## 3 Computational Approach
### Algorithm Code
For the purpose of this study, data from Margarin were meticulously gathered through web crawling techniques, whereas the Delicious dataset was generously provided as referenced in [66]. To provide a more detailed overview, the Margarin dataset encompassed a total of 15,765 distinct resources, accompanied by 11,065 unique tags. Throughout the observation period, users bookmarked links 18,850 times. In contrast, the Delicious dataset was more extensive, featuring 43,028 individual resources and 9383 separate tags. Users on Delicious showed more prolific bookmarking behavior, with a grand total of 104,687 bookmarking actions. The subsequent sections will delve more deeply into a descriptive breakdown of the data sourced from both platforms. Table 6 contains the information on the datasets. During the data assessment phase, weights were derived from the frequency of tags which users employed and the timestamps of their tagging actions. For the Margarin platform, the research constructed a user-resource weight matrix with approximately 4.7 million cells. Similarly, the Delicious dataset resulted in a matrix containing approximately 12.9 million cells. Every user's similarity with every other user was computed, implying that calculations took place for all possible user combinations. The selection of neighborhood size was pivotal for the efficacy of CF. To this end, the study evaluated varying neighborhood sizes, ranging from 3 to 30 in increments of 3, leading to 10 distinct calculations. Additionally, by adjusting the \(\lambda\) value in intervals of 0.1, ranging from 0 to 1, the experiment was iterated 11 times. Consequently, the Margarin dataset necessitated 520,245,000 operations, whereas the Delicious dataset required a whopping 1,419,924,000 operations. To gauge the efficiency of the recommended algorithm, it was juxtaposed against the foundational CF methodology. The latter determines recommendations based on user bookmarking activities, employing a binary-coded user-resource matrix and leveraging the cosine distance metric, as cited in [27; 33]. For the experimental phase, each data subset was bifurcated: the training set encompassed the initial 80% of entries, while the latter 20% formed the testing set. Margarin's dataset showcased 15,765 resources interlaced with 11,065 tags. On the other hand, Delicious featured a comprehensive set of 43,028 resources and 9383 tags. A subsequent section elaborates on the performance assessment. The top 10 resources were extracted from the training dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data** & \
\begin{tabular}{c} **Number of** \\ **Resources** \\ \end{tabular} & **Number of Tags** &
\begin{tabular}{c} **Number of** \\ **Bookmarks** \\ \end{tabular} \\ \hline Margarin & 15,765 & 11,065 & 18,850 \\ Delicious & 43,028 & 9383 & 104,687 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The description of datasets. ### Evaluation Metrics

In this research, the effectiveness of the introduced model was gauged using three primary metrics: precision, recall, and F-measure [6; 67; 68]. Precision measures the proportion of accurately recommended items to the total items in the recommendation list. Its value can be influenced by the length of this list. A higher value of precision indicates more accurate recommendations. The formula for calculating precision, denoted by Equation (6), is:

\[\text{Precision}=\frac{\text{size of hit set}}{\text{size of recommended set}}=\frac{|\text{test}\cap\text{top N}|}{N} \tag{6}\]

Recall, on the other hand, captures the fraction of items that have been rightly recommended out of all the relevant items. In the context of this study, relevant items refer to the resources that users saved in the test dataset. The value of recall can also vary with the size of the recommendation list, and a higher recall value signifies better accuracy.