# Light Graph Convolutional Recommendation Algorithm Based on Hybrid Spreading
## 4 Experiments
### Evaluation Indicators  
Accuracy and diversity are important metrics for evaluating personalized recommendation algorithms. Accuracy is evaluated using Precision, Recall, F1 Score, and Normalized Discounted Cumulative Gain.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **\#Users** & **\#Items** & **\#Ratings** & **Sparsity** \\ \hline MovieLens & 38,493 & 27,278 & 20,000,263 & 0.019047 \\ Douban & 639,125 & 140,502 & 4,428,475 & 0.000049 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dataset information.  
Precision (P) evaluates the proportion of items in the recommendation list that are of interest to the user, while Recall (R) evaluates the proportion of items of interest to the user that are included in the recommendation list. The F1 score (F1) is the harmonic mean of Precision and Recall, combining the performance of both metrics. The Normalized Discounted Cumulative Gain (NDCG) considers the ranking of items in the recommendation list and relevance between users and items.  
These four metrics range between \([0,1]\), with higher values indicating better recommendation accuracy. The formulae are as follows:  
\[\begin{split}&\text{P}=\frac{TP}{TP+FP}\\ &\text{R}=\frac{TP+FN}{TP+FN}\\ &\text{F1}=\frac{2P\cdot R}{P+R}\\ &\text{NDCG}=\frac{\sum_{i=1}^{L}\frac{2^{rel_{i}}-1}{\log_{2}(i+ 1)}}{\sum_{i=1}^{|rel_{i}|}\frac{2^{rel_{i}}-1}{\log_{2}(i+1)}}\end{split} \tag{13}\]  
where \(TP\), \(FP\) and \(FN\) denotes the number of true positive, false positive and false negative samples, respectively. \(L\) is the size of the recommendation list, \(R_{i}(L)\) is the recommendation list of user \(u_{i}\), \(T_{i}\) is the set of items that user \(u_{i}\) has interacted with in the test set, \(|rel_{L}|\) is a list of \(L\) items sorted by relevance, and \(rel_{i}\in\{0,1\}\) is the hierarchical relevance of the recommendation list at position \(i\) (1 if the item is in the test set, 0 otherwise).  
For diversity, considering both user diversity and individual diversity, average Hamming distance and average internal similarity are used for assessment.  
The average Hamming distance(H) effectively evaluates the differences in recommendation lists between users, with values ranging from \([0,1]\). A higher value indicates greater differences in recommendation lists between users, reflecting a higher the degree of user diversity. The formula is as follows:  
\[\text{H}=\frac{1}{m(m-1)}\sum_{i=1}^{m}\sum_{j=1,j\
eq i}^{m}\left(1-\frac{Q_{ ij}}{L}\right) \tag{14}\]  
where \(m\) is the number of users, \(L\) is the size of the recommendation list, \(Q_{ij}\) is the number of overlapping items in the recommendation lists of user \(i\) and user \(j\).  
Additionally, recommendation algorithms should exhibit a certain degree of diversity in recommendation lists for individual users, otherwise, users may become fatigued by receiving recommendation on the same topic. Therefore, this research utilizes Intra-similarity (I) to evaluate individual diversity, with values ranging from \([0,1]\). A smaller value indicates higher individual diversity. The formula is as follows:  
\[\text{I}=\frac{1}{mL(L-1)}\sum_{l=1}^{m}\sum_{o_{i},o_{j}\in\mathbf{E}_{p},l \
eq j}\frac{\sum_{l=1}^{m}a_{li}a_{lj}}{\sqrt{k(o_{i})k(o_{j})}} \tag{15}\]  
where \(m\) is the number of users, \(L\) is the size of the recommendation list, \(k(o_{i}),k(o_{j})\) denotes the degree of items \(o_{i},o_{j}\), \(a_{li},a_{lj}\) is the preference of user \(u_{l}\) for items \(o_{i},o_{j}\), which is usually an interaction matrix indicating whether the user has interactive behavior with the items.