The cascade of 2D geometric transformations were exploited to model relations between entities in a knowledge graph (KG), leading to an effective KG embedding (KGE) model, CompoundE. Furthermore, the rotation in the 3D space was proposed as a new KGE model, Rotate3D, by leveraging its non-commutative property. Inspired by CompoundE and Rotate3D, we leverage 3D compound geometric transformations, including translation, rotation, scaling, reflection, and shear and propose a family of KGE models, named CompoundE3D, in this work. CompoundE3D allows multiple design variants to match rich underlying characteristics of a KG. Since each variant has its own advantages on a subset of relations, an ensemble of multiple variants can yield superior performance. The effectiveness and flexibility of CompoundE3D are experimentally verified on four popular link prediction datasets.
In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic effect: for sufficiently large vertex size, the accuracy of vertex classification consistently benefits from the incorporation of additional graphs. We establish the mathematical foundation for the method, including the asymptotic convergence of the embedding, a sufficient condition for asymptotic optimal classification, and the proof of the synergistic effect for vertex classification. Our comprehensive simulations and real data experiments provide compelling evidence supporting the effectiveness of our proposed method, showcasing the pronounced synergistic effect for multiple graphs from disparate sources.
Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in $\mathbb{R}^n$. Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze, qualitatively and quantitatively, several graph projection methods that have been used to embed ontologies, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms.
The link prediction task aims to predict missing entities or relations in the knowledge graph and is essential for the downstream application. Existing well-known models deal with this task by mainly focusing on representing knowledge graph triplets in the distance space or semantic space. However, they can not fully capture the information of head and tail entities, nor even make good use of hierarchical level information. Thus, in this paper, we propose a novel knowledge graph embedding model for the link prediction task, namely, HIE, which models each triplet (\textit{h}, \textit{r}, \textit{t}) into distance measurement space and semantic measurement space, simultaneously. Moreover, HIE is introduced into hierarchical-aware space to leverage rich hierarchical information of entities and relations for better representation learning. Specifically, we apply distance transformation operation on the head entity in distance space to obtain the tail entity instead of translation-based or rotation-based approaches. Experimental results of HIE on four real-world datasets show that HIE outperforms several existing state-of-the-art knowledge graph embedding methods on the link prediction task and deals with complex relations accurately.
Graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on Twitter with over one billion edges. Most existing graph embedding methods fall short of reaching high data scalability. In this paper, we present a general-purpose, distributed, information-centric random walk-based graph embedding framework, DistGER, which can scale to embed billion-edge graphs. DistGER incrementally computes information-centric random walks. It further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines. DistGER also improves the distributed Skip-Gram learning model to generate node embeddings by optimizing the access locality, CPU throughput, and synchronization efficiency. Experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including KnightKing, DistDGL, and Pytorch-BigGraph, DistGER exhibits 2.33x-129x acceleration, 45% reduction in cross-machines communication, and > 10% effectiveness improvement in downstream tasks.
Link prediction with knowledge graph embedding (KGE) is a popular method for knowledge graph completion. Furthermore, training KGEs on non-English knowledge graph promote knowledge extraction and knowledge graph reasoning in the context of these languages. However, many challenges in non-English KGEs pose to learning a low-dimensional representation of a knowledge graph's entities and relations. This paper proposes "Farspredict" a Persian knowledge graph based on Farsbase (the most comprehensive knowledge graph in Persian). It also explains how the knowledge graph structure affects link prediction accuracy in KGE. To evaluate Farspredict, we implemented the popular models of KGE on it and compared the results with Freebase. Given the analysis results, some optimizations on the knowledge graph are carried out to improve its functionality in the KGE. As a result, a new Persian knowledge graph is achieved. Implementation results in the KGE models on Farspredict outperforming Freebases in many cases. At last, we discuss what improvements could be effective in enhancing the quality of Farspredict and how much it improves.
In this work, we present an end-to-end Knowledge Graph Question Answering (KGQA) system named GETT-QA. GETT-QA uses T5, a popular text-to-text pre-trained language model. The model takes a question in natural language as input and produces a simpler form of the intended SPARQL query. In the simpler form, the model does not directly produce entity and relation IDs. Instead, it produces corresponding entity and relation labels. The labels are grounded to KG entity and relation IDs in a subsequent step. To further improve the results, we instruct the model to produce a truncated version of the KG embedding for each entity. The truncated KG embedding enables a finer search for disambiguation purposes. We find that T5 is able to learn the truncated KG embeddings without any change of loss function, improving KGQA performance. As a result, we report strong results for LC-QuAD 2.0 and SimpleQuestions-Wikidata datasets on end-to-end KGQA over Wikidata.
Knowledge graph embedding (KGE) that maps entities and relations into vector representations is essential for downstream applications. Conventional KGE methods require high-dimensional representations to learn the complex structure of knowledge graph, but lead to oversized model parameters. Recent advances reduce parameters by low-dimensional entity representations, while developing techniques (e.g., knowledge distillation or reinvented representation forms) to compensate for reduced dimension. However, such operations introduce complicated computations and model designs that may not benefit large knowledge graphs. To seek a simple strategy to improve the parameter efficiency of conventional KGE models, we take inspiration from that deeper neural networks require exponentially fewer parameters to achieve expressiveness comparable to wider networks for compositional structures. We view all entity representations as a single-layer embedding network, and conventional KGE methods that adopt high-dimensional entity representations equal widening the embedding network to gain expressiveness. To achieve parameter efficiency, we instead propose a deeper embedding network for entity representations, i.e., a narrow entity embedding layer plus a multi-layer dimension lifting network (LiftNet). Experiments on three public datasets show that by integrating LiftNet, four conventional KGE methods with 16-dimensional representations achieve comparable link prediction accuracy as original models that adopt 512-dimensional representations, saving 68.4% to 96.9% parameters.
In this paper, we propose a novel model called SGFormer, Semantic Graph TransFormer for point cloud-based 3D scene graph generation. The task aims to parse a point cloud-based scene into a semantic structural graph, with the core challenge of modeling the complex global structure. Existing methods based on graph convolutional networks (GCNs) suffer from the over-smoothing dilemma and can only propagate information from limited neighboring nodes. In contrast, SGFormer uses Transformer layers as the base building block to allow global information passing, with two types of newly-designed layers tailored for the 3D scene graph generation task. Specifically, we introduce the graph embedding layer to best utilize the global information in graph edges while maintaining comparable computation costs. Furthermore, we propose the semantic injection layer to leverage linguistic knowledge from large-scale language model (i.e., ChatGPT), to enhance objects' visual features. We benchmark our SGFormer on the established 3DSSG dataset and achieve a 40.94% absolute improvement in relationship prediction's R@50 and an 88.36% boost on the subset with complex scenes over the state-of-the-art. Our analyses further show SGFormer's superiority in the long-tail and zero-shot scenarios. Our source code is available at https://github.com/Andy20178/SGFormer.
Searching for local communities is an important research challenge that allows for personalized community discovery and supports advanced data analysis in various complex networks, such as the World Wide Web, social networks, and brain networks. The evolution of these networks over time has motivated several recent studies to identify local communities in temporal networks. Given any query nodes, Community Search aims to find a densely connected subgraph containing query nodes. However, existing community search approaches in temporal networks have two main limitations: (1) they adopt pre-defined subgraph patterns to model communities, which cannot find communities that do not conform to these patterns in real-world networks, and (2) they only use the aggregation of disjoint structural information to measure quality, missing the dynamic of connections and temporal properties. In this paper, we propose a query-driven Temporal Graph Convolutional Network (CS-TGN) that can capture flexible community structures by learning from the ground-truth communities in a data-driven manner. CS-TGN first combines the local query-dependent structure and the global graph embedding in each snapshot of the network and then uses a GRU cell with contextual attention to learn the dynamics of interactions and update node embeddings over time. We demonstrate how this model can be used for interactive community search in an online setting, allowing users to evaluate the found communities and provide feedback. Experiments on real-world temporal graphs with ground-truth communities validate the superior quality of the solutions obtained and the efficiency of our model in both temporal and interactive static settings.
We present a framework for learning Node Embeddings from Static Subgraphs (NESS) using a graph autoencoder (GAE) in a transductive setting. NESS is based on two key ideas: i) Partitioning the training graph to multiple static, sparse subgraphs with non-overlapping edges using random edge split during data pre-processing, ii) Aggregating the node representations learned from each subgraph to obtain a joint representation of the graph at test time. Moreover, we propose an optional contrastive learning approach in transductive setting. We demonstrate that NESS gives a better node representation for link prediction tasks compared to current autoencoding methods that use either the whole graph or stochastic subgraphs. Our experiments also show that NESS improves the performance of a wide range of graph encoders and achieves state-of-the-art results for link prediction on multiple real-world datasets with edge homophily ratio ranging from strong heterophily to strong homophily.
Due to its complexity, graph learning-based multi-modal integration and classification is one of the most challenging obstacles for disease prediction. To effectively offset the negative impact between modalities in the process of multi-modal integration and extract heterogeneous information from graphs, we propose a novel method called MMKGL (Multi-modal Multi-Kernel Graph Learning). For the problem of negative impact between modalities, we propose a multi-modal graph embedding module to construct a multi-modal graph. Different from conventional methods that manually construct static graphs for all modalities, each modality generates a separate graph by adaptive learning, where a function graph and a supervision graph are introduced for optimization during the multi-graph fusion embedding process. We then propose a multi-kernel graph learning module to extract heterogeneous information from the multi-modal graph. The information in the multi-modal graph at different levels is aggregated by convolutional kernels with different receptive field sizes, followed by generating a cross-kernel discovery tensor for disease prediction. Our method is evaluated on the benchmark Autism Brain Imaging Data Exchange (ABIDE) dataset and outperforms the state-of-the-art methods. In addition, discriminative brain regions associated with autism are identified by our model, providing guidance for the study of autism pathology.
Knowledge graph embedding models (KGEMs) are used for various tasks related to knowledge graphs (KGs), including link prediction. They are trained with loss functions that consider batches of true and false triples. However, different kinds of false triples exist and recent works suggest that they should not be valued equally, leading to specific negative sampling procedures. In line with this recent assumption, we posit that negative triples that are semantically valid w.r.t. signatures of relations (domain and range) are high-quality negatives. Hence, we enrich the three main loss functions for link prediction such that all kinds of negatives are sampled but treated differently based on their semantic validity. In an extensive and controlled experimental setting, we show that the proposed loss functions systematically provide satisfying results which demonstrates both the generality and superiority of our proposed approach. In fact, the proposed loss functions (1) lead to better MRR and Hits@10 values, and (2) drive KGEMs towards better semantic correctness as measured by the Sem@K metric. This highlights that relation signatures globally improve KGEMs, and thus should be incorporated into loss functions. Domains and ranges of relations being largely available in schema-defined KGs, this makes our approach both beneficial and widely usable in practice.
With the widespread use of knowledge graphs (KG) in various automated AI systems and applications, it is very important to ensure that information retrieval algorithms leveraging them are free from societal biases. Previous works have depicted biases that persist in KGs, as well as employed several metrics for measuring the biases. However, such studies lack the systematic exploration of the sensitivity of the bias measurements, through varying sources of data, or the embedding algorithms used. To address this research gap, in this work, we present a holistic analysis of bias measurement on the knowledge graph. First, we attempt to reveal data biases that surface in Wikidata for thirteen different demographics selected from seven continents. Next, we attempt to unfold the variance in the detection of biases by two different knowledge graph embedding algorithms - TransE and ComplEx. We conduct our extensive experiments on a large number of occupations sampled from the thirteen demographics with respect to the sensitive attribute, i.e., gender. Our results show that the inherent data bias that persists in KG can be altered by specific algorithm bias as incorporated by KG embedding learning algorithms. Further, we show that the choice of the state-of-the-art KG embedding algorithm has a strong impact on the ranking of biased occupations irrespective of gender. We observe that the similarity of the biased occupations across demographics is minimal which reflects the socio-cultural differences around the globe. We believe that this full-scale audit of the bias measurement pipeline will raise awareness among the community while deriving insights related to design choices of data and algorithms both and refrain from the popular dogma of ``one-size-fits-all''.
SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance). $k$-nn graphs restrict the points to have a fixed number of neighbors regardless of the local statistics around them. We proposed a new SpectralNet similarity metric based on random projection trees (rpTrees). Our experiments revealed that SpectralNet produces better clustering accuracy using rpTree similarity metric compared to $k$-nn graph with a distance metric. Also, we found out that rpTree parameters do not affect the clustering accuracy. These parameters include the leaf size and the selection of projection direction. It is computationally efficient to keep the leaf size in order of $\log(n)$, and project the points onto a random direction instead of trying to find the direction with the maximum dispersion.
Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single mean. However, these methods need a graph where vertices in the same cluster are connected by edges of large weights. To achieve this goal, many studies have proposed graph reduction methods with parameters. Unfortunately, these parameters have to be tuned for every dataset. We introduce a graph reduction method that does not require any parameters. First, the distances from every point $p$ to its neighbors are filtered using an adaptive threshold to only keep neighbors with similar surrounding density. Second, the similarities with close neighbors are computed and only high similarities are kept. The edges that survive these two filtering steps form the constructed graph that was passed to spectral clustering and SpectralNet. The experiments showed that our method provides a stable alternative, where other methods performance fluctuated according to the setting of their parameters.
Analytically thorough understanding of causal, probabilistic, and informational linkages amongst modern, highly-interconnected capital markets is fundamental to the promotion of capital-market innovation, efficiency, and resilience; whereupon innovative, efficient, and resilient capital markets are fundamental to the sustainable economic development of any nation and the robust financial stability of her economy. Whereas analytics derived essentially from some form of linear correlation matrix remains to this day the archetype model representation of return co-movements within a single stock exchange, analysis of financial random multi-variates, especially across domestic/international/regional/global/ domains, warrants a generalised multi-paradigm investigation. In lieu of employing a particular quantitative technique to test a specific theoretically-motivated hypothesis, our aim here is to apply a multitude of analytical tools from semi-/non-parametric statistics, from time-series econometrics, from graph-theoretic network analysis, and from Graph Neural Network (GNN)/Geometric Deep Learning (GDL) paradigms to investigate quantifiable linkages amongst 14 selected variables representing Thai/Asia/Emerging Market/US foreign-exchange, fixed-income, and equity market movements, as well as foreign portfolio-investment flows into Thailand’s domestic equity and bond markets. In particular, Bivariate/Vine Copulas, Granger Causality, Network Centrality, and GNN/Graph Embedding together enable us to tease out subtle quantitative relations amongst said linked capital-market variables, which could in turn be exploited, for instance, in the form of better specified Monte Carlo Value-at-Risk/Expected Shortfall estimation for hypothetical portfolios comprising multi-national assets. Our experiments thus far delivered incremental, rather than game-changing, improvements w.r.t. market insights and accuracy gains. Nonetheless, our multi-paradigm framework, along with the publicly shared codebase, can be applied to any other “linkage” phenomena of future research interest and real-world application.
Graph convolutional networks (GCNs) were a great step towards extending deep learning to unstructured data such as graphs. But GCNs still need a constructed graph to work with. To solve this problem, classical graphs such as $k$-nearest neighbor are usually used to initialize the GCN. Although it is computationally efficient to construct $k$-nn graphs, the constructed graph might not be very useful for learning. In a $k$-nn graph, points are restricted to have a fixed number of edges, and all edges in the graph have equal weights. We present a new way to construct the graph and initialize the GCN. It is based on random projection forest (rpForest). rpForest enables us to assign varying weights on edges indicating varying importance, which enhanced the learning. The number of trees is a hyperparameter in rpForest. We performed spectral analysis to help us setting this parameter in the right range. In the experiments, initializing the GCN using rpForest provides better results compared to $k$-nn initialization.
Graph Neural Networks (GNNs) are increasingly becoming the favorite method for graph learning. They exploit the semi-supervised nature of deep learning, and they bypass computational bottlenecks associated with traditional graph learning methods. In addition to the feature matrix $X$, GNNs need an adjacency matrix $A$ to perform feature propagation. In many cases, the adjacency matrix $A$ is missing. We introduce a graph construction scheme that constructs the adjacency matrix $A$ using unsupervised and supervised information. Unsupervised information characterizes the neighborhood around points. We used Principal Axis trees (PA-trees) as a source for unsupervised information, where we create edges between points falling onto the same leaf node. For supervised information, we used the concept of penalty and intrinsic graphs. A penalty graph connects points with different class labels, whereas an intrinsic graph connects points with the same class labels. We used the penalty and intrinsic graphs to remove or add edges to the graph constructed via PA-tree. We tested this graph construction scheme on two well-known GNNs: 1) Graph Convolutional Network (GCN) and 2) Simple Graph Convolution (SGC). The experiments show that it is better to use SGC because it is faster and delivers better or the same results as GCN. We also test the effect of oversmoothing on both GCN and SGC. We found out that the level of smoothing has to be carefully selected for SGC to avoid oversmoothing.
Approximate spectral clustering (ASC) was developed to overcome heavy computational demands of spectral clustering (SC). It maintains SC ability in predicting non-convex clusters. Since it involves a preprocessing step, ASC defines new similarity measures to assign weights on graph edges. Connectivity matrix (CONN) is an efficient similarity measure to construct graphs for ASC. It defines the weight between two vertices as the number of points assigned to them during vector quantization training. However, this relationship is undirected, where it is not clear which of the vertices is contributing more to that edge. Also, CONN could be tricked by noisy density between clusters. We defined a directed version of CONN, named DCONN, to get insights on vertices contributions to edges. Also, we provided filtering schemes to ensure CONN edges are highlighting potential clusters. Experiments reveal that the proposed filtering was highly efficient when noise cannot be tolerated by CONN.