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WfccmAlgorithmWGA
(06 Feb 2012,
WillGray
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---+ WGA Algorithm WGA = %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} \frac{d_b}{k_1d_{1}+k_2d_{2}+\alpha} \end{displaymath} %ENDLATEX% --- * description of letters * %$n_i$% is the total number of items in group i. * %$t_i$% is the number of pairings within a group. * %$d_i$% is the average distance among all sample pairs within the group. * %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} \alpha \end{displaymath} %ENDLATEX% is used to make sure that division by zero never happens. * detailed formula * %$d_b = | mean_1 - mean_2 |$% * %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} t_i = (n_i-1)+(n_i-2)+...+(n_i-(n_i-1)) = \frac{n_i(n_i-1)}{2} \end{displaymath} %ENDLATEX% * %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} k_1=\frac{t_1}{t_1+t_2} \end{displaymath} %ENDLATEX% * %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} k_2=\frac{t_2}{t_1+t_2} \end{displaymath} %ENDLATEX% * %$d_i = \frac{|v_1 - v_2| + |v_1 - v_3| + ... + |v_1 - v_{n_i}| + |v_2 - v_3| + ... + |v_2 - v_{n_i}| + ... + |v_{n_{i-1}} - v_{n_i}|}{t_i} $% * %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} \alpha \end{displaymath} %ENDLATEX% * if %$k_1d_{1}+k_2d_{2}$% == 0 * if %$ d_{b}$% == 0 then WGA = 0 * else %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} \alpha \end{displaymath} %ENDLATEX% = %$\frac {d_{b}} {1000}$% %GRAY% WGA = 1000 means there is no sample variation between two groups, therefore, it is an alarm of that gene/protein %ENDCOLOR% * else %BEGINLATEX{inline="1" density="160"}% \begin{displaymath} \alpha \end{displaymath} %ENDLATEX% = 0 ---++ WGA documentations * Paper * [[http://content.nejm.org/cgi/content/full/344/8/539/ URL]] * [[%ATTACHURL%/WGA.pdf][PDF version]] * [[http://research.nhgri.nih.gov/microarray/ Supplemental Information]]
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Topic revision: r20 - 06 Feb 2012,
WillGray
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