IV-GNN : interval valued data handling using graph neural network

Interval-valued data is an effective way to represent complex information where uncertainty, inaccuracy etc. are involved in the data space and they are worthy of taking into account. Interval analysis together with neural network has proven to work well on Euclidean data. However, in real-life scenarios, data follows a much more complex structure and is often represented as graphs, which is non-Euclidean in nature. Graph Neural Network is a powerful tool to handle graph like data with countable feature space. So, there is a research gap between the interval-valued data handling approaches and existing GNN model. No model in GNN literature can handle a graph with interval-valued features and, on the other hand, Multi Layer Perceptron (MLP) based on interval mathematics can not process the same due to non-Euclidean structure behind the graph. This article proposes an Interval-Valued Graph Neural Network, a novel GNN model where, for the first time, we relax the restriction of the feature space being countable without compromising the time complexity of the best performing GNN model in the literature. Our model is much more general than existing models as any countable set is always a subset of the universal set [Formula: see text] , which is uncountable. Here, to deal with interval-valued feature vectors, we propose a new aggregation scheme of intervals and show its expressive power to capture different interval structures. We validate our theoretical findings about our model for graph classification task by comparing its performance with those of the state-of-the-art models on several benchmark and synthetic network datasets.