# Dirichlet Matrix Factorization: A Reliable Classification-Based Recommender System
## 1 Introduction  
In the latest years, society is becoming more and more saturated with the overwhelming amount of information available to costumers. For this reason, the use of algorithms for information retrieval and sorting is becoming a cornerstone in the technological solutions offered. An important instance of these methods is Recommender Systems (RSs), which aid users to match with items in the most efficient way possible, taking into account both the user's own preferences and those of others with similar tastes. An evidence of the deep penetration of these algorithms in the industry is the high number of companies that use RSs as part of their business model, such as Amazon, eBay, Netflix, Twitter and many others. However, although improving recommendation accuracy has been the main target for academic researchers [1], other objectives that are beyond improving accuracy have also attracted the interest of the community in recent years [2]. Metrics such as coverage, diversity and novelty are goals of cutting-edge research since users typically prefer to be recommended items with a certain degree of novelty. Recent RSs research suggests that accurate recommendations are possible [3]: when RSs recommend a restaurant by awarding it five stars, a human is likely to be skeptical of the rating. Some RSs provide some extra data that help us to deduce the rating's trustworthiness such as the number of individuals who have voted for the restaurant. Almost everyone prefers a restaurant with an average rating of 4 stars and 5000 reviews to one with just 5 reviews and an average rating of 5 stars. In this framework, a recommendation does not only comprise the recommended item, but also an associated reliability value provided through RSs techniques and models for trustworthiness. The core of every RS is its filtering mechanism. Broadly speaking, the system makes recommendations based on context [4], content [5], social environment [6], demographic data [7] and collaborative information, the latter being the most widely used approach [8]. Hybrid methods [9], which combine Collaborative Filtering (CF) and other filtering sources, are commonly used in commercial RS designs. Among CF methods, Probabilistic Matrix Factorization (PMF) [10] is arguably the most relevant contribution to the area in the latest times. It models the process of assigning a rating as regression process that follows a normal distribution with mean given by the inner product of two 'hidden vectors' associated to each user and item. Since it inception, other CF models have been proposed to extend the ideas PMF to work with more general frameworks. One of the most promising lines is to combine the hidden vectors in a non-linear way, in sharp contrast with the usual operation of PMF. For instance, in [11], two new models are proposed inspired by deep learning techniques, namely, Generalized Matrix Factorization (GMF) and Neural Collaborative Filtering (NCF). In the former, instead of the standard inner product in the euclidean space, a more general inner product is allowed, which is learned during the training process. To definitely break with linearity, this work also proposes NCF, in which the inner product is fully substituted by a neural network able to combine the hidden vectors in a highly non-linear way. Despite these advances, recent works show that, in the RSs field, providing precise reliability values that are connected with forecasts is a major aim, as it provides many advantages: new ways of providing recommendations to the user that take into account the reliability of the prediction, achieving better accuracy by filtering low reliability recommendations, and identifying a cold start problem when every recommendation for an user has low reliability.