## 3 Proposed System
### Detail Implementation Flow
#### 3.3.2 Phase Two
### Recommendation Results

Experimental results demonstrate the efficacy of the proposed approach in comparison to baseline methods. Table 1 evaluates how many of the top-k recommendations are relevant and the recommendation result analysis. The current study selects various \(k\) evaluations. A higher P@k value indicates a greater number of relevant recommendations of the top-k items, making the model more effective in its suggestions. To provide convenience analysis, the study divides the results into three parts, including Surprise, Cornac, and the proposed model from our side. In the first part, we discuss the Surprise library; in the second, we analyze performance using Cornac; and, finally, we present the results from our proposed model. Table 1 presents a comparative analysis of the recommendation system from various library perspectives. Figure 4 displays the visualization results from our implementation techniques. The study shows the recommendation performance between the benchmark models and our models. The graph includes a variety of models, such as SVD, k-Nearest Neighbors (KNN) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **P@5** & **P@10** & **P@15** & **P@20** \\ \hline SVD & 0.7756 & 0.7651 & 0.7608 & 0.7578 \\ KNNBasic & 0.7948 & 0.7831 & 0.7792 & 0.7755 \\ KNNWithZScore & 0.6615 & 0.6578 & 0.6505 & 0.6493 \\ KNNBaseline & 0.7513 & 0.7420 & 0.7391 & 0.7347 \\ SVDpp & 0.7922 & 0.7802 & 0.7733 & 0.7682 \\ \hline GMF & 0.3935 & 0.3560 & 0.3286 & 0.3088 \\ MLP & 0.4150 & 0.3674 & 0.3350 & 0.3104 \\ MMMF & 0.1162 & 0.1133 & 0.1030 & 0.0922 \\ NeuMF & 0.4240 & 0.3728 & 0.3412 & 0.3166 \\ VAECF & 0.2195 & 0.1900 & 0.1712 & 0.1570 \\ \hline OURS (Adadelta) & 0.6933 & 0.6907 & 0.6948 & 0.6982 \\ OURS (Adam) & 0.7445 & 0.7344 & 0.7241 & 0.7258 \\ OURS (SGD) & 0.7391 & 0.7445 & 0.7464 & 0.7448 \\ OURS (RMSprop) & 0.6880 & 0.6771 & 0.6752 & 0.6838 \\ OURS (Adamax) & 0.6908 & 0.6792 & 0.6832 & 0.6868 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance Results of Recommendation Models. based models with different optimizations, Singular Value Decomposition++ (SVDpp), Generalized Matrix Factorization (GMF), Multi-Layer Perceptron (MLP), and others, including several variations of a model denoted as \"OURS\", with different optimizations like AdaGrad, SGD, RMSprop, and Adamax. We conduct a test of metrics evaluation score for each model at different levels of k (5, 10, 15, 20), which evaluates the models on how well they predict the top 5, 10, 15, and 20 items on a recommendation list. The scores are typically between 0 and 1, with 1 being a perfect score. First, we introduce the evaluation model from our work. Among the five optimizer techniques that are used with the system, OURS (Adam and SGD) yields the best result among OURS (Adadelta, Adamax, RMSprop). The Adam optimizer is the model that performs best at P@5, while the SGD optimizer leads at P@10, P@15, and P@20 (0.7445, 0.7464, 0.7448). The lowest model within the proposed system is OURS (RMSprop). It shows the lowest performance across all the k values (0.6880, 0.6771, 0.6752, 0.6838). The Adadelta (0.6933, 0.6907, 0.6948, 0.6982) and Adamax (0.6908, 0.6792, 0.6832, 0.6868) optimizers perform better than RMSprop but do not outperform Adam and SGD. Next, we compare them with other benchmark models. Among all comparison models, KNNbasic achieves the highest precision values across all k values (0.7948, 0.7831, 0.7792, 0.7755), indicating that it is the best-performing model. The second-best model with precision values of 0.7922, 0.7802, 0.7733, 0.7682, SVD shows consistent performance with a slight decline as k increases (0.7756, 0.7651, 0.7608, 0.7578). KNNBaseline performs slightly worse than SVD (0.7513, 0.7420, 0.7391, 0.7347). KNNWiZScore has the lowest performance in the Surprise library (0.6615, 0.6578, 0.6505, 0.6493). The benchmark models from the Cornac library demonstrates the worst performance.