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\title{Cluster Weighted Modelling: A mixture of E-M experts applied to 
analysis of biometric data}

\input epsf

\author{Matthew Gray}


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\begin{document}
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{\samepage \clearpage $c_m$
}


\newpage

{\samepage \clearpage $s$
}


\newpage

{\samepage \clearpage $\vec{x}$
}


\newpage

{\samepage \clearpage \begin{equation}p(\vec{x}, s) = \sum_{m=1}^{M} p(s|\vec{x},c_m) p(\vec{x}|c_m) p(c_m)
\end{equation}
}


\newpage

{\samepage \clearpage $p(\vec{x}|c_m)$
}


\newpage

{\samepage \clearpage $p(s_m|\vec{x}, c_m) = 1$
}


\newpage

{\samepage \clearpage \begin{equation}p(c_m|\vec{x},s) = \frac{p(\vec{x},s|c_m) p(c_m)}{\sum_{m=1}^M p(\vec{x}, s|c_m) p(c_m)}
\end{equation}
}


\newpage

{\samepage \clearpage $p(c_m)$
}


\newpage

{\samepage \clearpage $p(\vec{x}, s)$
}


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{\samepage \clearpage \begin{figure}[bht]
\begin{center}
\mbox{\epsfysize=3in \epsfbox{cvalid.ps}}
\end{center}

\label{fig:cv}
\end{figure}
}


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{\samepage \clearpage \begin{figure}[htb]
\begin{center}
\mbox{\epsfysize=3in \epsfbox{res.ps}}
\end{center}

\label{prob}
\end{figure}
}


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\end{document}
