500hPa Geopotential Height

Figure 4 shows a graph of the proportion of correctly classified test patterns against values of k ranging from 1 to 100, for k-nearest neighbour classifiers used to reproduce the Grosswetterlagen catalogue on the basis of the first 18 principal components of the 500hPa geopotential height field. In each case a leave-one-out cross-validation strategy was employed to estimate the true generalisation error of the classifier. The optimal value for k was found to be 1, at which point 71.02% of the test patterns were classified correctly.

**Figure 3:** Graph of the proportion of correctly classified patterns against kfor k-nearest neighbour classifiers reproducing the Grosswetterlagen catalogue on the basis of the first 18 principal components of the 500hPa geopotential height field.
$\begin{figure} \begin{centering} \includegraphics[scale=0.6]{results/partc/knn.eps} \end{centering}\end{figure}$

Table 3 shows a confusion matrix for the optimal 1-nearest neighbour classifier, again using a leave-one-out cross validation approach to estimate the true generalisation performance.

**Table 3:** Confusion matrix for a 1-nearest neighbour classifier reproducing the Grosswetterlagen catalogue on the basis of the first 18 principal components of the 500hPa geopotential height field.
		Model Classification
		$\begin{sideways}Wa \end{sideways}$	$\begin{sideways}Wz \end{sideways}$	$\begin{sideways}Ws \end{sideways}$	$\begin{sideways}Ww \end{sideways}$	$\begin{sideways}SWa \end{sideways}$	$\begin{sideways}SWz \end{sideways}$	$\begin{sideways}NWa \end{sideways}$	$\begin{sideways}NWz \end{sideways}$	$\begin{sideways}HM \end{sideways}$	$\begin{sideways}BM \end{sideways}$	$\begin{sideways}TM \end{sideways}$	$\begin{sideways}Na \end{sideways}$	$\begin{sideways}Nz \end{sideways}$	$\begin{sideways}HNa \end{sideways}$	$\begin{sideways}HNz \end{sideways}$	$\begin{sideways}HB \end{sideways}$	$\begin{sideways}TrM \end{sideways}$	$\begin{sideways}NEa \end{sideways}$	$\begin{sideways}NEz \end{sideways}$	$\begin{sideways}HFa \end{sideways}$	$\begin{sideways}HFz \end{sideways}$	$\begin{sideways}HNFa\end{sideways}$	$\begin{sideways}HNFz\end{sideways}$	$\begin{sideways}SEa \end{sideways}$	$\begin{sideways}SEz \end{sideways}$	$\begin{sideways}Sa \end{sideways}$	$\begin{sideways}Sz \end{sideways}$	$\begin{sideways}TB \end{sideways}$	$\begin{sideways}TrW \end{sideways}$	$\begin{sideways}U \end{sideways}$
	Wa	422	56	1	4	9	5	7	10	20	31	0	0	5	1	3	2	4	2	4	1	0	1	1	1	0	3	0	2	4	7
	Wz	70	1168	14	12	14	21	14	30	18	49	2	1	14	2	2	4	30	1	2	3	4	0	1	3	0	1	2	9	20	13
	Ws	0	17	213	3	1	4	2	2	0	3	2	0	2	2	1	1	1	0	1	0	0	1	2	2	1	0	1	0	5	3
	Ww	3	8	7	135	3	3	0	2	6	9	1	1	1	0	0	1	2	0	0	6	3	1	1	3	3	1	0	2	4	2
	SWa	9	11	2	2	201	7	3	2	11	12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	6	1	2	4	4
	SWz	7	20	7	5	7	237	1	4	4	5	1	1	0	0	1	1	1	0	1	2	1	1	1	2	2	4	0	3	4	5
	NWa	8	9	0	0	2	0	167	2	6	11	1	0	2	1	1	5	1	0	1	0	0	0	0	0	0	0	0	0	4	3
	NWz	11	26	2	3	2	2	3	291	9	15	2	3	8	1	2	4	12	1	2	0	0	0	0	0	0	0	0	0	4	9
	HM	24	8	0	3	10	5	5	3	370	32	0	4	3	1	2	17	2	2	1	8	0	2	1	5	1	2	2	1	4	5
	BM	24	45	3	8	11	7	14	15	33	727	8	0	6	3	2	14	13	7	3	8	6	7	5	9	2	8	0	0	14	13
	TM	0	5	3	1	0	0	0	3	1	8	168	1	1	0	4	2	9	2	0	1	3	0	2	3	4	1	0	2	7	6
	Na	0	0	0	1	0	0	0	2	0	5	0	47	1	0	0	1	0	4	0	0	1	0	0	0	1	0	1	0	0	1
	Nz	2	18	1	0	1	0	2	6	2	6	2	1	189	2	1	3	7	1	2	1	1	0	1	1	0	0	0	1	4	3
	HNa	1	2	1	0	0	0	2	0	2	5	0	0	4	130	2	2	1	1	1	3	1	0	1	0	0	0	0	1	0	2
$\begin{sideways}\makebox[0pt]{True Classification} \end{sideways}$	HNz	1	3	1	0	0	0	1	1	3	2	1	0	2	2	134	2	2	1	1	0	2	4	2	0	1	1	0	1	3	5
	HB	4	2	0	0	0	1	6	6	10	13	3	0	3	6	2	245	4	1	5	6	1	3	0	2	0	0	1	0	2	1
	TrM	7	25	4	3	0	0	0	13	4	12	7	0	5	0	2	6	263	1	5	2	3	0	0	2	0	0	0	9	14	7
	NEa	1	1	0	1	1	0	2	2	0	5	1	3	2	2	0	6	1	90	6	4	2	1	0	0	0	0	0	0	0	2
	NEz	1	1	1	0	0	1	2	3	4	6	0	0	3	2	0	7	3	6	101	3	1	0	1	2	2	0	0	0	1	3
	HFa	0	4	1	3	0	1	0	2	3	16	1	0	2	3	0	9	3	6	2	216	6	6	6	4	6	2	0	3	0	4
	HFz	0	2	1	3	0	2	0	0	2	4	7	1	1	1	0	3	2	0	1	5	133	1	1	5	4	1	0	4	3	1
	HNFa	0	0	0	0	0	1	0	0	4	5	2	0	0	1	3	4	0	2	1	3	1	91	3	2	2	0	0	0	5	0
	HNFz	1	0	2	1	0	3	0	0	1	5	5	2	3	1	1	2	0	0	2	3	1	2	107	2	3	1	0	1	3	0
	SEa	1	2	0	6	0	2	1	1	6	8	0	0	1	3	2	0	1	0	2	5	2	1	2	127	2	4	1	3	4	3
	SEz	1	1	2	4	1	2	0	0	1	4	7	0	0	0	0	0	0	0	1	4	5	2	0	3	84	1	2	2	2	0
	Sa	5	1	0	0	5	2	0	0	7	11	0	0	0	0	1	0	0	0	1	1	2	1	0	7	4	113	0	1	2	0
	Sz	1	0	1	0	3	0	0	0	3	3	0	1	0	1	0	1	1	0	0	2	0	1	0	1	0	2	51	0	1	0
	TB	2	10	1	1	1	5	0	0	2	2	2	0	2	1	1	0	3	1	2	2	5	0	2	4	0	0	0	165	7	6
	TrW	6	21	9	4	3	4	5	6	4	14	8	0	3	1	2	2	12	3	2	3	2	3	3	3	1	3	0	8	347	5
	U	9	12	4	2	6	5	2	10	12	18	3	1	4	4	3	5	11	1	1	1	2	0	1	4	1	5	0	2	13	13