
\section{KCross algorithm}


We are looking for the impact of the $K$ parameter of the $K$cross validation algorithm. It was tested on a donut with 10\% of noise with 3NN. We tried the following values for $K$:
\begin{itemize}
  \item[\textbullet] 3
  \item[\textbullet] 10
  \item[\textbullet] 100
  \item[\textbullet] 1000 (leave on out validation)
\end{itemize}

\begin{figure}[!h]
	\begin{center}
		\includegraphics[width=12cm]{images/different-kcross}
	\end{center}
	\caption{Results of KNN on a donut with different K parameters to Kcross}
\end{figure}

The results shows that the value of $K$ does not impact on the final results, but does impact a lot on the variance.\par
Indeed, for example, when we are using \emph{Leave On Out}, the results of the cross validation is 0\% or 100\%. When we use bigger sets to test, the average is more constant from a test to an other one, and therefore the variance is smaller.\par
In this example, all the values of $K$ give the same results. We should therefore prefer a small value of $K$, which provides lower error and a better execution time.