## 3 Results from Patent Data Mining across the Countries
### Total Correlation Matrix of the Patenting Activities among the Countries  
As discussed previously, the records in an official patent database of a country can indicate two things. A high number of patents being applied for in a given area may connote a strong or potentially strong domestic market for the technologies in that area (in terms of the IPC code(s)) in that country, while this may also denote the degree to which the IPs that are relevant to these technologies are protected in that country. Patents applied for with the latter purpose usually have the aim of crowd out (blocking out) similar technologies, so such patents usually imply a 'battle' against the original technological strengths of the country in which the patents are applied for. This is especially true when the company which is applying for the patent is a foreign company. Regardless of the dual potential purposes of these patenting activities, the extent of such activities in an area in a given country is an important indicator of the technical strength of the country in that field. Therefore, by examining the strengths of a country in all relevant technology domains (in terms of the IPCs), a'spectrum of the technical strengths' (STS) in these domains can be determined for the country. In order to obtain the STSs for the technological powers, in each country's patent database, a subtotal for each 3-tuple is accumulated, so that the 'patenting volume' of the technology domain can be recorded and analysed according to its IPC prefix. These numbers then form a'statistical variable' that is titled with the abbreviated country name (e.g., GER). Each statistical variable, on the other side, can be treated as a vector whose elements are ordered [26; 27] according to a certain sequence of all possible 3-tuples that are prefixed by G or H. Thus, 9 such variables (vectors) are obtained, so the correlation between each pair of these variables is then identified. A so-called 'correlation matrix', which is shown in Table 2, is then obtained by filling in these numbers. This reveals the pairwise correlational degrees between the STSs of all pairs of two technological powers. Numerous insights revealed by Table 2 are of considerable value. However, for space reasons, only some empirical insights regarding how the STS of Taiwan is related to those of other countries are explored. The analytical case standing in the position of other countries is analogous. \begin{table}
\begin{tabular}{c|c c c c c c c c c} \hline
**Country vs. Country a** & **CAN** & **CHN** & **GER** & **EU** & **GBR** & **JPN** & **KOR** & **TWN** & **USA** \\
**CAN** & 1.000 & 0.892 & 0.607 & 0.900 & 0.921 & 0.602 & 0.651 & 0.495 & 0.812 \\
**CHN** & 0.892 & 1.000 & 0.778 & 0.981 & 0.934 & 0.796 & 0.814 & 0.757 & 0.939 \\
**GER** & 0.607 & 0.778 & 1.000 & 0.750 & 0.636 & 0.775 & 0.765 & 0.770 & 0.683 \\
**EU** & 0.900 & 0.981 & 0.750 & 1.000 & 0.932 & 0.801 & 0.825 & 0.737 & 0.924 \\
**GBR** & 0.921 & 0.934 & 0.636 & 0.932 & 1.000 & 0.711 & 0.732 & 0.646 & 0.940 \\
**JPN** & 0.602 & 0.796 & 0.775 & 0.801 & 0.711 & 1.000 & 0.895 & 0.879 & 0.810 \\
**KOR** & 0.651 & 0.814 & 0.765 & 0.825 & 0.732 & 0.895 & 1.000 & 0.925 & 0.839 \\
**TWN** & 0.495 & 0.757 & 0.770 & 0.737 & 0.646 & 0.879 & 0.925 & 1.000 & 0.818 \\
**USA** & 0.812 & 0.939 & 0.683 & 0.924 & 0.940 & 0.810 & 0.839 & 0.818 & 1.000 \\ \hline \end{tabular}  
* The list is alphabetically ordered. CAN: Canada; CHN: People’s Republic of China; GER: Germany; EU: Europa or European Union; GBR: United Kingdom; JPN: Japan; KOR: South Korea; TWN: Taiwan or Republic of China; USA: United States of America).  
\end{table} 
Table 2: Correlation between each pair of technology powers in terms of the STS vectors. * Among the correlational numbers that involve the STS of TWN, the highest one is 0.925, i.e., TWN's STS correlates with KOR's STS to a high degree.