Information Sciences 518 (2020) 56–70 Contents lists available at ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins CAGE: Constrained deep Attributed Graph Embedding Debora Nozza ∗ , Elisabetta Fersini, Enza Messina DISCo, University of Milano-Bicocca, Viale Sarca, 336 -20126 Milan, Italy a r t i c l e i n f o Article history: Received 3 June 2019 Revised 15 November 2019 Accepted 30 December 2019 Available online 31 December 2019 Keywords: Deep learning Representation learning Graph embedding Attributed graph a b s t r a c t In this paper we deal with complex attributed graphs which can exhibit rich connectivity patterns and whose nodes are often associated with attributes, such as text or images. In order to analyze these graphs, the primary challenge is to find an effective way to repre- sent them by preserving both structural properties and node attribute information. To cre- ate low-dimensional and meaningful embedded representations of these complex graphs, we propose a fully unsupervised model based on Deep Learning architectures, called Con- strained Attributed Graph Embedding model (CAGE). The main contribution of the pro- posed model is the definition of a novel two-phase optimization problem that explicitly models node attributes to obtain a higher representation expressiveness while preserving the local and the global structural properties of the graph. We validated our approach on two different benchmark datasets for node classification. Experimental results demonstrate that this novel representation provides significant improvements compared to state of the art approaches, also showing higher robustness with respect to the size of the training data. © 2020 Elsevier Inc. All rights reserved. 1. Introduction Real-world data are often characterized by an underlying relational structure, usually represented by graphs. Social and communication networks, citation networks, transport and utility networks are only some of the most common examples where we can observe complex relational interactions among a potentially large number of entities. Efficient and scalable approaches for handling these large, complex and sparse graphs regard the learning of graph rep- resentations, or Graph Embeddings [2,12], aimed at creating low-dimensional and meaningful representation of nodes by observing different graph properties. This permits to effectively apply off-the-shelf machine learning algorithms designed for handling vector representations on rich relational data for solving a wide variety of data analytics problems [6,38]. At the state of the art, most of the graph Representation Learning approaches derive graph embeddings by preserving the relational structure [26,31,33]. However, they disregard the fact that in real-world domains the nodes in a graph are often associated with a rich set of features or attributes (e.g. text, image, audio), and therefore they would be modeled by the so-called attributed graphs [37]. Capturing also the attribute information could be of paramount importance, especially when nodes are not structurally related but they are similar looking at their attributes. Starting from the primary source of information given by the rela- tional structure, the creation of graph embeddings can take advantage of attributes to enrich the knowledge about nodes and in particular when the graph is sparse and with noisy connections. ∗ Corresponding author. E-mail addresses: debora.nozza@unimib.it (D. Nozza), elisabetta.fersini@unimib.it (E. Fersini), enza.messina@unimib.it (E. Messina). https://doi.org/10.1016/j.ins.2019.12.082 0020-0255/© 2020 Elsevier Inc. All rights reserved.