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\centerline{\large PS Einf\"{u}hrung in die Bioinformatik SS2001}
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NC-001-2001
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\today

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\centerline{\Large\bf Sensitivity Analysis Of Neurons In ANN }
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\centerline{\Large\bf }

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\centerline{\bf Report}
\centerline{\bf }

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\centerline{\large Sebastian Gumpold \hfill Annemarie Mayer}
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\centerline{sgumpold@cosy.sbg.ac.at \hfill ammayer@cosy.sbg.ac.at}
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\centerline{Academic Supervisor Mag. Dipl.-Ing. Schwaiger Roland}

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\centerline{\large Department of Computer Science}
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\centerline{\large University of Salzburg}

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Correspondence to: \\
\centerline{Universit\"{a}t Salzburg} \\
\centerline{Institut f\"{u}r Computerwissenschaften und Systemanalyse} \\
\centerline{Jakob--Haringer--Stra\ss e 2} \\
\centerline{A--5020 Salzburg} \\
\centerline{Austria}

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\title{\Large\bf Sensitivity Analysis Of Neurons In ANN }

\author{{\large Sebastian Gumpold and Annemarie Mayer}\\
{\small Department of Computer Science} \\
{\small University of Salzburg} \\
{\small A--5020 Salzburg, Austria} \\
{\small \{sgumpold\}, \{ammayer\}@cosy.sbg.ac.at}}

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\chapter{Introduction}

\section{Overview}

As soon as a Neural Net is trained it solves a 
specific problem. In other words, the underlying 
structure of the problem is recognized by the Net. 
\\

If the original process is not well understood or 
not formally describeable, then the information 
which is extracted from the ANN can be a good basis 
for the process analysis. \\

Also, the significant parameters which influence the 
process and so the output are shown.

Therefore, we can extract from a Neural Network:
\begin{itemize}
  \item information about the model structure
  \item relationships between input and output
\end{itemize}

This is important to fulfill the following tasks:
\begin{itemize}
  \item model validation
  \item process optimation
  \item process control
\end{itemize}

\section{Methods}

\begin{description}
  \item{[Deif, 1983]:} The sensitivity of one input value
                       with respect to the others is found
                       by obtaining the partial derivative of
                       the responsible interest while holding the
                       others constant. The results are used to
                       determine which input factors have the greatest
                       relative influence on the output.
  \item{[Klimasaukas, 1991]:} This approach consists of the perturbation
                 of one input variable at a time and monitoring the outputs'
                 variations.
  \item{[Hashem, 1992]:} He describes a method for computing the network 
                 output sensitivities with respect to variations on the
                 inputs for multilayer feedforward ANNs with differentiable
                 activation functions. The sensitivities are computed one layer
                 at a time, starting from the output layer and proceeding
                 backwards towards the input layer.
  \item{[Zurada, 1993]:} He first defines a metric for the individual
                 input-output sensitivities, and then shows how this
                 metric can be used to determine the sensitivities of
                 each input to each output over the entire trainig set.
                 He also provides a prunning algorithm to prune irrelevant
                 input parameters.
  \item{[Engelbrecht, Cloete]:} Their sensitivity analysis originates from
                 a Taylor expansion of the NN output function $\mathcal{F}$ around
                 its parameters $\theta$, where $\theta$ can be an input
                 unit, hidden unit or a weight. Using this propertiy they
                 derive equations to calculate the sensitivity of the
                 network output to changes in input values, hidden unit
                 activations, and weights. This method can be used to
                 order input parameters according to significance, to
                 select the most informative patterns during training
                 and to refine rules extracted from trained networks.
\end{description}


\chapter{Next Section} 
... here goes your text...

\appendix
\chapter{Protocols}
\section{2001/03/21}

\begin{enumerate}
\item Responsible person for protocol: Annemarie Mayer
\item Participating persons: Sebastian Gumpold, Annemarie Mayer
\item Topics talked about:
   \begin{itemize}
      \item What is a neural network?
      \item What is sensitivity analysis?
      \item Which methods can be used to perform SA?
   \end{itemize}
\item New assignments
   \begin{itemize}
      \item Introduction
   \end{itemize}
\item Open questions
   \begin{itemize}
      \item What's about additional information in the secretariate?
      \item Is there a possibility to analyse only single neurons?
      \item Under which aspects shall we order the different methods?
      \item Shall we develop our own methods?
      \item Do we have to treat this topic only theoretically?
      \item \ldots
   \end{itemize}
\end{enumerate}


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