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.
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.
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.
The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for multiple real applications, where $n$ could be large. This stimulates researchers to propose the approximate spectral clustering (ASC). However, most of ASC methods assumed that the number of clusters $k$ was known. In practice, manual setting of $k$ could be subjective or time consuming. The proposed algorithm has two relevance metrics for estimating $k$ in two vital steps of ASC. One for selecting the eigenvectors spanning the embedding space, and the other to discover the number of clusters in that space. The algorithm used a growing neural gas (GNG) approximation, GNG is superior in preserving input data topology. The experimental setup demonstrates the efficiency of the proposed algorithm and its ability to compete with similar methods where $k$ was set manually.
Spectral clustering became a popular choice for data clustering for its ability of uncovering clusters of different shapes. However, it is not always preferable over other clustering methods due to its computational demands. One of the effective ways to bypass these computational demands is to perform spectral clustering on a subset of points (data representatives) then generalize the clustering outcome, this is known as approximate spectral clustering (ASC). ASC uses sampling or quantization to select data representatives. This makes it vulnerable to 1) performance inconsistency (since these methods have a random step either in initialization or training), 2) local statistics loss (because the pairwise similarities are extracted from data representatives instead of data points). We proposed a refined version of $k$-nearest neighbor graph, in which we keep data points and aggressively reduce number of edges for computational efficiency. Local statistics were exploited to keep the edges that do not violate the intra-cluster distances and nullify all other edges in the $k$-nearest neighbor graph. We also introduced an optional step to automatically select the number of clusters $C$. The proposed method was tested on synthetic and real datasets. Compared to ASC methods, the proposed method delivered a consistent performance despite significant reduction of edges.
Recent applications of pattern recognition techniques on brain connectome classification using functional connectivity (FC) are shifting towards acknowledging the non-Euclidean topology and dynamic aspects of brain connectivity across time. In this paper, a deep spatiotemporal variational Bayes (DSVB) framework is proposed to learn time-varying topological structures in dynamic FC networks for identifying autism spectrum disorder (ASD) in human participants. The framework incorporates a spatial-aware recurrent neural network with an attention-based message passing scheme to capture rich spatiotemporal patterns across dynamic FC networks. To overcome model overfitting on limited training datasets, an adversarial training strategy is introduced to learn graph embedding models that generalize well to unseen brain networks. Evaluation on the ABIDE resting-state functional magnetic resonance imaging dataset shows that our proposed framework substantially outperforms state-of-the-art methods in identifying patients with ASD. Dynamic FC analyses with DSVB-learned embeddings reveal apparent group differences between ASD and healthy controls in brain network connectivity patterns and switching dynamics of brain states. The code is available at https://github.com/Monash-NeuroAI/Deep-Spatiotemporal-Variational-Bayes.
Temporal interaction graphs (TIGs), consisting of sequences of timestamped interaction events, are prevalent in fields like e-commerce and social networks. To better learn dynamic node embeddings that vary over time, researchers have proposed a series of temporal graph neural networks for TIGs. However, due to the entangled temporal and structural dependencies, existing methods have to process the sequence of events chronologically and consecutively to ensure node representations are up-to-date. This prevents existing models from parallelization and reduces their flexibility in industrial applications. To tackle the above challenge, in this paper, we propose TIGER, a TIG embedding model that can restart at any timestamp. We introduce a restarter module that generates surrogate representations acting as the warm initialization of node representations. By restarting from multiple timestamps simultaneously, we divide the sequence into multiple chunks and naturally enable the parallelization of the model. Moreover, in contrast to previous models that utilize a single memory unit, we introduce a dual memory module to better exploit neighborhood information and alleviate the staleness problem. Extensive experiments on four public datasets and one industrial dataset are conducted, and the results verify both the effectiveness and the efficiency of our work.
(Dis)agreement detection aims to identify the authors' attitudes or positions (\textit{{agree, disagree, neutral}}) towards a specific text. It is limited for existing methods merely using textual information for identifying (dis)agreements, especially for cross-domain settings. Social relation information can play an assistant role in the (dis)agreement task besides textual information. We propose a novel method to extract such relation information from (dis)agreement data into an inductive social relation graph, merely using the comment-reply pairs without any additional platform-specific information. The inductive social relation globally considers the historical discussion and the relation between authors. Textual information based on a pre-trained language model and social relation information encoded by pre-trained RGCN are jointly considered for (dis)agreement detection. Experimental results show that our model achieves state-of-the-art performance for both the in-domain and cross-domain tasks on the benchmark -- DEBAGREEMENT. We find social relations can boost the performance of the (dis)agreement detection model, especially for the long-token comment-reply pairs, demonstrating the effectiveness of the social relation graph. We also explore the effect of the knowledge graph embedding methods, the information fusing method, and the time interval in constructing the social relation graph, which shows the effectiveness of our model.
Knowledge graphs represent known facts using triplets. While existing knowledge graph embedding methods only consider the connections between entities, we propose considering the relationships between triplets. For example, let us consider two triplets $T_1$ and $T_2$ where $T_1$ is (Academy_Awards, Nominates, Avatar) and $T_2$ is (Avatar, Wins, Academy_Awards). Given these two base-level triplets, we see that $T_1$ is a prerequisite for $T_2$. In this paper, we define a higher-level triplet to represent a relationship between triplets, e.g., $\langle T_1$, PrerequisiteFor, $T_2\rangle$ where PrerequisiteFor is a higher-level relation. We define a bi-level knowledge graph that consists of the base-level and the higher-level triplets. We also propose a data augmentation strategy based on the random walks on the bi-level knowledge graph to augment plausible triplets. Our model called BiVE learns embeddings by taking into account the structures of the base-level and the higher-level triplets, with additional consideration of the augmented triplets. We propose two new tasks: triplet prediction and conditional link prediction. Given a triplet $T_1$ and a higher-level relation, the triplet prediction predicts a triplet that is likely to be connected to $T_1$ by the higher-level relation, e.g., $\langle T_1$, PrerequisiteFor, ?$\rangle$. The conditional link prediction predicts a missing entity in a triplet conditioned on another triplet, e.g., $\langle T_1$, PrerequisiteFor, (Avatar, Wins, ?)$\rangle$. Experimental results show that BiVE significantly outperforms all other methods in the two new tasks and the typical base-level link prediction in real-world bi-level knowledge graphs.
We propose an entity-agnostic representation learning method for handling the problem of inefficient parameter storage costs brought by embedding knowledge graphs. Conventional knowledge graph embedding methods map elements in a knowledge graph, including entities and relations, into continuous vector spaces by assigning them one or multiple specific embeddings (i.e., vector representations). Thus the number of embedding parameters increases linearly as the growth of knowledge graphs. In our proposed model, Entity-Agnostic Representation Learning (EARL), we only learn the embeddings for a small set of entities and refer to them as reserved entities. To obtain the embeddings for the full set of entities, we encode their distinguishable information from their connected relations, k-nearest reserved entities, and multi-hop neighbors. We learn universal and entity-agnostic encoders for transforming distinguishable information into entity embeddings. This approach allows our proposed EARL to have a static, efficient, and lower parameter count than conventional knowledge graph embedding methods. Experimental results show that EARL uses fewer parameters and performs better on link prediction tasks than baselines, reflecting its parameter efficiency.
Graph alignment, which aims at identifying corresponding entities across multiple networks, has been widely applied in various domains. As the graphs to be aligned are usually constructed from different sources, the inconsistency issues of structures and features between two graphs are ubiquitous in real-world applications. Most existing methods follow the ``embed-then-cross-compare'' paradigm, which computes node embeddings in each graph and then processes node correspondences based on cross-graph embedding comparison. However, we find these methods are unstable and sub-optimal when structure or feature inconsistency appears. To this end, we propose SLOTAlign, an unsupervised graph alignment framework that jointly performs Structure Learning and Optimal Transport Alignment. We convert graph alignment to an optimal transport problem between two intra-graph matrices without the requirement of cross-graph comparison. We further incorporate multi-view structure learning to enhance graph representation power and reduce the effect of structure and feature inconsistency inherited across graphs. Moreover, an alternating scheme based algorithm has been developed to address the joint optimization problem in SLOTAlign, and the provable convergence result is also established. Finally, we conduct extensive experiments on six unsupervised graph alignment datasets and the DBP15K knowledge graph (KG) alignment benchmark dataset. The proposed SLOTAlign shows superior performance and strongest robustness over seven unsupervised graph alignment methods and five specialized KG alignment methods.
Using knowledge graph embedding models (KGEMs) is a popular approach for predicting links in knowledge graphs (KGs). Traditionally, the performance of KGEMs for link prediction is assessed using rank-based metrics, which evaluate their ability to give high scores to ground-truth entities. However, the literature claims that the KGEM evaluation procedure would benefit from adding supplementary dimensions to assess. That is why, in this paper, we extend our previously introduced metric Sem@K that measures the capability of models to predict valid entities w.r.t. domain and range constraints. In particular, we consider a broad range of KGs and take their respective characteristics into account to propose different versions of Sem@K. We also perform an extensive study to qualify the abilities of KGEMs as measured by our metric. Our experiments show that Sem@K provides a new perspective on KGEM quality. Its joint analysis with rank-based metrics offers different conclusions on the predictive power of models. Regarding Sem@K, some KGEMs are inherently better than others, but this semantic superiority is not indicative of their performance w.r.t. rank-based metrics. In this work, we generalize conclusions about the relative performance of KGEMs w.r.t. rank-based and semantic-oriented metrics at the level of families of models. The joint analysis of the aforementioned metrics gives more insight into the peculiarities of each model. This work paves the way for a more comprehensive evaluation of KGEM adequacy for specific downstream tasks.
Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster structure or the fact that the data is known to lie along a tree- or graph-structured topology. However, generic methods to ensure such structure is salient in the low-dimensional representations are lacking. This negatively impacts the interpretability of low-dimensional embeddings, and plausibly downstream learning tasks. To address this issue, we introduce topological regularization: a generic approach based on algebraic topology to incorporate topological prior knowledge into low-dimensional embeddings. We introduce a class of topological loss functions, and show that jointly optimizing an embedding loss with such a topological loss function as a regularizer yields embeddings that reflect not only local proximities but also the desired topological structure. We include a self-contained overview of the required foundational concepts in algebraic topology, and provide intuitive guidance on how to design topological loss functions for a variety of shapes, such as clusters, cycles, and bifurcations. We empirically evaluate the proposed approach on computational efficiency, robustness, and versatility in combination with linear and non-linear dimensionality reduction and graph embedding methods.
Knowledge graph embedding (KGE), which maps entities and relations in a knowledge graph into continuous vector spaces, has achieved great success in predicting missing links in knowledge graphs. However, knowledge graphs often contain incomplete triples that are difficult to inductively infer by KGEs. To address this challenge, we resort to analogical inference and propose a novel and general self-supervised framework AnKGE to enhance KGE models with analogical inference capability. We propose an analogical object retriever that retrieves appropriate analogical objects from entity-level, relation-level, and triple-level. And in AnKGE, we train an analogy function for each level of analogical inference with the original element embedding from a well-trained KGE model as input, which outputs the analogical object embedding. In order to combine inductive inference capability from the original KGE model and analogical inference capability enhanced by AnKGE, we interpolate the analogy score with the base model score and introduce the adaptive weights in the score function for prediction. Through extensive experiments on FB15k-237 and WN18RR datasets, we show that AnKGE achieves competitive results on link prediction task and well performs analogical inference.