Motivation
| Storm Type | Rainy Season | Duration |
|---|---|---|
| Frontal Rain | Nov. - Apr. | > 1 h |
| Meiyu | May and June |
|
| Convective Storms | July - Oct. | 1-12 h |
| Typhoons | July - Oct. | > 12 h |
\[\begin{equation} \tag{2} min_{C_1,...,C_k}\lbrace\sum^K_{k=1} V(C_k)\rbrace \end{equation}\]
\[\begin{equation} \tag{3} V(C_k)=\frac{1}{|C_k|} \sum_{i,i'\in C_k} \sum^p_{j=1}(x_{ij}-x{i'j})^2 \end{equation}\]
\[\begin{equation} \tag{4} \min_{C_1,...,C_k}\lbrace\sum^K_{k=1} \frac{1}{|C_k|} \sum_{i,i'\in C_k} \sum^p_{j=1}(x_{ij}-x{i'j})^2 \rbrace \end{equation}\]
PCA is used to
Why use PCA?
\[\begin{equation} \tag{5} \mathbf Z = \mathbf \Phi^T \mathbf X \end{equation}\]
\[\begin{equation} \tag{6} Z_1=z_{i1}=\phi_{11}x_{i1} + \phi_{21}x_{i2} + ... + \phi_{p1}x_{ip} \end{equation}\]
\[\begin{equation} \tag{13} d = \sqrt{Z_1^2+Z_2^2} \ge d_{i,j,p} \end{equation}\]
\[\begin{equation} \tag{13} d^{'} = \sqrt{Z_1^2+Z_2^2} \ge d^{'}_{i,j,p} \end{equation}\]
Figure 1.
5 variables for conducting the K-Means cluster analysis:
Figure 3.
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Figure 5.
Figure 6.
Frontal Rain, Cluster 4
東河、成功、池上、鹿野、紅石、明里、台東、紅葉山
Figure 7.
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Figure 10.
Figure 11.
Figure 16.
Figure 17.
Figure 24.
Figure 25.