Graph Signal Representation with Wasserstein Barycenters

In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised dimensionality reduction methods for graph signals have focused on dictionary learning. In these works the graph is taken into consideration by imposing a structure or a parametrization on the dictionary and the signals are represented as linear combinations of the atoms in the dictionary. However, the assumption that graph signals can be represented using linear combinations of atoms is not always appropriate. In this paper we propose a novel representation framework based on non-linear and geometry-aware combinations of graph signals by leveraging the mathematical theory of Optimal Transport. We represent graph signals as Wasserstein barycenters and demonstrate through our experiments the potential of our proposed framework for low-dimensional graph signal representation

End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion

Knowledge graph embedding has been an active research topic for knowledge base completion, with progressive improvement from the initial TransE, TransH, DistMult et al to the current state-of-the-art ConvE. ConvE uses 2D convolution over embeddings and multiple layers of nonlinear features to model knowledge graphs. The model can be efficiently trained and scalable to large knowledge graphs. However, there is no structure enforcement in the embedding space of ConvE. The recent graph convolutional network (GCN) provides another way of learning graph node embedding by successfully utilizing graph connectivity structure. In this work, we propose a novel end-to-end Structure-Aware Convolutional Network (SACN) that takes the benefit of GCN and ConvE together. SACN consists of an encoder of a weighted graph convolutional network (WGCN), and a decoder of a convolutional network called Conv-TransE. WGCN utilizes knowledge graph node structure, node attributes and edge relation types. It has learnable weights that adapt the amount of information from neighbors used in local aggregation, leading to more accurate embeddings of graph nodes. Node attributes in the graph are represented as additional nodes in the WGCN. The decoder Conv-TransE enables the state-of-the-art ConvE to be translational between entities and relations while keeps the same link prediction performance as ConvE. We demonstrate the effectiveness of the proposed SACN on standard FB15k-237 and WN18RR datasets, and it gives about 10% relative improvement over the state-of-the-art ConvE in terms of HITS@1, HITS@3 and [email protected]: The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI 2019