Graph Neural Networks for Homogeneous and Heterogeneous Graphs:

Abstract

A graph is used to represent complex systems where both entities and their interconnections are equally important. Real-life situations, e.g., social networks, biological networks, recommender systems, etc., are better modeled in terms of graphical structures, as the information about individual entities is not enough to understand the whole system. Due to the existence of non-uniformity in graphical data, traditional machine learning algorithms that perform tasks like prediction, classification, etc., can not be applied directly to such data. Graph Neural Networks (GNNs) are robust variants of deep neural network models that are typically designed to learn from such graphical data. GNN involves transforming graph data into Euclidean representations that various machine-learning algorithms can utilize. In this thesis, two types of graphs have been studied. In the first two contributory chapters, the graphs considered are homogeneous, where all nodes are of the same type. Chapter 2 describes a model called Interval-Valued Graph Neural Network (IV-GNN), which has been developed to handle homogeneous graphs with interval-valued node features. This model relaxes the restriction that the node features should be singlevalued. Here, interval-valued features are allowed, and the corresponding GNN model, along with its mathematical analysis, is presented. Chapter 3 discusses the importance of hierarchical structure learning within a graph. It describes a model called GraMMy, which is designed for hierarchical semantics-driven graph representation learning based on Micro-Macro analysis. It focuses on the graph at different levels of abstraction to allow the flexible flow of information between the higher-order neighborhoods. The task that we aim to perform on the homogeneous graphs in Chapter 2 and 3 is graph classification. The second part of the thesis deals with heterogeneous graphs. We consider the social recommender system as an area of application. We have modeled the problem of predicting missing rating value for a user to an item as a link prediction task in a heterogeneous graph setting where multiple types of nodes are present in the data. In our third contribution (Chapter 4), the aim is to quantify the usefulness of the ratings given by the user to an item. For this purpose, a metric called Influence Score of a user has been defined and incorporated into a GNN-based recommender system to develop a Social Influence-aware recommendation system, SInGER. Although SInGER improves the prediction quality, a limitation of the approach is the uniform definition of the Influence Score, irrespective of the data set considered. To overcome this, in the fourth work (Chapter 5), we develop a neural architecture to capA graph is used to represent complex systems where both entities and their interconnections are equally important. Real-life situations, e.g., social networks, biological networks, recommender systems, etc., are better modeled in terms of graphical structures, as the information about individual entities is not enough to understand the whole system. Due to the existence of non-uniformity in graphical data, traditional machine learning algorithms that perform tasks like prediction, classification, etc., can not be applied directly to such data. Graph Neural Networks (GNNs) are robust variants of deep neural network models that are typically designed to learn from such graphical data. GNN involves transforming graph data into Euclidean representations that various machine-learning algorithms can utilize. In this thesis, two types of graphs have been studied. In the first two contributory chapters, the graphs considered are homogeneous, where all nodes are of the same type. Chapter 2 describes a model called Interval-Valued Graph Neural Network (IV-GNN), which has been developed to handle homogeneous graphs with interval-valued node features. This model relaxes the restriction that the node features should be singlevalued. Here, interval-valued features are allowed, and the corresponding GNN model, along with its mathematical analysis, is presented. Chapter 3 discusses the importance of hierarchical structure learning within a graph. It describes a model called GraMMy, which is designed for hierarchical semantics-driven graph representation learning based on Micro-Macro analysis. It focuses on the graph at different levels of abstraction to allow the flexible flow of information between the higher-order neighborhoods. The task that we aim to perform on the homogeneous graphs in Chapter 2 and 3 is graph classification. The second part of the thesis deals with heterogeneous graphs. We consider the social recommender system as an area of application. We have modeled the problem of predicting missing rating value for a user to an item as a link prediction task in a heterogeneous graph setting where multiple types of nodes are present in the data. In our third contribution (Chapter 4), the aim is to quantify the usefulness of the ratings given by the user to an item. For this purpose, a metric called Influence Score of a user has been defined and incorporated into a GNN-based recommender system to develop a Social Influence-aware recommendation system, SInGER. Although SInGER improves the prediction quality, a limitation of the approach is the uniform definition of the Influence Score, irrespective of the data set considered. To overcome this, in the fourth work (Chapter 5), we develop a neural architecture to capA graph is used to represent complex systems where both entities and their interconnections are equally important. Real-life situations, e.g., social networks, biological networks, recommender systems, etc., are better modeled in terms of graphical structures, as the information about individual entities is not enough to understand the whole system. Due to the existence of non-uniformity in graphical data, traditional machine learning algorithms that perform tasks like prediction, classification, etc., can not be applied directly to such data. Graph Neural Networks (GNNs) are robust variants of deep neural network models that are typically designed to learn from such graphical data. GNN involves transforming graph data into Euclidean representations that various machine-learning algorithms can utilize. In this thesis, two types of graphs have been studied. In the first two contributory chapters, the graphs considered are homogeneous, where all nodes are of the same type. Chapter 2 describes a model called Interval-Valued Graph Neural Network (IV-GNN), which has been developed to handle homogeneous graphs with interval-valued node features. This model relaxes the restriction that the node features should be singlevalued. Here, interval-valued features are allowed, and the corresponding GNN model, along with its mathematical analysis, is presented. Chapter 3 discusses the importance of hierarchical structure learning within a graph. It describes a model called GraMMy, which is designed for hierarchical semantics-driven graph representation learning based on Micro-Macro analysis. It focuses on the graph at different levels of abstraction to allow the flexible flow of information between the higher-order neighborhoods. The task that we aim to perform on the homogeneous graphs in Chapter 2 and 3 is graph classification. The second part of the thesis deals with heterogeneous graphs. We consider the social recommender system as an area of application. We have modeled the problem of predicting missing rating value for a user to an item as a link prediction task in a heterogeneous graph setting where multiple types of nodes are present in the data. In our third contribution (Chapter 4), the aim is to quantify the usefulness of the ratings given by the user to an item. For this purpose, a metric called Influence Score of a user has been defined and incorporated into a GNN-based recommender system to develop a Social Influence-aware recommendation system, SInGER. Although SInGER improves the prediction quality, a limitation of the approach is the uniform definition of the Influence Score, irrespective of the data set considered. To overcome this, in the fourth work (Chapter 5), we develop a neural architecture to capture user trust without explicitly defining it. It provides an effective means of implicitly accounting for trust propagation and composability while performing GNN-based analyses to accomplish the overall task of item rating prediction.