## 4 Further Analysis with Discussions and Implications
### The Most Important Technologies and the Associated Implications
From the fact that \"in patent databases, those hottest technologies are also the most important technologies\", it can be concluded that \"a technology's importance can be roughly estimated based on its popularity because they are strongly correlated\" and that \"a technology's volume of patents, when observed from the patent databases, may indicate the importance of this technology\". In other words, through this analysis, the longstanding missing link between importance and popularity (of a technology) is established and supported. * _The ten hottest and most important technologies are, in fact, closely related to our daily lives._ These technologies cover several areas that are generally relevant to our daily lives nowadays, i.e., wireless communications and networking, digital image transmission, cellular battery modules, optical lenses and fin-tech products (including data-driven decision models). The angular-based analysis in Section 4.2 also reflects the following conclusion: these areas concur with the main areas addressed by the countries in group (i) (i.e., the USA, EUR and CHN). In the PCA model established in 4.1, the estimated loading factors indicated that the USA, EUR and CHN are the most influential technological powers around the world. The set of the ten hottest and most important technological fields are exactly the IPC subclasses that these economies emphasised during the study period and in which they have applied for a considerable number of patents (indicating that the popularity of these subclasses increased). To provide a short summary, according to the analytical results in this section, all of the technologies in Sections G and H should be clustered into 7 groups in terms of their IPC codes in the patent databases of the 9 technological power countries around the world. In addition, the 10'most important technologies' identified in this section fully concur with the 10 'hottest technologies' identified in a previous section (Section 3.3). Moreover, the areas of these 10 technologies are closely related to our daily lives, and they are exactly the IPC subclasses that the technological powers in group (i) have emphasised during the study period. In this sense, the different analytical methods used and applied by this study (i.e., descriptive statistics, the correlation matrix method, the angular-based analysis and the machine-learning-based clustering) may cross-validate each other, since similar outcomes are obtained by them. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline
**IPC** & **X** & **Y** & **Magnitude** & **Rank** & **CID** & **IPC** & **X** & **Y** & **Magnitude** & **Rank** & **CID** \\ \hline G01B & \(-\) 7379.54249 & \(-\)2990.0055 & 8279.026633 & 117 & 2 & G10H & ( 2765.5573 & \(-\)587.916233 ) & 27662.10561 & 61 & 6 \\ G01C & \(-\)1329.38785 & \(-\)2868.29083 & 3161.380561 & 127 & 2 & G10K & ( 2596.52729 & \(-\)597.930216 ) & 25973.9043 & 70 & 6 \\ G01D & \(\{\)15437.23071 & \(-\)1385.6492 & 1 & 1549.29404 & 101 & 2 & G10L & ( 11396.9956 & \(-\)1763.38027 ) & 11532.60674 & 110 & 2 \\ G01F & \(\{\)16599.97106  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**CID** & **IPC Cat** & **Center X** & **Center Y** & **Dist. To O** & **Tan\({}^{-1}\) (\({}^{\circ}\))** & **Within GRP VAR** & **Avg. VAR** & **IPC Codes** \\ \hline
**5** & 13 & \(-\)30428.3 & 5807.446 & 30977.5 & \(-\)10.8054 & 230028.9 & 17694.53 & \({}^{\circ}\)G957, \({}^{