Quaternion Graph Neural Networks

Recently, graph neural networks (GNNs) become a principal research direction to learn low-dimensional continuous embeddings of nodes and graphs to predict node and graph labels, respectively. However, Euclidean embeddings have high distortion when using GNNs to model complex graphs such as social networks. Furthermore, existing GNNs are not very efficient with the high number of model parameters when increasing the number of hidden layers. Therefore, we move beyond the Euclidean space to a hyper-complex vector space to improve graph representation quality and reduce the number of model parameters. To this end, we propose quaternion graph neural networks (QGNN) to generalize GCNs within the Quaternion space to learn quaternion embeddings for nodes and graphs. The Quaternion space, a hyper-complex vector space, provides highly meaningful computations through Hamilton product compared to the Euclidean and complex vector spaces. As a result, our QGNN can reduce the model size up to four times and enhance learning better graph representations. Experimental results show that the proposed QGNN produces state-of-the-art accuracies on a range of well-known benchmark datasets for three downstream tasks, including graph classification, semi-supervised node classification, and text (node) classification. Our code is available at: https://github.com/daiquocnguyen/QGNNComment: The extended abstract has been accepted to NeurIPS 2020 Workshop on Differential Geometry meets Deep Learning (DiffGeo4DL). The code in Pytorch and Tensorflow is available at: https://github.com/daiquocnguyen/QGN

Two-view Graph Neural Networks for Knowledge Graph Completion

We present an effective GNN-based knowledge graph embedding model, named WGE, to capture entity- and relation-focused graph structures. In particular, given the knowledge graph, WGE builds a single undirected entity-focused graph that views entities as nodes. In addition, WGE also constructs another single undirected graph from relation-focused constraints, which views entities and relations as nodes. WGE then proposes a GNN-based architecture to better learn vector representations of entities and relations from these two single entity- and relation-focused graphs. WGE feeds the learned entity and relation representations into a weighted score function to return the triple scores for knowledge graph completion. Experimental results show that WGE outperforms competitive baselines, obtaining state-of-the-art performances on seven benchmark datasets for knowledge graph completion.Comment: 13 pages; 3 tables; 3 figure

Multiobjective Logistics Optimization for Automated ATM Cash Replenishment Process

In the digital transformation era, integrating digital technology into every aspect of banking operations improves process automation, cost efficiency, and service level improvement. Although logistics for ATM cash is a crucial task that impacts operating costs and consumer satisfaction, there has been little effort to enhance it. Specifically, in Vietnam, with a market of more than 20,000 ATMs nationally, research and technological solutions that can resolve this issue remain scarce. In this paper, we generalized the vehicle routing problem for ATM cash replenishment, suggested a mathematical model and then offered a tool to evaluate various situations. When being evaluated on the simulated dataset, our proposed model and method produced encouraging results with the benefits of cutting ATM cash operating costs

Transport Jc in Bulk Superconductors: A Practical Approach?

The characterisation of the critical current density of bulk high temperature superconductors is typically performed using magnetometry, which involves numerous assumptions including, significantly, that Jc within the sample is uniform. Unfortunately, magnetometry is particularly challenging to apply where a local measurement of Jc across a feature, such as a grain boundary, is desired. Although transport measurements appear to be an attractive alternative to magnetization, it is extremely challenging to reduce the cross-sectional area of a bulk sample sufficiently to achieve a sufficiently low critical current that can be generated by a practical current source. In the work described here, we present a technique that enables transport measurements to be performed on sections of bulk superconductors. Metallographic techniques and resin reinforcement were used to create an I-shaped sample of bulk superconductor from a section of Gd-Ba-Cu-O containing 15 wt % Ag2O. The resulting superconducting track had a cross-sectional area of 0.44 mm2. The sample was found to support a critical current of 110 A using a field criterion in the narrowed track region of 1 μV cm-1. We conclude, therefore, that it is possible to measure critical current densities in excess of 2.5 x 108 A m-2 in sections of a bulk superconductor.This work was supported by the Engineering and Physical Sciences Research Council, via a Doctoral Training Award (grant number is EP/L504920/1) and funding from grant number EP/K02910X/1. This work was also supported by the Boeing Company. All data are provided in full in the results section of this paper.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TASC.2016.253764