Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) isin IR^m that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

In this paper, we will consider the approximation properties of a recently introduced neural network model called graph neural network (GNN), which can be used to process-structured data inputs, e.g., acyclic graphs, cyclic graphs, and directed or undirected graphs. This class of neural networks implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n onto an m-dimensional Euclidean space. We characterize the functions that can be approximated by GNNs, in probability, up to any prescribed degree of precision. This set contains the maps that satisfy a property called preservation of the unfolding equivalence, and includes most of the practically useful functions on graphs; the only known exception is when the input graph contains particular patterns of symmetries when unfolding equivalence may not be preserved. The result can be considered an extension of the universal approximation property established for the classic feedforward neural networks (FNNs). Some experimental examples are used to show the computational capabilities of the proposed model.

An artificial neural network model, capable of processing general types of graph structured data, has recently been proposed. This paper applies the new model to the computation of customised page ranks problem in the World Wide Web. The class of customised page ranks that can be implemented in this way is very general and easy because the neural network model is learned by examples. Some preliminary experimental findings show that the model generalizes well over unseen Web pages, and hence, may be suitable for the task of page rank computation on a large Web graph.

Breast cancer is the most common cancer affecting females worldwide. Breast cancer survivability prediction is challenging and a complex research task. Existing approaches engage statistical methods or supervised machine learning to assess/predict the survival prospects of patients. The main objectives of this paper is to develop a robust data analytical model which can assist in (i) a better understanding of breast cancer survivability in presence of missing data, (ii) providing better insights into factors associated with patient survivability, and (iii) establishing cohorts of patients that share similar properties. Unsupervised data mining methods viz. the self-organising map (SOM) and density-based spatial clustering of applications with noise (DBSCAN) is used to create patient cohort clusters. These clusters, with associated patterns, were used to train multilayer perceptron (MLP) model for improved patient survivability analysis. A large dataset available from SEER program is used in this study to identify patterns associated with the survivability of breast cancer patients. Information gain was computed for the purpose of variable selection. All of these methods are data-driven and require little (if any) input from users or experts. SOM consolidated patients into cohorts of patients with similar properties. From this, DBSCAN identified and extracted nine cohorts (clusters). It is found that patients in each of the nine clusters have different survivability time. The separation of patients into clusters improved the overall survival prediction accuracy based on MLP and revealed intricate conditions that affect the accuracy of a prediction. A new, entirely data driven approach based on unsupervised learning methods improves understanding and helps identify patterns associated with the survivability of patient. The results of the analysis can be used to segment the historical patient data into clusters or subsets, which share common variable values and survivability. The survivability prediction accuracy of a MLP is improved by using identified patient cohorts as opposed to using raw historical data. Analysis of variable values in each cohort provide better insights into survivability of a particular subgroup of breast cancer patients.