## 6 Novel Initialization Method Using Content-Based Information for Matrix Factorization Techniques  
As introduced in Section 2.2, matrix factorization is a well-known technique for discovering latent features. Although this technique performs well on extremely sparse data such as rating matrix, it lacks explainability: latent factors achieved after training a matrix factorization model are most likely uninterpretable. Furthermore, traditional matrix factorization methods randomly initialize user and item vectors during the training process that may lead to slow convergence. Especially, NMF is greatly affected by the initialization: if the initial values of \(p_{u}\) and \(q_{i}\) are not good, it is more likely that the training will be unstable, and even unable to converge [11; 48]. Recent years have witnessed a large number of efforts to eliminate these problems. One of the highly promising approaches is to initialize the latent vectors with more meaningful values [15; 16]. In this paper, a new method of initialization in matrix factorization is proposed: instead of learning user and item features from randomly valued vectors, we attempt to integrate both content- and rating-based information into the initial vectors. Currently, one of the common ways to describe user preferences is using the interactions that a user assigned to the movies she watched. However, by using this method, rating data and movie attributes are treated independently, which may cause a huge waste of information. To tackle this issue, a new way of generally profiling a user that incorporates content-based data of all the movies she rated is introduced as follows. \[P_{u}=\frac{1}{|R(u)|}\sum_{i\in R(u)}(\tilde{r}_{ui}\times Q_{i}) \tag{13}\]  
where \(\tilde{r}_{ui}\) denotes the rating user \(u\) gave to movie \(i\) which has been normalized to the range of \([0,1]\), and \(Q_{i}\) is the feature vector of movie \(i\) that reflects its content-related information. Recall that \(R(u)\) denotes the set of all movies rated by user \(u\). In such a manner, a user vector \(P_{u}\) has the same dimension and range of values as a movie vector \(Q_{i}\). More importantly, each user is characterized in an explainable way: elements with grearer values indicate that the user has a greater preference for the respective movie attributes and vice versa. Finally, both the user and movie latent features of the matrix factorization model are initialized using the vectors \(P_{u}\)'s and \(Q_{i}\)'s described above. During the scope of this work, the Tag Genome is utilized to demonstrate the content of each movie. In order to comprehensively evaluate the new method of initialization, different representations of a movie based on these metadata are experimented: the 1128 original genome tags, the shortened 1044 ones using NLP [39], and the two 600-element feature vectors generated using the newly proposed HCAE and the DAE which yield the best results in the previous section. We refer to the proposed models with _-genome_ suffix to indicate that the user and movie genome scores are integrated into the learning process where the number of latent factors \(k\) must match the dimension of corresponding feature vectors. In our experiments, SVD-genome and NMF-genome models are trained with the learning rate of 0.005 and the regularization strength of 0.02. The randomly initialized counterparts are trained 20 times using the same hyperparameters to select the most precise models for comparison. For clarity, we only include RMSE in Table 5.  
As displayed in Table 5, incorporating rating data and movie attributes into the initialization significantly boosts SVD-genome and NMF-genome models over their original versions. In detail, the proposed models show an exceptionally faster convergence rate against the competitors in all experiments: the training time measured by the number of epochs is reduced to at least 34.43%, especially up to 63.40% and 78.57% with the models utilizing HCAE-generated feature vectors.