## 3 Computational Approach
### Algorithm Code  
Algorithm 1 is designed to evaluate the synergy of 'tag' and 'time' data in a CF recommendation system using the dataset. The raw user interaction logs, tags, and timestamps are initially loaded. To experiment with the effect of the mixture of tag and time data, iterations are performed with varying weights to combine the two datasets. For each user pair, cosine similarity is calculated based on this mixture, creating a similarity matrix. Then, a neighborhood scaling process is applied, determining the similarity level with varying numbers of neighbors. The top preferences for each user are sorted and stored for different neighborhood sizes. In the evaluation phase, the generated preference matrix is compared against a test dataset to measure the recall and precision of the top 10 recommendations. This approach aids in identifying the optimal mix of tag and time data and the best neighborhood size for accurate recommendations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Meaning** \\ \hline \(u\) & User \\ \(v\) & Neighbor User \\ \(r\) & Resource \\ \(R\) & Set of Resources \\ \(i\) & A Certain User \(i\) \\ \(W_{tag}\)(\(u\),\(r\)) & Weight from Tags by User ’_u_’ for Resource ’_r_’ \\ \(W_{time}\)(\(u\),\(r\)) & Temporal Weight of User ’u’ towards Resource ’_r_’ \\ \(W_{light}\)(\(u\),\(r\)) & Combined Tag-Time Weight for User ’u’ and Resource ’_r_’ \\ \(\hat{W}_{i}\)(\(u\),\(r\)) & Composite Weight Profile of User ’u’ for Resource ’_r_’ \\ \(W_{i}\)(\(v\),\(r\)) & Each Weight Vector of Neighbor User ’_v_’ to Resource ’_r_’ \\ \(\lambda\) & Parameter for Balancing Tag-Based and Time-Based Weights \\ \(sim\)(\(u\),\(v\)) & Similarity Score Between User ’u’ and User ’_v_’ \\ \(S_{tag}\), \(S_{time}\), \(S_{hybrid}\) & Tag-Based, Time-Based, and Hybrid Similarities, respectively \\ _KNN_(\(u\)) & Set of ’k’ Nearest Neighbors of User ’u’ \\ _Score_(\(u\),\(r\)) & Predicted Preference Score of User ’u’ for Resource ’_r_’ \\ \(t\) & Relative Time Point Value \\ \(t_{i}\) & Tagging Day \\ \(t_{l}\) & Last Tagging Day \\ \(t_{f}\) & First Tagging Day \\ \(hl_{t}\) & Half-Life for Each User \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Symbol and meaning. ```
rawlog=load('MarTraLog.txt'); rawtag=load('MarTraTag.txt'); rawtime=load('MarTraTime.txt'); Test01=load('MarTraTest.txt'); % Iteration Experiment Start for hi=1:11  rawmix=rawtag*(1-0.1*(hi-1))+rawtime*0.1*(hi-1); fori=1:id  simmix(i,j)=rawmix(i,:)*rawmix(j,:)/(norm(rawmix(i,:))*norm(rawmix(j,:)));  end  end % Neighbor scale parameter=[36912151821242730]; forj=1:length(parameter) k=parameter(j); fori=1:id [m1]=sort(simmix(i,:),'descend'); index=n(2:k+1);  Prerefer_mat(i,:)=simmix(i,index)*rawmix(index,:)/k; Result[j]=prefer_mat;  end end % Evaluation Part forj=1:length(parameter) prefer01=Result[j]; fori=1:size(prefer01,1) [pmpn]=sort(prefer01(i,:),'descend'); index=pn(1:10);  Recall10(i,1)=length(find(Test01(i,index)==1))/length(find(Test01(i,:)-=0));  Precision01(i,1)=length(find(Test01(i,index)=1))/10;  end  Recall_001(:j+10*(hi-1))=Recall01;  Precision_001(:j+10*(hi-1))=Precision01;  end end
```  
**Algorithm 1**Algorithm code. ```

## 4 Experiment

In this section, we introduce the dataset and experimental procedure of a real virtual online community where our proposed model was applied. Additionally, we present performance evaluation metrics and display the results of the analysis in which we applied our model to the actual experimental data. ### Dataset and Experimental Procedure

This research utilized two authentic datasets, one each from Margarin [64] and Delicious [65]. Margarin is a popular social bookmarking platform in Korea, whereas Delicious holds a significant presence in the American digital landscape. Social bookmarking platforms like these allow users to earmark or bookmark specific URLs they find interesting, valuable, or worth sharing. To further categorize and describe these bookmarks, users have the flexibility to attach tags to them.