# Zero-Inflated Patent Data Analysis Using Generating Synthetic Samples
## 4 Results  
### Experimental Result Using Patent Big Data  
To show the performance and validity of our method, we conducted experiments using the text data of patent documents related to disaster prevention technology. We retrieved the patent data from the patent databases of the United States Patent and Trademark Office (USPTO) and the Korea Intellectual Property Rights Information Service (KIPRIS) [26; 27]. We accessed the databases and retrieved the patent documents issued from 2000 to 2020. We mainly collected patent documents from KIPRIS and supplemented the collection results of KIPRIS using the USPTO search results. We used the R data language and its various packages for data preprocessing and analysis [12; 13; 14]. We obtained 16,875 patents through the valid patent selection process. Using the text mining techniques we extracted 162 keywords from the valid patent documents. For the experiment, we selected four keywords, fire, temperature, wind and pressure, among all keywords. Therefore, the data have 16,875 patents and the four keywords as a matrix format. We found that the sparsity of this matrix is 0.9369. That is, 95% of all elements of this matrix are zero values. The descriptive statistics of four keywords are shown in Table 1.  
The minimum and median of all keywords are both zero. The statistics in Table 1 and the sparsity of the data matrix show the zero-inflated problem. We applied various analysis methods including synthetic sample generation to the patent data that had the zero-inflated problem. In this experiment, we considered the following linear model:  
\[Fire=b_{0}+b_{1}Temperature+b_{2}Wind+b_{3}Pressure. \tag{7}\]  
Table 2 shows the performance evaluation results between the compared models. It has parameter estimates and their standard errors of each explanatory keyword. The AIC in Equation (6) of each method is shown in the last column. We applied six methods to analyze the zero-inflated patent data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistic** & **Fire** & **Temperature** & **Wind** & **Pressure** \\ \hline Min. & 0 & 0 & 0 & 0 \\ Median & 0 & 0 & 0 & 0 \\ Mean & 0.1146 & 0.6642 & 0.4925 & 0.4427 \\ Max. & 42 & 70 & 88 & 49 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of four keywords. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Parameter** & **Temperature** & **Wind** & **Pressure** & **AIC** \\ \hline \multirow{2}{*}{Original} & b & 0.0284 & \(-\)0.0013 & 0.0053 & \multirow{2}{*}{58193.7} \\  & SE (b) & 0.0034 & 0.0030 & 0.0045 & \\ \hline \multirow{2}{*}{With noise (SD = 0.1)} & b & 0.0284 & \(-\)0.0014 & 0.0055 & \multirow{2}{*}{58193.7} \\  & SE (b) & 0.0034 & 0.0030 & 0.0045 & \\ \hline \multirow{2}{*}{With noise (SD = 0.5)} & b & 0.0276 & \(-\)0.0017 & 0.0060 & \multirow{2}{*}{58194.9} \\  & SE (b) & 0.0034 & 0.0030 & 0.0045 & \\ \hline \multirow{2}{*}{With noise (SD = 1)} & b & 0.0256 & \(-\)0.0020 & 0.0063 & \multirow{2}{*}{58199.2} \\  & SE (b) & 0.0034 & 0.0030 & 0.0045 & \\ \hline \multirow{2}{*}{Zero-inflated Negative Binomial} & b & 0.0556 & \(-\)0.0461 & \(-\)0.0301 & \multirow{2}{*}{4537.4} \\  & SE (b) & 0.0304 & 0.0293 & 0.0293 & \\ \hline \multirow{2}{*}{Zero-inflated Poisson} & b & 0.0211 & \(-\)0.0391 & \(-\)0.0092 & \multirow{2}{*}{6177.7} \\  & SE (b) & 0.0033 & 0.0118 & 0.0086 & \\ \hline \multirow{2}{*}{Synthetic sample} & b & 0.0036 & \(-\)0.0021 & \(-\)0.0037 & \multirow{2}{*}{1647.4} \\  & SE (b) & 0.0047 & 0.0055 & 0.0085 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance evaluation between comparative methods (patent keyword data). Our first approach is to apply the linear model in Equation (7) to the original data having the zero-inflated problem. Next, we illustrate the analysis results of datasets with some noise added.