Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of problems where the connectivity patterns of data may not be directly accessible. In this work, we generalize the discrete Differentiable Graph Module (dDGM) for latent graph learning. The original dDGM architecture used the Euclidean plane to encode latent features based on which the latent graphs were generated. By incorporating Riemannian geometry into the model and generating more complex embedding spaces, we can improve the performance of the latent graph inference system. In particular, we propose a computationally tractable approach to produce product manifolds of constant curvature model spaces that can encode latent features of varying structure. The latent representations mapped onto the inferred product manifold are used to compute richer similarity measures that are leveraged by the latent graph learning model to obtain optimized latent graphs. Moreover, the curvature of the product manifold is learned during training alongside the rest of the network parameters and based on the downstream task, rather than it being a static embedding space. Our novel approach is tested on a wide range of datasets, and outperforms the original dDGM model.
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In this study, formant tracking is investigated by refining the formants tracked by an existing data-driven tracker, DeepFormants, using the formants estimated in a model-driven manner by linear prediction (LP)-based methods. As LP-based formant estimation methods, conventional covariance analysis (LP-COV) and the recently proposed quasi-closed phase forward-backward (QCP-FB) analysis are used. In the proposed refinement approach, the contours of the three lowest formants are first predicted by the data-driven DeepFormants tracker, and the predicted formants are replaced frame-wise with local spectral peaks shown by the model-driven LP-based methods. The refinement procedure can be plugged into the DeepFormants tracker with no need for any new data learning. Two refined DeepFormants trackers were compared with the original DeepFormants and with five known traditional trackers using the popular vocal tract resonance (VTR) corpus. The results indicated that the data-driven DeepFormants trackers outperformed the conventional trackers and that the best performance was obtained by refining the formants predicted by DeepFormants using QCP-FB analysis. In addition, by tracking formants using VTR speech that was corrupted by additive noise, the study showed that the refined DeepFormants trackers were more resilient to noise than the reference trackers. In general, these results suggest that LP-based model-driven approaches, which have traditionally been used in formant estimation, can be combined with a modern data-driven tracker easily with no further training to improve the tracker's performance.
The Weighted Connectivity Augmentation Problem is the problem of augmenting the edge-connectivity of a given graph by adding links of minimum total cost. This work focuses on connectivity augmentation problems in the Steiner setting, where we are not interested in the connectivity between all nodes of the graph, but only the connectivity between a specified subset of terminals. We consider two related settings. In the Steiner Augmentation of a Graph problem ($k$-SAG), we are given a $k$-edge-connected subgraph $H$ of a graph $G$. The goal is to augment $H$ by including links and nodes from $G$ of minimum cost so that the edge-connectivity between nodes of $H$ increases by 1. In the Steiner Connectivity Augmentation Problem ($k$-SCAP), we are given a Steiner $k$-edge-connected graph connecting terminals $R$, and we seek to add links of minimum cost to create a Steiner $(k+1)$-edge-connected graph for $R$. Note that $k$-SAG is a special case of $k$-SCAP. All of the above problems can be approximated to within a factor of 2 using e.g. Jain's iterative rounding algorithm for Survivable Network Design. In this work, we leverage the framework of Traub and Zenklusen to give a $(1 + \ln{2} +\varepsilon)$-approximation for the Steiner Ring Augmentation Problem (SRAP): given a cycle $H = (V(H),E)$ embedded in a larger graph $G = (V, E \cup L)$ and a subset of terminals $R \subseteq V(H)$, choose a subset of links $S \subseteq L$ of minimum cost so that $(V, E \cup S)$ has 3 pairwise edge-disjoint paths between every pair of terminals. We show this yields a polynomial time algorithm with approximation ratio $(1 + \ln{2} + \varepsilon)$ for $2$-SCAP. We obtain an improved approximation guarantee of $(1.5+\varepsilon)$ for SRAP in the case that $R = V(H)$, which yields a $(1.5+\varepsilon)$-approximation for $k$-SAG for any $k$.
As a scene graph compactly summarizes the high-level content of an image in a structured and symbolic manner, the similarity between scene graphs of two images reflects the relevance of their contents. Based on this idea, we propose a novel approach for image-to-image retrieval using scene graph similarity measured by graph neural networks. In our approach, graph neural networks are trained to predict the proxy image relevance measure, computed from human-annotated captions using a pre-trained sentence similarity model. We collect and publish the dataset for image relevance measured by human annotators to evaluate retrieval algorithms. The collected dataset shows that our method agrees well with the human perception of image similarity than other competitive baselines.
In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.
There has been appreciable progress in unsupervised network representation learning (UNRL) approaches over graphs recently with flexible random-walk approaches, new optimization objectives and deep architectures. However, there is no common ground for systematic comparison of embeddings to understand their behavior for different graphs and tasks. In this paper we theoretically group different approaches under a unifying framework and empirically investigate the effectiveness of different network representation methods. In particular, we argue that most of the UNRL approaches either explicitly or implicit model and exploit context information of a node. Consequently, we propose a framework that casts a variety of approaches -- random walk based, matrix factorization and deep learning based -- into a unified context-based optimization function. We systematically group the methods based on their similarities and differences. We study the differences among these methods in detail which we later use to explain their performance differences (on downstream tasks). We conduct a large-scale empirical study considering 9 popular and recent UNRL techniques and 11 real-world datasets with varying structural properties and two common tasks -- node classification and link prediction. We find that there is no single method that is a clear winner and that the choice of a suitable method is dictated by certain properties of the embedding methods, task and structural properties of the underlying graph. In addition we also report the common pitfalls in evaluation of UNRL methods and come up with suggestions for experimental design and interpretation of results.
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.
How can we estimate the importance of nodes in a knowledge graph (KG)? A KG is a multi-relational graph that has proven valuable for many tasks including question answering and semantic search. In this paper, we present GENI, a method for tackling the problem of estimating node importance in KGs, which enables several downstream applications such as item recommendation and resource allocation. While a number of approaches have been developed to address this problem for general graphs, they do not fully utilize information available in KGs, or lack flexibility needed to model complex relationship between entities and their importance. To address these limitations, we explore supervised machine learning algorithms. In particular, building upon recent advancement of graph neural networks (GNNs), we develop GENI, a GNN-based method designed to deal with distinctive challenges involved with predicting node importance in KGs. Our method performs an aggregation of importance scores instead of aggregating node embeddings via predicate-aware attention mechanism and flexible centrality adjustment. In our evaluation of GENI and existing methods on predicting node importance in real-world KGs with different characteristics, GENI achieves 5-17% higher NDCG@100 than the state of the art.
Graph convolutional networks (GCNs) have recently become one of the most powerful tools for graph analytics tasks in numerous applications, ranging from social networks and natural language processing to bioinformatics and chemoinformatics, thanks to their ability to capture the complex relationships between concepts. At present, the vast majority of GCNs use a neighborhood aggregation framework to learn a continuous and compact vector, then performing a pooling operation to generalize graph embedding for the classification task. These approaches have two disadvantages in the graph classification task: (1)when only the largest sub-graph structure ($k$-hop neighbor) is used for neighborhood aggregation, a large amount of early-stage information is lost during the graph convolution step; (2) simple average/sum pooling or max pooling utilized, which loses the characteristics of each node and the topology between nodes. In this paper, we propose a novel framework called, dual attention graph convolutional networks (DAGCN) to address these problems. DAGCN automatically learns the importance of neighbors at different hops using a novel attention graph convolution layer, and then employs a second attention component, a self-attention pooling layer, to generalize the graph representation from the various aspects of a matrix graph embedding. The dual attention network is trained in an end-to-end manner for the graph classification task. We compare our model with state-of-the-art graph kernels and other deep learning methods. The experimental results show that our framework not only outperforms other baselines but also achieves a better rate of convergence.
Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.
Automatically creating the description of an image using any natural languages sentence like English is a very challenging task. It requires expertise of both image processing as well as natural language processing. This paper discuss about different available models for image captioning task. We have also discussed about how the advancement in the task of object recognition and machine translation has greatly improved the performance of image captioning model in recent years. In addition to that we have discussed how this model can be implemented. In the end, we have also evaluated the performance of model using standard evaluation matrices.
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