 

$key = q/xcirclearrowleft{calN}(mu,Sigma);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.gif"
 ALT="$ x \circlearrowleft {\cal
N}(\mu,\Sigma)$">|; 

$key = q/B;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img52.gif"
 ALT="$ B$">|; 

$key = q/{calN}_1:;ensuremathboldsymbol{Theta}_1=left(left[{array}{c}7301090{array}right],left[{array}{cc}8000&00&8000{array}right]right);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="258" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.gif"
 ALT="$ {\cal N}_1: \; \ensuremath\boldsymbol{\Theta}_1 = \left(
\left[\begin{array}{...
...right],
\left[\begin{array}{cc}8000 &amp; 0  0 &amp; 8000\end{array}\right]
\right)$">|; 

$key = q/displaystyleSigma_2=left[{array}{cc}8000&00&18500{array}right];MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.gif"
 ALT="$\displaystyle \Sigma_2 = \left[ \begin{array}{cc}
8000 &amp; 0 \\\\
0 &amp; 18500
\end{array} \right]
$">|; 

$key = q/displaystyle{calL}(Theta);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.gif"
 ALT="$\displaystyle {\cal L}(\Theta)$">|; 

$key = q/logP(q_{text{slasheslash}}|x);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.gif"
 ALT="$ \log P(q_{\text{/e/}}\vert x)$">|; 

$key = q/logleft(detleft(Sigmaright)right);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.gif"
 ALT="$ \log \left( \det\left(\Sigma\right) \right)$">|; 

$key = q/hat{mu}_{(10000)}=;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.gif"
 ALT="$ \hat{\mu}_{(10000)}
=$">|; 

$key = q/hat{ensuremathboldsymbol{mu}}_{(10000)}=;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.gif"
 ALT="$ \hat{\ensuremath\boldsymbol{\mu}}_{(10000)}
=$">|; 

$key = q/ensuremathboldsymbol{Theta}_i=(ensuremathboldsymbol{mu}_i,ensuremathboldsymbol{Sigma}_i);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.gif"
 ALT="$ \ensuremath\boldsymbol{\Theta}_i = (\ensuremath\boldsymbol{\mu}_i,\ensuremath\boldsymbol{\Sigma}_i)$">|; 

$key = q/F_1;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.gif"
 ALT="$ F_1$">|; 

$key = q/{calN}left(mu_{text{slashislash}},Sigma_{text{slasheslash}}right);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.gif"
 ALT="$ {\cal N}\left (\mu _{\text {/i/}},\Sigma _{\text {/e/}}\right )$">|; 

$key = q/Box;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img43.gif"
 ALT="$ \Box$">|; 

$key = q/p(X|q_k,ensuremathboldsymbol{Theta})P(q_k|ensuremathboldsymbol{Theta});MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.gif"
 ALT="$ p(X\vert q_k,\ensuremath\boldsymbol{\Theta}) P(q_k\vert\ensuremath\boldsymbol{\Theta})$">|; 

$key = q/d-1;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.gif"
 ALT="$ d-1$">|; 

$key = q/ensuremathboldsymbol{Sigma};MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.gif"
 ALT="$ \ensuremath\boldsymbol{\Sigma}$">|; 

$key = q/displaystylep(X|ensuremathboldsymbol{Theta})=prod_{i=1}^{N}p(ensuremathmathbf{x}hboldsymbol{mu},ensuremathboldsymbol{Sigma})}(ensuremathmathbf{x}_i);MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.gif"
 ALT="$\displaystyle p(X\vert\ensuremath\boldsymbol{\Theta}) =
 \prod_{i=1}^{N} p(\ens...
...emath\boldsymbol{\mu},\ensuremath\boldsymbol{\Sigma})}(\ensuremath\mathbf{x}_i)$">|; 

$key = q/displaystyleensuremathboldsymbol{Sigma}_3=left[{array}{cc}8000&84008400&18500{array}right];MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.gif"
 ALT="$\displaystyle \ensuremath\boldsymbol{\Sigma}_3 = \left[ \begin{array}{cc}
8000 &amp; 8400 \\\\
8400 &amp; 18500
\end{array} \right]
$">|; 

$key = q/parallelA-Bparallel_2;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.gif"
 ALT="$ \parallel A-B \parallel_2$">|; 

$key = q/displaystylefrac{P(q_k^{(i)}|Theta^{(i)})cdotp(x_n|mu_k^{(i)},Sigma_k^{(i)})}{sum_jP(q_j^{(i)}|Theta^{(i)})cdotp(x_n|mu_j^{(i)},Sigma_j^{(i)})};MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.gif"
 ALT="$\displaystyle \frac{P(q_k^{(i)}\vert\Theta^{(i)}) \cdot p(x_n\vert\mu_k^{(i)},\...
...m_j P(q_j^{(i)}\vert\Theta^{(i)}) \cdot p(x_n\vert\mu_j^{(i)},\Sigma_j^{(i)}) }$">|; 

$key = q/x_i;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.gif"
 ALT="$ x_i$">|; 

$key = q/hat{Sigma}_{(1000)}=;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.gif"
 ALT="$ \hat{\Sigma}_{(1000)} =$">|; 

$key = q/ensuremathboldsymbol{mu}_k;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.gif"
 ALT="$ \ensuremath\boldsymbol{\mu}_k$">|; 

$key = q/displaystyle=logsum_QP(Q|X,ensuremathboldsymbol{Theta})p(X|ensuremathboldsymbol{Theta});MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="175" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.gif"
 ALT="$\displaystyle = \log \sum_Q P(Q\vert X,\ensuremath\boldsymbol{\Theta})p(X\vert\ensuremath\boldsymbol{\Theta})$">|; 

$key = q/displaystyleP(q_k^{(i+1)}|Theta^{(i+1)})=frac{1}{N}sum_{n=1}^{N}P(q_k^{(i)}|x_n,Theta^{(i)});MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.gif"
 ALT="$\displaystyle P(q_k^{(i+1)}\vert\Theta^{(i+1)}) = \frac{1}{N} \sum_{n=1}^{N} P(q_k^{(i)}\vert x_n,\Theta^{(i)}) $">|; 

$key = q/[P_{text{slashaslash}},P_{text{slasheslash}},P_{text{slashislash}},P_{text{slashoslash}},P_{text{slashyslash}}];MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.gif"
 ALT="$ [P_{\text{/a/}},P_{\text{/e/}},P_{\text{/i/}},P_{\text{/o/}},P_{\text{/y/}}]$">|; 

$key = q/A;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img51.gif"
 ALT="$ A$">|; 

$key = q/displaystylesum_{k=1}^{K}sum_{ensuremathmathbf{x}_ninq_k}logp(ensuremathmathbf{x}_n|ensuremathboldsymbol{Theta}_k),;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.gif"
 ALT="$\displaystyle \sum_{k=1}^{K} \sum_{\ensuremath\mathbf{x}_n \in q_k} \log p(\ensuremath\mathbf{x}_n\vert\ensuremath\boldsymbol{\Theta}_k),$">|; 

$key = q/K;MSF=1.4;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.gif"