# Evolving Matrix-Factorization-Based Collaborative Filtering Using Genetic Programming
## 4 Discussion  
This paper presents a new approach to improve the quality of predictions provided by MF models applied to CF-based RS. Related work shows that MF models aggregate the learned factors of users and items through a linear combination of them, i.e., the inner product of the vector that represents the latent factors of the users and the vector that represents the latent factors of the items. This aggregation is based on the assumption that the ratings of a CF system must be modeled by means of a lineal factorization model. This restriction is enforced during the model design so it is not learned from the data. To impose apriorisms in the design of machine learning algorithms is a bad practice that should be avoided. This contribution breaks from this apriorism and lets the data to find the optimal mathematical function to aggregate the user and item latent factors without any restriction. Experimental results show that there exists better approaches to aggregate latent factors spaces than the traditional lineal aggregation. This work must be analyzed as a preliminary work in this field since these conclusions are supported by two datasets with a low number of ratings due to the high computational cost of the proposed method. One of the drawbacks of using evolutionary computation is, precisely, the high computational cost. As a population-based method that needs to evaluate the fitness of the individuals following a generational scheme, the critical point of the computational complexity of such methods is the evaluation function. In the case of EMF, the evaluation function performs the MF according to the evolved function represented by the individual and then computes the MAE. Due to the high computational cost of this process, which is executed several times on each generation, we had to use rather small datasets for the experimentation. Although using GP in MF might be seen as counterproductive due to the high computational cost, that problem can be mitigated with a proper setup of the algorithm, that is, reducing the size of the population as well as the number of generations. In fact, according to our experimental results, the most significant improvements in the quality of the solutions happen within the first generations (see Figure 4). Hence, we can deal with the aforementioned issue keeping a low number of generations and population size while obtaining promising results compared to other MF methods. Even though it is not possible to guarantee that EMF reaches a global optimum, as evolutionary algorithms are approximate optimization methods, we analyzed the best individuals of each EMF execution to study its exploration capabilities. Figure 7: Graphical representation of the distances between the best individuals of each execution of EMF for the (**a**) MovieLens and (**b**) FilmTrust datasets. The length of the edges is proportional to the \(L^{2}\) distance between the corresponding aggregate functions. The mean distance in the MovieLens graph is 70% bigger than the mean distance in FilmTrust. In this work, the fitness function proposed for the GP-based optimization method has been designed to increase the accuracy of the predictions performed by the CF method. However, there are other measures widely used to evaluate the quality of the output of a RS [31]. On one hand, to evaluate the quality of the recommendations, measures such as precision, recall, and F1 are commonly used. On the other hand, to evaluate the quality of a list of recommendations, nDCG is the most used measure. In future work, we propose to apply multiobjective GP-based optimization in such a way that the accuracy of predictions, the veracity of the recommendations, and the quality of the list of recommendations are boosted. Another improvement to the evolutionary process of EMF is to include an additional step within the breeding pipeline to reduce the complexity of the generated trees by using rewriting tools.