Surface Level Pressure

Figure 2 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 26 principal components of the daily surface level pressure 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 61.45% of the test patterns were classified correctly.

**Figure 1:** Graph of the proportion of correctly classified patterns against kfor k-nearest neighbour classifiers reproducing the Grosswetterlagen catalogue on the basis of the first 26 principal components of the daily surface level pressure field.
$\begin{figure} \begin{centering} \includegraphics[scale=0.6]{results/parta/knn.eps} \end{centering}\end{figure}$

Table 1 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 1:** Confusion matrix for a 1-nearest neighbour classifier reproducing the Grosswetterlagen catalogue on the basis of the first 26 principal components of the daily surface level pressure 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	372	72	1	4	8	5	13	8	31	47	0	0	3	2	4	5	7	2	3	2	0	0	0	2	0	4	0	2	7	2
	Wz	77	1075	20	11	28	27	11	38	24	65	3	1	15	3	10	2	31	1	3	3	1	0	1	1	4	1	3	9	46	10
	Ws	0	19	206	2	2	4	1	4	0	3	1	4	2	1	1	1	4	0	1	2	0	0	1	0	1	0	1	1	6	2
	Ww	5	13	2	133	5	3	1	2	4	8	0	1	2	0	0	0	2	1	1	5	3	0	0	1	3	3	0	1	8	1
	SWa	8	19	1	7	159	11	2	1	10	26	0	0	0	1	0	0	0	0	0	1	0	0	1	2	0	8	2	2	7	9
	SWz	3	31	9	4	12	212	1	1	6	9	1	0	2	2	1	1	1	1	1	2	2	0	2	3	0	2	1	6	4	8
	NWa	19	12	1	0	3	2	134	5	6	11	1	2	3	1	3	9	2	2	1	0	1	0	1	1	0	1	1	0	1	1
	NWz	17	47	3	3	2	0	10	227	8	11	2	2	17	2	5	9	15	1	1	7	0	0	0	1	0	0	1	0	11	10
	HM	32	20	1	3	13	8	9	5	279	66	0	1	1	4	2	15	4	1	1	15	2	2	2	7	1	10	4	2	8	5
	BM	42	56	3	7	15	9	18	16	56	634	8	5	9	3	1	18	16	5	9	10	7	5	4	13	4	9	3	2	20	8
	TM	2	8	2	1	0	0	1	4	0	9	144	0	5	1	4	2	14	3	1	1	3	1	4	4	3	0	0	6	11	3
	Na	0	2	4	1	0	0	1	2	1	4	1	33	1	2	2	0	1	3	0	1	1	0	2	0	0	0	0	0	3	0
	Nz	4	13	2	1	1	1	5	12	5	10	4	1	158	4	2	13	3	2	5	1	0	0	2	0	1	0	0	3	2	3
	HNa	1	1	3	0	1	2	2	0	2	3	2	1	6	108	2	6	1	1	1	3	1	5	2	2	0	0	1	1	1	3
$\begin{sideways}\makebox[0pt]{True Classification} \end{sideways}$	HNz	3	6	2	0	1	0	3	2	5	4	3	1	1	3	110	2	3	3	1	2	2	3	5	2	0	0	0	2	2	5
	HB	5	2	0	0	0	3	12	5	14	28	4	3	8	9	7	186	6	6	3	7	2	5	1	2	0	1	0	1	2	5
	TrM	8	30	1	4	2	0	1	14	2	16	14	1	9	1	5	7	215	1	13	0	1	0	0	3	3	0	1	7	28	7
	NEa	1	2	0	1	1	0	1	2	0	7	3	1	0	0	0	5	1	88	4	4	5	3	1	1	0	0	0	0	1	1
	NEz	2	1	1	0	0	0	2	2	1	15	1	2	3	0	2	5	4	6	90	5	2	2	0	2	3	0	0	0	1	2
	HFa	3	4	3	3	0	2	0	1	6	16	2	1	1	3	0	5	2	14	3	197	9	5	6	9	6	2	2	1	1	2
	HFz	0	6	2	3	0	2	0	0	2	7	8	2	0	0	2	1	1	4	1	13	106	0	5	5	10	1	1	1	5	0
	HNFa	0	1	0	1	1	1	0	0	2	2	2	0	1	2	3	3	0	4	4	6	1	84	6	1	0	0	0	0	4	1
	HNFz	0	0	2	1	1	1	2	0	2	3	5	1	3	1	2	1	0	5	2	6	2	5	94	1	2	1	0	3	5	1
	SEa	2	1	0	1	0	1	2	0	9	6	1	0	0	2	3	2	2	0	0	7	3	0	1	113	5	10	2	3	10	4
	SEz	0	2	3	5	0	3	0	1	1	5	3	0	0	0	0	2	3	1	2	5	7	0	1	4	70	3	0	2	5	1
	Sa	3	1	0	2	9	2	0	0	9	11	1	0	0	1	1	0	2	0	0	1	1	3	0	8	3	96	2	3	2	3
	Sz	1	3	2	0	5	0	2	0	2	0	2	1	0	1	0	0	1	0	0	1	1	0	0	1	0	6	41	1	1	1
	TB	1	9	2	3	3	4	0	0	1	4	2	0	2	1	1	0	2	0	0	1	2	1	1	2	0	1	1	167	10	6
	TrW	7	30	7	6	10	9	2	9	6	20	12	1	4	0	3	1	23	1	3	2	3	4	5	7	2	4	0	12	287	7
	U	7	13	3	2	5	11	3	7	8	16	3	0	4	4	5	5	11	2	3	3	2	0	1	2	0	4	1	5	7	18