## 3 Results
### Experimental Design
#### 3.1.2 Experimental Setup  
We experimented with leave-one-out cross-validation. Specifically, after sorting using the timestamp column, only the movie that each user watched last was collected and saved as a test set. The hit ratio (HR) and normalized discounted cumulative gain (NDCG), which are frequently used terms in recommendation, were used as evaluation metrics. The HR was used to check whether an item was included in the top ranking, and the NDCG was affected by the position in the top ranking. To calculate these two metrics, a list of 100 movies that comprised the one left out at the end for testing and 99 randomly sampled movies unseen by the user were employed.  
We first constructed a user graph for each user and extracted the frequent subgraph. The function of minimum support value was set as follows:  
\[f(x)=\left\{\begin{array}{cc}2&(3\leq x<8)\\ [lnx]&(x\geq 8)\end{array}\right. \tag{13}\]  
where the number of movies the user has watched is \(x\).  
Most users only watched a few movies, but some watched hundreds or thousands. Thus, applying the same value to all the users would not be fair. However, if an excessively high threshold is applied to those who watch many movies, the criterion for judging the user preference exhibits an excessively large difference. Thus, considering both the absolute and relative values, we used \(ln\ x\) which gradually increases; the value was approximated to an integer. Regarding the case wherein eight or less movies were watched, the value of \(f(x)\) was one; hence, we set the value to two because a triple that appears once should not be considered frequent.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **ml-Small** & **ml-1m** \\ \hline Users & 630 (671) & 6040 (6070) \\ Items & 9048 (9066) & 3666 (3706) \\ Interactions & 99,898 (100,004) & 997,407 (1,000,209) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Dataset Information.  
After the frequent subgraphs were selected, they were vectorized through user profiling. The movie pool for negative sampling was a set of all the items \(I\) that at least one user had interacted with, and the number of negative samples for each positive sample was four. Finally, 100 movies were ranked based on the probability value \(\hat{y}_{ui}\) derived from the neural network.  
The neural network model was implemented in TensorFlow, and the tested learning rates were 0.0005, 0.001, 0.002, and 0.005; the batch sizes were 256, 512, and 1024, and the dimensions of the embedding vector were 32, 64, 128, and 256.  
The main baseline models were as follows: itemPop (item popularity) simply recommends items based on their popularity [25]; itemKNN [26] uses the similarities between items to identify the set of items to be recommended; Bayesian personalized ranking (BPR) employs the optimization criterion BPR-Opt and solves the recommendation problem from a Bayesian point of view [27]; the factored item similarity model (FISM) uses an item-item similarity matrix as the product of two latent factor matrices [28]; neural attentive item similarity (NAIS) uses a neural network model involving the application of the attention mechanism [29]; hamming spatial graph convolutional networks (HS-GCN) [30] capture hamming similarity between users and items through graph convolution operation; and recurrent KG embedding (RKGE) [31] obtains graph embeddings for recommendation using recurrent neural networks.