%%\documentstyle[12pt,eclepsf]{article}
\documentstyle[eclepsf]{article}
\textheight 260mm
\topmargin 5mm
\textwidth 180mm
\oddsidemargin -7mm

\pagestyle{myheadings}
\markright{(PRIP-2005 -- at Minsk, Belarus)}
\thispagestyle{empty}

\begin{document}
\begin{Large}


%% --- (title) ---
\begin{center}
{\LARGE{\bf 
Can a negative selection detect unique non-self cell \\
in an infinitely large number of self cells? \\
\hspace*{1in}\\
\hspace*{1in}\\
\hspace*{1in}\\ 
Akira Imada  \\
\hspace*{1in}\\
Brest State Technical University \\ 
\hspace*{1in}\\
Republic of Belarus}}
\end{center}

%% Brest is ... I like the city and Misk is also one of my favarite ... 
%% I'm happy to have this oportunity to ...
%% Let me start with why this title. -> 

%% ----- motivation -----
\clearpage
\begin{center}
{\bf
``Can a negative selection detect unique non-self cell \\
in an infinitely large number of self cells?'' \\

\hspace*{1in}\\
$\Downarrow$ \\
\hspace*{1in}\\

Our Goal is \\
\hspace*{1in}\\
to search for only one ABNORMAL(no-self) pattern \\
\hspace*{1in}\\
hidden in \\
\hspace*{1in}\\
an enormous amount of NORMAL (self) patterns\\
\hspace*{1in}\\
by \\
\hspace*{1in}\\
NEGATIVE SELECTION of Artificial Immune System\\
}
\end{center}

%% --- The topic was motivated by our work a couple of years ago ---
\clearpage
\begin{center}
{\bf 
We came accross \\
\hspace*{1in}\\
an extremely difficult \\
PEAK \\
to be searched for \\
\hspace*{1in}\\
in a \\
FITNESS LANDSCAPE \\
\hspace*{1in}\\
explored by an \\
EVOLUTIONARY COMPUTATION
}
\end{center}


%% --- to be more specific \clearpage
\clearpage
\begin{center}
{\bf 
To realize an \\
\hspace*{1in}\\
ASSOCIATIVE MEMORY\\
\hspace*{1in}\\
we use \\
\hspace*{1in}\\
SPIKING NEURONS \\
\hspace*{1in}\\
whose learning is by\\
\hspace*{1in}\\
EVOLUTIONARY COMPUTATIONS.
}
\end{center}



%% --- before that topic of exploiting spiking neurons, our interest was on traditional... 
%% --- also using evolutinary computations.
\clearpage
\noindent
{\bf $\Box$ Fitness Landscape on all possible configuration of weights}\\

\begin{itemize}
\item Traditional Hopfield Model 
   \begin{itemize}
   \item[]$\Rightarrow$ Everywhere rugged and many peaks.
   \end{itemize}
\item[]
\item Spiking Neurons 
   \begin{itemize}
   \item[]$\Rightarrow$ unique peak and everywhere else 
                        is flatland of fitness 0.
   \end{itemize}
\end{itemize}

%% --- what is fitness landscape
\clearpage
\noindent
{\bf $\Box$ A fictitious plot of fitness landscape}\\
\begin{figure}[h]
 \begin{center}
  \epsfile{file=fitness-ls-2d.eps,width=11.25cm,height=6cm}
 \end{center}
\end{figure}



%% --- our problem might remind us of
\clearpage
\noindent
{\bf $\Box$ A Needle in a Haystack}\\
\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=a-needle-0.eps,width=15cm,height=3cm}
 \end{center}
\end{figure}


%% --- Our peculiar fitness landscape is somehow ...
\clearpage
\noindent
{\bf $\Box$ A tiny-flat-island-in-a-huge-lake}\\
\begin{figure}[hbtp]
 \begin{center}
  \epsfile{file=island-0.eps,width=15cm,height=3cm}
 \end{center}
\end{figure}

%% due to a synaptic plasticity
%% cirtain reageon of top area

%% this is our terget function and  we can controll the complexity by...
%% but essentially equivalent to a-needle...
%%
%% but here our target is the extreme case of needle

%% --- (Figure) ---
\clearpage
\noindent
{\bf $\Box$ What can we do?}\\

%% Hinton Nowlan's needle is one configuration of 20 binary bits. So...

\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=needle-b-box.eps,width=13.5cm,height=6cm}
 \end{center}
\end{figure}




%% --- how difficult
\clearpage
\noindent
{\bf $\Box$ How difficult?}\\

\begin{itemize}
\item Random Search  %% example  
\begin{center}
$2^{20} = 1,048,576$
\end{center}
%% within, say, 1 minute search at most.
%% we observed however, more than 25
\item[]
\item Lifetime Learning -- Baldwin Effect (Hinton \& Nowlan 1995?)
%% again not possible for more than 25 bits
\end{itemize}
\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=a-needle-0.eps,width=10cm,height=2cm}
%% \caption{Search with lifetime learning (Boldwin Effect)}
 \end{center}
\end{figure}


\clearpage
\noindent
{\bf $\Box$ Random Search vs Baldwin Effect}\\
\begin{figure}[h] 
 \begin{center}
 \epsfile{file=mesa-random.eps,width=8cm,height=6.0cm}
  \epsfile{file=mesa-learning.eps,width=8cm,height=6.0cm}
%% \caption{Number of individuals who happens to be in a point in the target
%%          region $A$ out of randomly created 10,000 individuals.}
%% \caption{Average Number of random individuals needed to find a one who 
%%          succeeded in reaching the target via 1000 times of lifetime 
%%          learning.}
 \end{center}
\end{figure}






%% --- When we talk about this issue in our community, many people claimed
\clearpage
\begin{center}
{\LARGE 
They say \\
\hspace*{1in}\\
``Why don't you use Artifitial Immune System? \\
It'll be easy?''  \\
\hspace*{1in}\\
\hspace*{1in}\\
Is it really true?
}
\end{center}



%% --- (Figure) ---
\clearpage
\noindent
{\bf 1. An immune approach --- Sphere Detectors}\\

\begin{figure}[h]
 \begin{center}
   \epsfile{file=detector.eps,width=12cm,height=6cm}
 \end{center}
\end{figure}

%% --- (Figure) ---
\clearpage
\noindent
{\bf What if top area shrinks?}\\

\begin{figure}[h]
 \begin{center}
%% \epsfile{file=result-2.eps,width=6.0cm,height=4.6cm}
 \epsfile{file=result-1.eps,width=14cm,height=6cm}
%\caption{The number of iteration required to find 500 successful detectors 
%         (Left), and the number of successes when 500 detectors tried to 
%          detect 500  non-self samples, 
%          that is, the number of successes out of 25000 events (Right). 
%          Both are as a function of value of $a$ 
%          when we experimented with the Algorithm-1 
%          with $r_s = 0.1$ in 2-dimensional space.
\end{center}
\end{figure}

%% --- (Figure) ---
\clearpage
\noindent
{\bf 2. A Fuzzy approach}

%% Not direct AIS but evolve fuzzy rule using AIS and or EC
%% 2. Fuzzy Rule for island -> figure
%%   (3 3 3 ... 3) -> but the smaller the more difficult

\begin{figure}[h]
 \begin{center}
   \epsfile{file=member-s.eps,width=7cm,height=3.5cm}
   \epsfile{file=mu-1.eps,width=7cm,height=3.5cm}
 \end{center}
\end{figure}

\hspace*{2in}$\Downarrow$ \\
\hspace*{2.5in}\\
\hspace*{1.35in}$(M M M M M M \cdots M)$ \\
\hspace*{2.5in}\\
\hspace*{2.223in}$\Downarrow$ \\
\hspace*{2.3in}\\
\noindent
IF $x_1$ is Middle, and $\cdots$, and $x_{20}$ is Middle THEN no-self.


%% --- (Figure) ---
\clearpage
\noindent
{\bf 3. Negative Selection}\\

%here
%negative selection 
%with the target of extreme case of needle not island

%% --- (Figure) ---
%actually we reach the needle if n is small enough

\newtheorem{algorithms}{Algorithm}
\begin{algorithms}[Exhaustive Detector Generating Algorithm]
\hspace{.5in}\\
\begin{itemize}
\setlength{\itemsep}{0pt}
\item[1.] Create $N_s$ samples of self cells at random.
\item[2.] Create a population of candidate detectors at random; 
\item[3.] Discard it if it matches self, otherwise 
          take it as a detector,
%% If it matches with any self cell, then it is discarded, 
%% otherwise it is added to D
%% \item[5.] Repeat 2 - 5 until D has $N_d$ valid detectors.
\end{itemize}
\end{algorithms}


%% --- (Figure) ---
\clearpage
\begin{figure}[hb]
 \begin{center}
 \epsfile{file=result.eps,width=14cm,height=6cm}
 %% \caption{Number of iterations needed to find a detector 
 %%            to detect the needle}
 \end{center}
\end{figure}

%alas worse than random search









%% --- (Figure) ---
\clearpage
\noindent
{\bf 3. Negative Selection -- II}\\
\hspace*{1in}\\
\begin{algorithms}[Greedy Detector Generating Algorithm]
\hspace{.5in}\\
\begin{center}
``perfect matching'' \\
$\Downarrow$\\ 
``r-contiguous matching'' 
\end{center}
\end{algorithms}

%% --- (Figure) ---
\clearpage
any 2-contiguous matching, e.g. (11*) works when\\
\begin{center}
(110), (111), (010), (011) $\Rightarrow$ SELF  \\
(000), (001), (100), (101) $\Rightarrow$ NO-SELF
\end{center}

no 2-contiguous matching, e.g. (11*) works when\\
\begin{center}
(110), (100), (011), (001) $\Rightarrow$ SELF  \\
(101), (111), (000), (010) $\Rightarrow$ NO-SELF
\end{center}


%% --- (Figure) ---
\clearpage
Still not easy if it might not be impossible.\\

However,\\

our original interst  on ``SEARCH for WEIGHTS''\\
is now on ``INTRUSION DETECTION''\\


1) Train the system with only but huge NORMAL sample.\\
 
Needle/Island $\Rightarrow$ intrusion





%% --- (Figure) ---
\clearpage
{\bf
\begin{table}[bhtp]
\begin{center}
\begin{tabular}{c c c c c}                                      \hline \hline
5.1      &   3.5    &   1.4    &   0.2    &   setosa         \\
4.9      &   3.0    &   1.4    &   0.2    &   setosa         \\
$\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$         \\
7.0      &   3.2    &   4.7    &   1.4    &   versicolor     \\
6.4      &   3.2    &   4.5    &   1.5    &   versicolor     \\
$\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$         \\
6.3      &   3.3    &   6.0    &   2.5    &   virginica      \\
5.8      &   2.7    &   5.1    &   1.9    &   virginica      \\
$\cdots$ & $\cdots$ & $\cdots$ & $\cdots$ & $\cdots$         \\ \hline\hline
\end{tabular}
\end{center}
\end{table}
}

%% --- (Figure) ---
\clearpage
\noindent
{\bf $\Box$ Let's visualize the Iris Dataset of 4D --- Sammon Mapping}
\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=init-2d.eps,width=18cm,height=8cm}
 \end{center}
\end{figure}

%%what is sammon

%% --- (Figure) ---
\clearpage
\noindent
{\bf $\Box$ An evolution \\
\hspace*{1in}--- maintaining distance relation as much as possible.}
\begin{figure}[h]
 \begin{center}
   \epsfile{file=iris-evolution.eps,width=18cm,height=8cm}
 \end{center}
\end{figure}

\clearpage
\noindent
{\bf $\Box$ Final location in 2D space mapped.}
\begin{figure}[h]
 \begin{center}
   \epsfile{file=final-2d.eps,width=18cm,height=8cm}
 \end{center}
\end{figure}

----
%%KDD cup


%% --- (Figure) ---
\clearpage
in conclusion
if we know anomalcy should be in a known set
its really easy to detect.

another
training should be only by nomal



e.g., Kim \&Bentley (2001) \\
\hspace*{1in}\\
three different data sets 
\hspace*{1in}\\
%%from this original data set \\
by taking one set as a SELF set and the rest as a NON-SELF set. \\
\hspace*{1in}\\
A tenfold cross-validation method \\

\hspace*{1in}\\
$\Downarrow$ \\
\hspace*{1in}\\

the best TP rate reached 100\%  \\
the worst FP average rate was only 1\%.
}
\end{center}

%% ----- for example
\clearpage
\begin{center}
{\bf tiny island in huge lake\\
needle in haystack\\
\hspace*{1in}\\
or\\
\hspace*{1in}\\
A random set of SELF and NON-SELF. (Ayara et al.)\\
\hspace*{1in}\\
All points in the space should be representative of transaction.\\



\hspace*{1in}\\
$\Downarrow$ \\
\hspace*{1in}\\

We doubt IRIS is not such a case.
}
\end{center}


%% --- (Figure) ---
\clearpage
in conclusion
if we know anomalcy should be in a known set
its really easy to detect.

another
training should be only by nomal




This is somewhat of old but 
worth while tuckle again
This talk was a call for...



\end{Large}
\end{document}
