700hPa Geopotential Height

Figure 3 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 700hPa 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 67.88% of the test patterns were classified correctly.

**Figure 2:** 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 700hPa geopotential height field.
$\begin{figure} \begin{centering} \includegraphics[scale=0.6]{results/partb/knn.eps} \end{centering}\end{figure}$

Table 2 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 2:** Confusion matrix for a 1-nearest neighbour classifier reproducing the Grosswetterlagen catalogue on the basis of the first 18 principal components of the 700hPa 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	403	69	0	7	8	5	13	12	21	27	0	0	4	1	3	1	6	2	1	1	0	0	1	2	0	5	0	0	8	6
	Wz	68	1169	16	11	16	33	10	33	17	40	4	3	14	2	1	4	29	1	2	1	2	0	1	2	1	0	4	5	25	10
	Ws	0	20	201	3	0	4	2	4	0	8	2	1	2	1	1	2	2	0	1	1	0	0	1	1	1	0	2	0	5	5
	Ww	9	10	3	134	2	3	0	2	4	9	1	0	1	0	0	1	2	0	0	4	4	1	0	3	1	3	1	3	5	2
	SWa	4	14	1	4	183	9	2	2	8	25	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	5	1	2	8	7
	SWz	4	34	6	4	5	231	1	2	5	6	1	0	0	1	0	2	3	0	0	1	1	0	3	1	1	3	0	4	3	6
	NWa	11	13	0	0	3	1	149	3	8	12	1	1	5	2	1	5	2	0	0	1	0	0	0	0	0	0	0	0	4	2
	NWz	11	36	7	2	2	1	6	262	5	15	2	5	12	2	2	6	12	1	2	2	0	0	1	0	0	1	0	1	7	9
	HM	28	15	1	4	6	8	10	3	332	46	1	2	3	1	4	17	4	2	2	8	1	2	2	3	1	4	2	1	5	5
	BM	25	45	8	7	17	7	17	19	54	651	5	5	13	1	3	17	17	6	3	16	5	6	3	12	3	15	0	0	19	16
	TM	0	5	3	1	0	0	2	4	0	10	164	1	5	0	3	0	5	3	1	3	3	0	3	1	2	1	0	8	6	3
	Na	0	1	0	0	0	0	0	2	0	5	2	49	1	0	0	1	0	3	0	0	1	0	0	0	0	0	0	0	0	0
	Nz	0	16	3	1	1	0	2	6	2	9	1	0	183	3	3	5	7	2	3	1	1	0	2	1	0	0	0	0	4	2
	HNa	2	1	1	0	0	0	1	1	1	4	0	0	4	130	2	2	0	1	0	4	0	1	3	0	0	0	0	1	0	3
$\begin{sideways}\makebox[0pt]{True Classification} \end{sideways}$	HNz	2	3	3	0	0	0	1	2	3	2	4	0	2	3	122	2	3	1	1	2	2	5	1	2	0	1	0	1	3	5
	HB	4	3	1	0	0	1	7	6	10	19	2	0	6	4	2	230	6	4	3	5	2	4	1	1	0	1	0	0	1	4
	TrM	5	42	0	5	0	0	1	15	4	12	11	0	5	0	5	6	244	1	6	2	2	0	0	2	0	0	1	4	15	6
	NEa	2	1	0	2	1	0	1	3	1	5	1	3	1	2	0	6	2	88	3	3	3	2	1	0	0	0	0	0	1	1
	NEz	2	2	2	0	1	0	3	1	4	4	1	0	3	1	0	5	4	9	100	1	2	2	1	2	1	0	0	0	1	2
	HFa	2	2	1	1	0	0	1	3	6	10	2	0	2	5	0	6	3	7	2	216	7	3	7	3	9	2	1	3	2	3
	HFz	0	3	0	3	1	2	0	0	3	5	7	1	1	0	0	2	1	1	2	8	125	3	1	5	6	1	0	3	3	1
	HNFa	0	0	0	0	0	0	0	0	4	2	1	0	0	2	2	4	0	2	3	6	0	94	6	0	1	0	0	0	3	0
	HNFz	2	0	2	2	0	3	0	0	1	3	5	1	3	3	2	2	0	0	1	2	1	3	101	3	6	1	0	1	4	0
	SEa	1	3	0	4	1	2	1	1	10	7	2	0	0	3	0	0	2	0	2	6	5	2	1	123	2	3	1	2	3	3
	SEz	0	0	2	4	0	3	0	0	0	3	5	0	0	0	0	0	0	0	1	4	4	1	1	4	90	3	0	0	4	0
	Sa	4	2	0	2	4	2	0	1	8	14	0	0	0	0	1	0	0	1	0	1	1	0	0	5	6	107	0	0	2	3
	Sz	0	2	2	2	3	1	0	0	2	3	0	1	0	0	0	0	2	0	0	2	0	0	0	1	1	1	49	0	1	0
	TB	2	7	2	1	0	5	0	0	1	5	4	0	1	1	1	0	3	0	1	2	3	0	2	4	0	1	0	169	8	4
	TrW	7	18	7	5	4	6	3	6	7	14	8	1	4	0	3	2	18	3	3	0	3	2	3	3	1	5	0	8	333	10
	U	10	10	7	1	5	7	2	12	14	15	4	0	3	4	4	8	11	0	2	0	2	1	1	5	0	2	0	2	8	15