\section{Cleaning and distilling algorithms}
% compare results of different combinaisons

We are using two different algorithms :
\begin{itemize}
  \item[\textbullet] Cleaning is aiming to remove the noise.
  \item[\textbullet] Distilling removes the points that does not contain a lot of informations as they are surrounded by points with the same label.
\end{itemize}

We will do several tests of combinaison of those algorithms on a noised donut (10\% of wrong labels).

\subsection{Distilling}
\begin{figure}[h!]
	\begin{center}
		\includegraphics[width=12cm]{images/clean-dist/distilling}
	\end{center}
	\caption{Distiling results}
\end{figure}

We see in this example that distilling is not appropriated to a noised donut, a lot of labels are wrong.
\newpage
\subsection{Cleaning}
\begin{figure}[h!]
	\begin{center}
		\includegraphics[width=12cm]{images/clean-dist/cleaning}
	\end{center}
	\caption{Cleaning results}
\end{figure}
The cleaning algorithm successfuly removed the wrong labels. Therefore, we can apply the cleaning algorithm.
\newpage
\subsection{Cleaning and distilling}
\begin{figure}[h]
	\begin{center}
		\includegraphics[width=12cm]{images/clean-dist/cleaning_distilling}
	\end{center}
	\caption{Cleaning and distiling results}
\end{figure}
As we guessed, as we removed the points with wrong labels, the error is way more inferior. However, a few wrong point was left in the top left of the donut and therefore the results is not totally good.
\newpage
\subsection{Cleaning, distilling and cleaning}
\begin{figure}[h!]
	\begin{center}
		\includegraphics[width=12cm]{images/clean-dist/cleaning_distilling_clean}
	\end{center}
	\caption{Cleaning, distiling and cleaning results}
\end{figure}
Applying cleaning on our last result achieved better results, as it removed the points that shouldn't be here.
\newpage
\subsection{Distilling cleaning}
\begin{figure}[h!]
	\begin{center}
		\includegraphics[width=12cm]{images/clean-dist/distilling_clean}
	\end{center}
	\caption{Cleaning results}
\end{figure}
With this combinaison we are getting results closes to the cleaning, distilling, cleaning sequence.\\\par
We showed that cleaning and distiling (with or without a preliminary cleaning) achieved excellent results: we only kept a few number of points (less than 10\%) but we still perfectly see the shape of the donut. % lancer de la KCROSS ?