## 2 Materials and Methods
### Implementation
#### 2.3.4 Recommender
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Users** & **Number of Movies** & **Before** & **After** \\ \hline \multirow{2}{*}{943} & \multirow{2}{*}{1682} & 943 \(\times\) 1682 & 60 \(\times\) 1682 \\  & & (1,586,126) & (100,920) \\ \hline \multirow{2}{*}{5000} & \multirow{2}{*}{10,000} & 5000 \(\times\) 10,000 & 60 \(\times\) 10,000 \\  & & (50,000,000) & (600,000) \\ \hline \multirow{2}{*}{10,000} & \multirow{2}{*}{20,000} & 10,000 \(\times\) 20,000 & 60 \(\times\) 20,000 \\  & & (200,000,000) & (1,200,000) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Matrix Size Before and After applying Persona. all users becomes infeasible due to the creation of a matrix with overlapping user and movie information. Regarding the DL model, the one with personas outperformed the model without personas, albeit marginally. With 70 topics and 35 personas, the NMF model achieved a precision@K performance of 65.11% for 100 users, while the DNN (Deep Neural Network) model achieved 80.52% [Figure 20]. With 200 users, under the same conditions, the NMF model's precision@K performance improved to 80.01%, and the DNN model's performance improved to 92.83%, with both showing improvements of approximately 15% and 10%, respectively. [Figure 21]. The experiment with 50 topics and 35 identical Personas showed that the NMF's precision@K performance was measured at 86.01% and DNN's precision@K performance was measured at 92.67% with 500 user data [Figure 22]. When measured with 50 topics and 45 Persona under the identical conditions and 900 users, NMF's precision@K performance was 97.04%, and DNN's precision@K performance was 95.55%, showing performance improvements of 10% and 5% or more, respectively [Figure 23]. These results indicate that the performance improves as the amount of movie rating data and user data increases, allowing it to adapt to changes in user personas. By managing data according to the number of user personas, storage space can be saved, and learning time can be reduced. Additionally, computation costs and time decrease since model updates only occur when user personas change. Figure 21: Precision@K Performance of NMF and DNN with 200 Users under the Conditions of 70 Topics and 35 Personas. Figure 20: Precision@K Performance of NMF and DNN with 100 Users under the Conditions of 70 Topics and 35 Persons. The process of creating user personas involves analyzing user behaviors, preferences, habits, and more to form groups with common characteristics. This approach defines groups of users showing similar behavioral patterns or preferences as personas and utilizes them as input for the recommender system. User personas thus created are employed to recommend items that the corresponding user groups are likely to prefer. Furthermore, merging user personas with other user data enables more sophisticated user modeling. For instance, by jointly modeling user demographic information (age, gender, occupation, etc. ), interaction data (movie ratings, click history, etc. ), and user behavior patterns that change over time, more personalized recommendations become possible. Integrating user personas with other user data allows for providing recommendations that reflect both individual user characteristics and common characteristics within groups. This surpasses conventional generic recommender systems, enabling highly personalized recommendations and enhancing user satisfaction. It is expected that user personas created in this manner can be utilized in other recommendation services and analyses as well. Typically, the performance of models improves with the increase in data volume. Our model is no exception to this. For instance, in programs that do not apply topic modeling and personas, the recommendation time is approximately 10 s with an accuracy of 10%. However, when our modeling approach is applied, the recommendation time is significantly reduced to about 3 s, and accuracy is enhanced to 40%.