Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space matches that of the graph. Euclidean spaces are often a poor choice for many types of real-world graphs, where hierarchical structure and a power-law degree distribution are linked to negative curvature. In this regard, it has recently been shown that hyperbolic spaces and more general manifolds, such as products of constant-curvature spaces and matrix manifolds, are advantageous to approximately match nodes pairwise distances. However, all these classes of manifolds are homogeneous, implying that the curvature distribution is the same at each point, making them unsuited to match the local curvature (and related structural properties) of the graph. In this paper, we study graph embeddings in a broader class of heterogeneous rotationally-symmetric manifolds. By adding a single extra radial dimension to any given existing homogeneous model, we can both account for heterogeneous curvature distributions on graphs and pairwise distances. We evaluate our approach on reconstruction tasks on synthetic and real datasets and show its potential in better preservation of high-order structures and heterogeneous random graphs generation.
Travelers may travel to locations they have never visited, which we call potential destinations of them. Especially under a very limited observation, travelers tend to show random movement patterns and usually have a large number of potential destinations, which make them difficult to handle for mobility prediction (e.g., destination prediction). In this paper, we develop a new knowledge graph-based framework (PDPFKG) for potential destination discovery of low predictability travelers by considering trip association relationships between them. We first construct a trip knowledge graph (TKG) to model the trip scenario by entities (e.g., travelers, destinations and time information) and their relationships, in which we introduce the concept of private relationship for complexity reduction. Then a modified knowledge graph embedding algorithm is implemented to optimize the overall graph representation. Based on the trip knowledge graph embedding model (TKGEM), the possible ranking of individuals' unobserved destinations to be chosen in the future can be obtained by calculating triples' distance. Empirically. PDPFKG is tested using an anonymous vehicular dataset from 138 intersections equipped with video-based vehicle detection systems in Xuancheng city, China. The results show that (i) the proposed method significantly outperforms baseline methods, and (ii) the results show strong consistency with traveler behavior in choosing potential destinations. Finally, we provide a comprehensive discussion of the innovative points of the methodology.
Recent approaches of computer vision utilize deep learning methods as they perform quite well if training and testing domains follow the same underlying data distribution. However, it has been shown that minor variations in the images that occur when using these methods in the real world can lead to unpredictable errors. Transfer learning is the area of machine learning that tries to prevent these errors. Especially, approaches that augment image data using auxiliary knowledge encoded in language embeddings or knowledge graphs (KGs) have achieved promising results in recent years. This survey focuses on visual transfer learning approaches using KGs. KGs can represent auxiliary knowledge either in an underlying graph-structured schema or in a vector-based knowledge graph embedding. Intending to enable the reader to solve visual transfer learning problems with the help of specific KG-DL configurations we start with a description of relevant modeling structures of a KG of various expressions, such as directed labeled graphs, hypergraphs, and hyper-relational graphs. We explain the notion of feature extractor, while specifically referring to visual and semantic features. We provide a broad overview of knowledge graph embedding methods and describe several joint training objectives suitable to combine them with high dimensional visual embeddings. The main section introduces four different categories on how a KG can be combined with a DL pipeline: 1) Knowledge Graph as a Reviewer; 2) Knowledge Graph as a Trainee; 3) Knowledge Graph as a Trainer; and 4) Knowledge Graph as a Peer. To help researchers find evaluation benchmarks, we provide an overview of generic KGs and a set of image processing datasets and benchmarks including various types of auxiliary knowledge. Last, we summarize related surveys and give an outlook about challenges and open issues for future research.
Recently, increasing efforts are put into learning continual representations for symbolic knowledge bases (KBs). However, these approaches either only embed the data-level knowledge (ABox) or suffer from inherent limitations when dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model the logical structure present in the KBs. We present BoxEL, a geometric KB embedding approach that allows for better capturing the logical structure (i.e., ABox and TBox axioms) in the description logic EL++. BoxEL models concepts in a KB as axis-parallel boxes that are suitable for modeling concept intersection, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the learned model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on (plausible) subsumption reasonings and a real-world application for protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.
Global pooling is one of the most significant operations in many machine learning models and tasks, whose implementation, however, is often empirical in practice. In this study, we develop a novel and solid global pooling framework through the lens of optimal transport. We demonstrate that most existing global pooling methods are equivalent to solving some specializations of an unbalanced optimal transport (UOT) problem. Making the parameters of the UOT problem learnable, we unify various global pooling methods in the same framework, and accordingly, propose a generalized global pooling layer called UOT-Pooling (UOTP) for neural networks. Besides implementing the UOTP layer based on the classic Sinkhorn-scaling algorithm, we design a new model architecture based on the Bregman ADMM algorithm, which has better numerical stability and can reproduce existing pooling layers more effectively. We test our UOTP layers in several application scenarios, including multi-instance learning, graph classification, and image classification. Our UOTP layers can either imitate conventional global pooling layers or learn some new pooling mechanisms leading to better performance.
Graph neural networks are powerful architectures for structured datasets. However, current methods struggle to represent long-range dependencies. Scaling the depth or width of GNNs is insufficient to broaden receptive fields as larger GNNs encounter optimization instabilities such as vanishing gradients and representation oversmoothing, while pooling-based approaches have yet to become as universally useful as in computer vision. In this work, we propose the use of Transformer-based self-attention to learn long-range pairwise relationships, with a novel "readout" mechanism to obtain a global graph embedding. Inspired by recent computer vision results that find position-invariant attention performant in learning long-range relationships, our method, which we call GraphTrans, applies a permutation-invariant Transformer module after a standard GNN module. This simple architecture leads to state-of-the-art results on several graph classification tasks, outperforming methods that explicitly encode graph structure. Our results suggest that purely-learning-based approaches without graph structure may be suitable for learning high-level, long-range relationships on graphs. Code for GraphTrans is available at https://github.com/ucbrise/graphtrans.
Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a low-dimensional vector representation (the embedding) for each node. Despite the widespread use of these embeddings for a variety of downstream transductive machine learning tasks, there is little principled analysis of the effectiveness of this approach for common tasks. In this work, we provide an empirical and theoretical analysis for the performance of a class of embeddings on the common task of pairwise community labeling. This is a binary variant of the classic community detection problem, which seeks to build a classifier to determine whether a pair of vertices participate in a community. In line with our goal of foundational understanding, we focus on a popular class of unsupervised embedding techniques that learn low rank factorizations of a vertex proximity matrix (this class includes methods like GraRep, DeepWalk, node2vec, NetMF). We perform detailed empirical analysis for community labeling over a variety of real and synthetic graphs with ground truth. In all cases we studied, the models trained from embedding features perform poorly on community labeling. In constrast, a simple logistic model with classic graph structural features handily outperforms the embedding models. For a more principled understanding, we provide a theoretical analysis for the (in)effectiveness of these embeddings in capturing the community structure. We formally prove that popular low-dimensional factorization methods either cannot produce community structure, or can only produce ``unstable" communities. These communities are inherently unstable under small perturbations.
Industrial alarm systems have recently progressed considerably in terms of network complexity and the number of alarms. The increase in complexity and number of alarms presents challenges in these systems that decrease system efficiency and cause distrust of the operator, which might result in widespread damages. One contributing factor in alarm inefficiency is the correlated alarms. These alarms do not contain new information and only confuse the operator. This paper tries to present a novel method for detecting correlated alarms based on artificial intelligence methods to help the operator. The proposed method is based on graph embedding and alarm clustering, resulting in the detection of correlated alarms. To evaluate the proposed method, a case study is conducted on the well-known Tennessee-Eastman process.
Graph contrastive learning attracts/disperses node representations for similar/dissimilar node pairs under some notion of similarity. It may be combined with a low-dimensional embedding of nodes to preserve intrinsic and structural properties of a graph. In this paper, we extend the celebrated Laplacian Eigenmaps with contrastive learning, and call them COntrastive Laplacian EigenmapS (COLES). Starting from a GAN-inspired contrastive formulation, we show that the Jensen-Shannon divergence underlying many contrastive graph embedding models fails under disjoint positive and negative distributions, which may naturally emerge during sampling in the contrastive setting. In contrast, we demonstrate analytically that COLES essentially minimizes a surrogate of Wasserstein distance, which is known to cope well under disjoint distributions. Moreover, we show that the loss of COLES belongs to the family of so-called block-contrastive losses, previously shown to be superior compared to pair-wise losses typically used by contrastive methods. We show on popular benchmarks/backbones that COLES offers favourable accuracy/scalability compared to DeepWalk, GCN, Graph2Gauss, DGI and GRACE baselines.
Previous knowledge graph embedding approaches usually map entities to representations and utilize score functions to predict the target entities, yet they typically struggle to reason rare or emerging unseen entities. In this paper, we propose kNN-KGE, a new knowledge graph embedding approach with pre-trained language models, by linearly interpolating its entity distribution with k-nearest neighbors. We compute the nearest neighbors based on the distance in the entity embedding space from the knowledge store. Our approach can allow rare or emerging entities to be memorized explicitly rather than implicitly in model parameters. Experimental results demonstrate that our approach can improve inductive and transductive link prediction results and yield better performance for low-resource settings with only a few triples, which might be easier to reason via explicit memory. Code is available at https://github.com/zjunlp/KNN-KG.
Graph embedding techniques have led to significant progress in recent years. However, present techniques are not effective enough to capture the patterns of networks. This paper propose neighbor2vec, a neighbor-based sampling strategy used algorithm to learn the neighborhood representations of node, a framework to gather the structure information by feature propagation between the node and its neighbors. We claim that neighbor2vec is a simple and effective approach to enhancing the scalability as well as equality of graph embedding, and it breaks the limits of the existing state-of-the-art unsupervised techniques. We conduct experiments on several node classification and link prediction tasks for networks such as ogbn-arxiv, ogbn-products, ogbn-proteins, ogbl-ppa,ogbl-collab and ogbl-citation2. The result shows that Neighbor2vec's representations provide an average accuracy scores up to 6.8 percent higher than competing methods in node classification tasks and 3.0 percent higher in link prediction tasks. The neighbor2vec's representations are able to outperform all baseline methods and two classical GNN models in all six experiments.
Developing scalable solutions for training Graph Neural Networks (GNNs) for link prediction tasks is challenging due to the high data dependencies which entail high computational cost and huge memory footprint. We propose a new method for scaling training of knowledge graph embedding models for link prediction to address these challenges. Towards this end, we propose the following algorithmic strategies: self-sufficient partitions, constraint-based negative sampling, and edge mini-batch training. Both, partitioning strategy and constraint-based negative sampling, avoid cross partition data transfer during training. In our experimental evaluation, we show that our scaling solution for GNN-based knowledge graph embedding models achieves a 16x speed up on benchmark datasets while maintaining a comparable model performance as non-distributed methods on standard metrics.
Knowledge graphs (KGs) are typically incomplete and we often wish to infer new facts given the existing ones. This can be thought of as a binary classification problem; we aim to predict if new facts are true or false. Unfortunately, we generally only have positive examples (the known facts) but we also need negative ones to train a classifier. To resolve this, it is usual to generate negative examples using a negative sampling strategy. However, this can produce false negatives which may reduce performance, is computationally expensive, and does not produce calibrated classification probabilities. In this paper, we propose a training procedure that obviates the need for negative sampling by adding a novel regularization term to the loss function. Our results for two relational embedding models (DistMult and SimplE) show the merit of our proposal both in terms of performance and speed.
Dynamic graph neural networks have been widely used in modeling and representation learning of graph structure data. Current dynamic representation learning focuses on either discrete learning which results in temporal information loss or continuous learning that involves heavy computation. In this work, we proposed a novel dynamic graph neural network, Sparse-Dyn. It adaptively encodes temporal information into a sequence of patches with an equal amount of temporal-topological structure. Therefore, while avoiding the use of snapshots which causes information loss, it also achieves a finer time granularity, which is close to what continuous networks could provide. In addition, we also designed a lightweight module, Sparse Temporal Transformer, to compute node representations through both structural neighborhoods and temporal dynamics. Since the fully-connected attention conjunction is simplified, the computation cost is far lower than the current state-of-the-arts. Link prediction experiments are conducted on both continuous and discrete graph datasets. Through comparing with several state-of-the-art graph embedding baselines, the experimental results demonstrate that Sparse-Dyn has a faster inference speed while having competitive performance.
Our goal is to efficiently compute low-dimensional latent coordinates for nodes in an input graph -- known as graph embedding -- for subsequent data processing such as clustering. Focusing on finite graphs that are interpreted as uniform samples on continuous manifolds (called manifold graphs), we leverage existing fast extreme eigenvector computation algorithms for speedy execution. We first pose a generalized eigenvalue problem for sparse matrix pair $(\A,\B)$, where $\A = \L - \mu \Q + \epsilon \I$ is a sum of graph Laplacian $\L$ and disconnected two-hop difference matrix $\Q$. Eigenvector $\v$ minimizing Rayleigh quotient $\frac{\v^{\top} \A \v}{\v^{\top} \v}$ thus minimizes $1$-hop neighbor distances while maximizing distances between disconnected $2$-hop neighbors, preserving graph structure. Matrix $\B = \text{diag}(\{\b_i\})$ that defines eigenvector orthogonality is then chosen so that boundary / interior nodes in the sampling domain have the same generalized degrees. $K$-dimensional latent vectors for the $N$ graph nodes are the first $K$ generalized eigenvectors for $(\A,\B)$, computed in $\cO(N)$ using LOBPCG, where $K \ll N$. Experiments show that our embedding is among the fastest in the literature, while producing the best clustering performance for manifold graphs.
We introduce an algorithm for computing geodesics on sampled manifolds that relies on simulation of quantum dynamics on a graph embedding of the sampled data. Our approach exploits classic results in semiclassical analysis and the quantum-classical correspondence, and forms a basis for techniques to learn the manifold from which a dataset is sampled, and subsequently for nonlinear dimensionality reduction of high-dimensional datasets. We illustrate the new algorithm with data sampled from model manifolds and also by a clustering demonstration based on COVID-19 mobility data. Finally, our method reveals interesting connections between the discretization provided by data sampling and quantization.
Controversial content refers to any content that attracts both positive and negative feedback. Its automatic identification, especially on social media, is a challenging task as it should be done on a large number of continuously evolving posts, covering a large variety of topics. Most of the existing approaches rely on the graph structure of a topic-discussion and/or the content of messages. This paper proposes a controversy detection approach based on both graph structure of a discussion and text features. Our proposed approach relies on Graph Neural Network (gnn) to encode the graph representation (including its texts) in an embedding vector before performing a graph classification task. The latter will classify the post as controversial or not. Two controversy detection strategies are proposed. The first one is based on a hierarchical graph representation learning. Graph user nodes are embedded hierarchically and iteratively to compute the whole graph embedding vector. The second one is based on the attention mechanism, which allows each user node to give more or less importance to its neighbors when computing node embeddings. We conduct experiments to evaluate our approach using different real-world datasets. Conducted experiments show the positive impact of combining textual features and structural information in terms of performance.
We present an effective graph neural network (GNN)-based knowledge graph embedding model, which we name WGE, to capture entity- and relation-focused graph structures. Given a knowledge graph, WGE builds a single undirected entity-focused graph that views entities as nodes. 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 strong baselines on seven benchmark datasets for knowledge graph completion.
Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional graph representations. Graph neural networks (GNNs) are currently the most popular model in graph embedding approaches. However, standard GNNs in the neighborhood aggregation paradigm suffer from limited discriminative power in distinguishing \emph{high-order} graph structures as opposed to \emph{low-order} structures. To capture high-order structures, researchers have resorted to motifs and developed motif-based GNNs. However, existing motif-based GNNs still often suffer from less discriminative power on high-order structures. To overcome the above limitations, we propose Motif Graph Neural Network (MGNN), a novel framework to better capture high-order structures, hinging on our proposed motif redundancy minimization operator and injective motif combination. First, MGNN produces a set of node representations w.r.t. each motif. The next phase is our proposed redundancy minimization among motifs which compares the motifs with each other and distills the features unique to each motif. Finally, MGNN performs the updating of node representations by combining multiple representations from different motifs. In particular, to enhance the discriminative power, MGNN utilizes an injective function to combine the representations w.r.t. different motifs. We further show that our proposed architecture increases the expressive power of GNNs with a theoretical analysis. We demonstrate that MGNN outperforms state-of-the-art methods on seven public benchmarks on both node classification and graph classification tasks.
Event analysis from news and social networks is very useful for a wide range of social studies and real-world applications. Recently, event graphs have been explored to model event datasets and their complex relationships, where events are vertices connected to other vertices representing locations, people's names, dates, and various other event metadata. Graph representation learning methods are promising for extracting latent features from event graphs to enable the use of different classification algorithms. However, existing methods fail to meet essential requirements for event graphs, such as (i) dealing with semi-supervised graph embedding to take advantage of some labeled events, (ii) automatically determining the importance of the relationships between event vertices and their metadata vertices, as well as (iii) dealing with the graph heterogeneity. This paper presents GNEE (GAT Neural Event Embeddings), a method that combines Graph Attention Networks and Graph Regularization. First, an event graph regularization is proposed to ensure that all graph vertices receive event features, thereby mitigating the graph heterogeneity drawback. Second, semi-supervised graph embedding with self-attention mechanism considers existing labeled events, as well as learns the importance of relationships in the event graph during the representation learning process. A statistical analysis of experimental results with five real-world event graphs and six graph embedding methods shows that our GNEE outperforms state-of-the-art semi-supervised graph embedding methods.