## 1 Introduction  
Recommender systems typically analyze user ratings and choice histories to provide tailored suggestions. Recommendation algorithms include content-based filtering, collaborative filtering, deep learning, and hybrid recommendation techniques. Content-based recommendation techniques analyze the properties of an item and recommend similar items. They recommend content similar to the items that users have used, preferred, or selected in the past. For example, in the context of movie recommendations, similar films are recommended to the user based on the genre, director, and actors of the movies that the user selected in the past. Content-based recommender systems directly reflect individual preferences. However, a drawback is that the accuracy of recommendations may decline in the absence of sufficient information about new items, or if the user lacks a diverse range of past experiences. On the other hand, collaborative filtering recommendation techniques are based on the choices of other users who have similar preferences to the user. These techniques fundamentally ground their recommendations in measures of user similarity. Specifically, user-based collaborative filtering employs user similarity metrics to generate recommendations, while item-based collaborative filtering relies on item similarity for the same purpose. Deep learning-based recommendation techniques employ deep learning models of neural networks, to predict interactions between users and items for the purpose of making recommendations. Lastly, hybrid recommendation techniques combine the above recommendation methods to offset the limitations inherent in each individual recommender system. Figure 1 illustrates the process of recommending movies with a conventional recommender system. After categorizing the features of each user's favored movies, the recommender system computes similarities based on users' rating matrices. For example, in Figure 1, Users 1 and 3 have high user similarity. Therefore, the other movie that User 3 favored are recommended to User 1. When a new user appears, the similarities between the existing users and the new are measured for the recommendation to the new user. Pearson correlation coefficient and the Cosine similarity are often used to measure such similarities. The Pearson correlation coefficient is a numerical measure indicating the relationship between two compared variables. It is used based on the ratings of items commonly rated by two users, with its formula being as follows:  
\[\text{r}=\frac{\sum_{i}^{n}\left(\text{X}_{i}-\ \overline{\text{X}}_{i} \right)\left(\text{Y}_{i}-\ \overline{\text{Y}}\right)}{\sqrt{\sum_{i}^{n}\left(\text{X}_{i}-\ \overline{\text{X}}\right)^{2}}\sqrt{\sum_{i}^{n}\left(\text{Y}_{i}-\ \overline{\text{Y}}\right)^{2}}}\]  
Here, X and Y represent the ratings of the main user, and are the average ratings of other users, with \(+1\) indicating a positive linear relationship, \(0\) indicating no linear relationship, and \(-1\) indicating a negative linear relationship. The cosine similarity for two users is defined by the cosine of the angle between two vectors of users, and the formula is,  
\[\text{Cosine\_similarity}\ =\frac{\sum_{i=1}^{n}\left(\text{X}_{i}\times\text{Y}_{i} \right)}{\sqrt{\sum_{i=1}^{n}\left(\text{X}_{i}\right)^{2}}\sqrt{\sum_{i=1}^ {n}\left(\text{Y}_{i}\right)^{2}}}\]  
Here, X and Y represent the rating vectors of two users. The cosine similarity is between \(-1\) and \(1\), where \(-1\) indicates a completely different direction (i.e., an angle of 180 degrees), \(1\) indicates the same direction, and \(0\) corresponds to an angle of 90 degrees. The closer the cosine similarity value is to \(1\), the higher the similarity is judged to be. Existing recommendation algorithms have to repeat similar calculations for new and rapidly created information (user or movie) using the Pearson correlation coefficient and Cosine similarity.