# Deep Matrix Factorization Approach for Collaborative Filtering Recommender Systems
## 4 Discussion  
In this paper, we presented DeepMF, a novel MF-based CF algorithm using a dl approach. As stated in Section 1 the dl is an incipient approach in the ml field that consists of a hierarchical self-training method that uses the information acquired from data. Although dl has been used mainly in artificial neural networks, the proposed model breaks this tendency by applying the foundations of dl to the field of mf. The essence of the proposed method lies in the dl approach. Our model performs successive matrix factorizations in order to successively refine the model output. Thus, the first factorization, the least deep one, represents the classic approach of mf-based CF models and seeks to predict the score that a user will give to an item. The second factorization seeks to refine the previous prediction by trying to increase the predictions that tend to be lower than the real rating and decrease those that tend to be higher. Subsequently, the learning is deepened by correcting the errors of the errors to build a dl model that converges towards a prediction as close as possible to the real value to be learned. This expected behavior is corroborated by the results of the experiment shown in Figure 3. On it, we plot the average value of the predictions provided by each factorization layer according to its depth. The same decreasing trend in the average prediction is observed in all the analyzed datasets: as factorization is deeper, errors to be refined tend to zero and the learning process converges. The Figure 3 includes the top 5 combinations of hyper-parameters obtained in the grid search shown in Table 3. Note that a logarithmic scale has been used on the \(y\)-axis to emphasize the differences in the deeper factorizations. Figure 3: Average value of the predictions provided by each factorization according to its depth. Top 5 combinations of hyper-parameters for each dataset included in Table 3 are shown. The hypothesis of this contribution was that a dl approach applied to a mf-based cf can improve the quality of both predictions and recommendations. This hypothesis has been confirmed with the experimental results showed in Section 3. The quality of the predictions (see Table 4) and recommendations (see Figure 2) of the proposed method, DeepMF, exceeds the baselines used in the 3 datasets analyzed: MovieLens 100K, MovieLens 1M and FilmTrust. Summarizing, the proposed model in this paper expands the landscape of matrix factorization models by importing a Deep Learning approach from the field of neural computing. From this point, several future research lines open. Maybe, the most obvious one would be to analyze the dl approach performed in this paper with other matrix factorization models and to define different loss functions depending on the depth of factorization. For example, experimental results show that SVD++ factorization works properly on MyAnimeList dataset, so it would be interesting to evaluate the performance of DeepMF using SVD++ as the initial factorization and other factorizations models for the deeper factorizations. A more ambitious prospective work would be transferring the ideas of this paper to a purely bioinspired framework. For instance, it can be studied the incorporation of DeepMF as a model to be implemented by the neurons of a fully connected or convolutional neural network. In this way, the knowledge of the scientific community about network architectures can be applied to give rise to deeper an more involved nested patterns of matrix factorizations. Conceptualization, R.L.-C. and A.G.-P. and F.O. ; formal analysis, A.G.-P.; methodology, R.L.-C. and F.O. ; software, A.G.-P. and F.O. ; writing--original draft preparation, R.L.-C. and A.G.-P. and F.O. ; writing--review and editing, R.L.-C. All authors have read and agreed to the published version of the manuscript. This work has been supported by Spanish Ministry of Science and Education and Competitivity (MINECO) and European Regional Development Fund (FEDER) under grants TIN2017-85727-C4-3-P (DeepBio).