Factorization threshold models for scale-free networks generation

Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks have been obtained by now and most of them are based on the preferential attachment approach. We will offer the model with another scale-free property explanation. The main idea is to approximate the network's adjacency matrix by multiplication of the matrices $V$ and $V^T$, where $V$ is the matrix of vertices' latent features. This approach is called matrix factorization and is successfully used in the link prediction problem. To create a generative model of scale-free networks we will sample latent features $V$ from some probabilistic distribution and try to generate a network's adjacency matrix. Entries in the generated matrix are dot products of latent features which are real numbers. In order to create an adjacency matrix, we approximate entries with the Boolean domain $\{0, 1\}$. We have incorporated the threshold parameter $\theta$ into the model for discretization of a dot product. Actually, we have been influenced by the geographical threshold models which were recently proven to have good results in a scale-free networks generation. The overview of our results is the following. First, we will describe our model formally. Second, we will tune the threshold $\theta$ in order to generate sparse growing networks. Finally, we will show that our model produces scale-free networks with the fixed power-law exponent which equals two. In order to generate oriented networks with tunable power-law exponents and to obtain other model properties, we will offer different modifications of our model. Some of our results will be demonstrated using computer simulation

Deep Learning based Recommender System: A Survey and New Perspectives

With the ever-growing volume of online information, recommender systems have been an effective strategy to overcome such information overload. The utility of recommender systems cannot be overstated, given its widespread adoption in many web applications, along with its potential impact to ameliorate many problems related to over-choice. In recent years, deep learning has garnered considerable interest in many research fields such as computer vision and natural language processing, owing not only to stellar performance but also the attractive property of learning feature representations from scratch. The influence of deep learning is also pervasive, recently demonstrating its effectiveness when applied to information retrieval and recommender systems research. Evidently, the field of deep learning in recommender system is flourishing. This article aims to provide a comprehensive review of recent research efforts on deep learning based recommender systems. More concretely, we provide and devise a taxonomy of deep learning based recommendation models, along with providing a comprehensive summary of the state-of-the-art. Finally, we expand on current trends and provide new perspectives pertaining to this new exciting development of the field.Comment: The paper has been accepted by ACM Computing Surveys. https://doi.acm.org/10.1145/328502