Graph Self-Supervised Learning (GSSL) has emerged as a powerful paradigm for generating high-quality representations for graph-structured data. While multi-scale graph contrastive learning has received increasing attention, many existing methods still predominantly focus on a single graph abstraction level. To address this limitation, we propose a unified contrastive framework that can target node-level, proximity-level, cluster-level, and graph-level information and integrate them through a linear combination of similarity scores on positive pairs and dissimilarity scores (i.e., similarity scores on negative pairs). Furthermore, current approaches typically assign uniform penalty strengths to all examples, which reduces optimization flexibility and leads to ambiguous convergence status. To overcome this, we introduce a novel parameter-free fine-grained self-weighting mechanism that adaptively assigns weights to individual similarity and dissimilarity scores. The proposed mechanism emphasizes the scores that deviate significantly from their target values. Our approach not only enhances optimization flexibility but also eliminates the computational overhead of hyperparameter tuning in conventional multi-task GSSL methods. Comprehensive experiments on real-world datasets show that our methods consistently outperform state-of-the-art approaches across downstream tasks, including classification, clustering, and link prediction, in both single-level and multi-level scenarios.

Subspace clustering methods face inherent scal-ability limits due to the$O(n^{3})$cost (with$n$denoting the number of data samples) of constructing full$n\times n$affinities and performing spectral decomposition. While deep learning-based approaches improve feature extraction, they maintain this computational bottleneck through exhaustive pairwise similarity computations. We propose SDSNet (Scalable Deep Subspace Network), a deep subspace clustering framework that achieves$\mathrm{O}(n)$complexity through (1) landmark-based approximation, avoiding full affinity matrices, (2) joint optimization of auto-encoder reconstruction with self-expression objectives, and (3) direct spectral clustering on factorized representations. The framework combines convolutional auto-encoders with subspace-preserving constraints. Experimental results demonstrate that SDSNet achieves comparable clustering quality to state-of-the-art methods with significantly improved computational efficiency.

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to embedding methods. In particular, the geometric distortions that might occur in the representational space have been overlooked in the literature. This work studies the problem of high-dimensional multiplex graph embedding from a geometric perspective. We find that the node representations reside on highly curved manifolds, thus rendering their exploitation more challenging for downstream tasks. Moreover, our study reveals that increasing the number of graph dimensions can cause further distortions to the highly curved manifolds. To address this problem, we propose a novel multiplex graph embedding method that harnesses hierarchical dimension embedding and Hyperbolic Graph Neural Networks. The proposed approach hierarchically extracts hyperbolic node representations that reside on Riemannian manifolds while gradually learning fewer and more expressive latent dimensions of the multiplex graph. Experimental results on real-world high-dimensional multiplex graphs show that the synergy between hierarchical and hyperbolic embeddings incurs much fewer geometric distortions and brings notable improvements over state-of-the-art approaches on downstream tasks.

We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the need for more effective and specialized approaches grows with the production of graph data with diverse characteristics. In particular, real-world multiplex graphs may exhibit a high number of dimensions, making it difficult to construct a single consensus representation. Furthermore, important information can be hidden in complex latent structures scattered in multiple dimensions. To address these issues, we propose HMGE, a novel embedding method based on hierarchical aggregation for high-dimensional multiplex graphs. Hierarchical aggregation consists in learning a hierarchical combination of the graph dimensions and refining the embeddings at each hierarchy level. Non-linear combinations are computed from previous ones, thus uncovering complex information and latent structures hidden in the multiplex graph dimensions. Moreover, we leverage mutual information maximization between local patches and global summaries to train the model without supervision. This allows to captures globally relevant information present in diverse locations of the graph. Detailed experiments on synthetic and real-world data illustrate the suitability of our approach on downstream supervised tasks, including link prediction and node classification.

We present a time-dependent approach for learning temporal co-variates explaining the subsequent user sentiments in social networks. In most of the existing approaches, we note that the underlying text classification setting, generally used to model user sentiments, is designed to ingest a user comment generated at time t to predict his corresponding sentiment at the same time. Under such constraint, user sentiments can only be given whenever she or he has generated a comment. Furthermore, the evolving historical sentiments are omitted and no anticipation of subsequent sentiments could be made. To alleviate this limitation, we propose a time-dependent approach that takes advantage of historical user comments to learn temporal co-variates that explain their evolving sentiments. We demonstrate that our approach could be used to predict user sentiments at subsequent times ahead. Experimental results on Tweets data, during the Covid-19 pandemic, illustrate the suitability of our approach.

Deep clustering models are trained based on self-supervision and pseudo-supervision. However, applying these techniques can cause Feature Randomness and Feature Drift. On one hand, Feature Randomness takes place when a considerable portion of the pseudo-labels do not match the true ones. On the other hand, Feature Drift takes place when there is a strong con-flict between the self-supervision and pseudo-supervision tasks. We propose ADEC (Adversarial Deep Embedded Clustering) a novel autoencoder-based clustering model, which relies on a discriminator network to reduce random features while avoiding the drifting effect. Experimental results validate that our model alleviates these problems and outperforms existing methods.

Recent graph clustering methods have resorted to Graph Auto-Encoders (GAEs). However, two important issues have been overlooked. First, the accumulative error, inflicted by learning from noisy clustering assignments, degrades the model’s effectiveness. This problem is called Feature Randomness (FR). Second, reconstructing the adjacency matrix sets the model to learn irrelevant similarities for the clustering task. This problem is called Feature Drift (FD). To address these issues, we first propose a sampling operator that triggers a protection mechanism against FR. second, we propose an operator Υ that triggers a correction mechanism against FD by transforming the reconstructed graph. Experimental results validate that our operators alleviate these problems and bring significant clustering improvement.

Variational Graph Auto-Encoders (VGAEs) have achieved promising performance in several applications. Some recent models incorporate the clustering inductive bias by imposing non-Gaussian prior distributions. However, the regularization term is practically insufficient to learn the clustering structures due to the mismatch between the target and the learned distributions. Thus, we formulate a new variational lower bound that incorporates an explicit clustering objective function. The introduction of a clustering objective leads to two problems. First, the latent information destroyed by the clustering process is critical for generating the between-cluster edges. Second, the noisy and sparse input graph does not benefit from the information learned during the clustering process. To address the first problem, we identify a new term overlooked by existing Evidence Lower BOunds (ELBOs). This term accounts for the difference between the variational posterior used for the clustering task and the variational posterior associated with the generation task. Furthermore, we find that the new term increases resistance to posterior collapse. Theoretically, we demonstrate that our lower bound is a tighter approximation of the log-likelihood function. To address the second problem, we propose a graph update algorithm that reduces the over-segmentation and under-segmentation problems. We conduct several experiments to validate the merits of our approach. Our results show that the proposed method considerably improves the clustering quality compared to state-of-the-art VGAE models.

We investigate the problem of discovering and modeling regime shifts in an ecosystem comprising multiple time series known as co-evolving time series. Regime shifts refer to the changing behaviors exhibited by series at different time intervals. Learning these changing behaviors is a key step toward time series forecasting. While advances have been made, existing methods suffer from one or more of the following shortcomings: (1) failure to take relationships between time series into consideration for discovering regimes in multiple time series; (2) lack of an effective approach that models time-dependent behaviors exhibited by series; (3) difficulties in handling data discontinuities which may be informative. Most of the existing methods are unable to handle all of these three issues in a unified framework. This, therefore, motivates our effort to devise a principled approach for modeling interactions and time-dependency in co-evolving time series. Specifically, we model an ecosystem of multiple time series by summarizing the heavy ensemble of time series into a lighter and more meaningful structure called a mapping grid . By using the mapping grid, our model first learns time series behavioral dependencies through a dynamic network representation, then learns the regime transition mechanism via a full time-dependent Cox regression model. The originality of our approach lies in modeling interactions between time series in regime identification and in modeling time-dependent regime transition probabilities, usually assumed to be static in existing work.

Most recent graph clustering methods have resorted to Graph Auto-Encoders (GAEs) to perform joint clustering and embedding learning. However, two critical issues have been overlooked. First, the accumulative error, inflicted by learning from noisy clustering assignments, degrades the effectiveness of the clustering model. This problem is called Feature Randomness. Second, reconstructing the adjacency matrix sets the model to learn irrelevant similarities for the clustering task. This problem is called Feature Drift. Furthermore, the theoretical relation between the aforementioned problems has not yet been investigated. We study these issues from two aspects: (1) there is a trade-off between Feature Randomness and Feature Drift when clustering and reconstruction are performed at the same level, and (2) the problem of Feature Drift is more pronounced for GAE models, compared with vanilla auto-encoder models. Thus, we reformulate the GAE-based clustering methodology. Our solution is two-fold. First, we propose a sampling operator$\Xi$that triggers a protection mechanism against Feature Randomness. Second, we propose an operator$\Upsilon$that triggers a correction mechanism against Feature Drift by gradually transforming the reconstructed graph into a clustering-oriented one. As principal advantages, our solution grants a considerable improvement in clustering effectiveness and can be easily tailored to GAE models.

We present a time-dependent approach for learning potential features that may explain the early risk of human self-harm. Rather than only extracting features from text posted by users, as suggested by several approaches, we propose remodeling the user posts into sequential data. We demonstrate that the sequences reflecting the longitudinal grammatical language of users allow the improved performance of classification algorithms in predicting self-harm behavior. The experimental results on the eRisk 2019 data corroborate our claim.

We devise a graph attention network-based approach for learning a scene triangle mesh representation in order to estimate an image camera position in a dynamic environment. Previous approaches built a scene-dependent model that explicitly or implicitly embeds the structure of the scene. They use convolution neural networks or decision trees to establish 2D/3D-3D correspondences. Such a mapping overfits the target scene and does not generalize well to dynamic changes in the environment. Our work introduces a novel approach to solve the camera relocalization problem by using the available triangle mesh. Our 3D-3D matching framework consists of three blocks: (1) a graph neural network to compute the embedding of mesh vertices, (2) a convolution neural network to compute the embedding of grid cells defined on the RGB-D image, and (3) a neural network model to establish the correspondence between the two embeddings. These three components are trained end-to-end. To predict the final pose, we run the RANSAC algorithm to generate camera pose hypotheses, and we refine the prediction using the point-cloud representation. Our approach significantly improves the camera pose accuracy of the state-of-the-art method from 0.358 to 0.506 on the RIO10 benchmark for dynamic indoor camera relocalization.

To overcome the absence of concrete supervisory signals, deep clustering models construct their own labels based on self-supervision and pseudo-supervision. However, applying these techniques can cause Feature Randomness and Feature Drift. In this paper, we formally characterize these two new concepts. On one hand, Feature Randomness takes place when a considerable portion of the pseudo-labels is deemed to be random. In this regard, the trained model can learn non-representative features. On the other hand, Feature Drift takes place when the pseudo-supervised and the reconstruction losses are jointly minimized. While penalizing the reconstruction loss aims to preserve all the inherent data information, optimizing the embedded-clustering objective drops the latent between-cluster variances. Due to this compromise, the clustering-friendly representations can be easily drifted. In this context, we propose ADEC (Adversarial Deep Embedded Clustering) a novel autoencoder-based clustering model, which relies on a discriminator network to reduce random features while avoiding the drifting effect. Our new metrics$\Delta _{FR}$and$\Delta _{FD}$allows to, respectively, assess the level of Feature Randomness and Feature Drift. We empirically demonstrate the suitability of our model on handling these problems using benchmark real datasets. Experimental results validate that our model outperforms state-of-the-art autoencoder-based clustering methods.

We investigate the problem of community detection in bipartite networks that are characterized by the presence of two types of nodes such that connections exist only between nodes of different types. While some approaches have been proposed to identify community structures in bipartite networks, there are a number of problems still to solve. In fact, the majority of the proposed approaches suffer from one or even more of the following limitations: (1) difficulty in detecting communities in the presence of many non-discriminating nodes with atypical connections that hide the community structures, (2) loss of relevant topological information due to the transformation of the bipartite network to standard plain graphs, and (3) manually specifying several input parameters, including the number of communities to be identified. To alleviate these problems, we propose BiNeTClus, a parameter-free community detection algorithm in bipartite networks that operates in two phases. The first phase focuses on identifying an initial grouping of nodes through a transactional data model capable of dealing with the situation that involves networks with many atypical connections, that is, sparsely connected nodes and nodes of one type that massively connect to all other nodes of the second type. The second phase aims to refine the clustering results of the first phase via an optimization strategy of the bipartite modularity to identify the final community structures. Our experiments on both synthetic and real networks illustrate the suitability of the proposed approach.

Most existing approaches for electricity load forecasting perform the task based on overall electricity consumption. However, using such a global methodology can affect load forecasting accuracy, as it does not consider the possibility that customers’ consumption behavior may change at any time. Predicting customers’ electricity consumption in the presence of unstable behaviors poses challenges to existing models. In this article, we propose a principled approach capable of handling customers’ changeable electricity consumption. We devise a network-based method that first builds and tracks clusters of customer consumption patterns over time. Then, on the evolving clusters, we develop a framework that exploits long short-term memory recurrent neural network and survival analysis techniques to forecast electricity consumption. Our experiments on real electricity consumption datasets illustrate the suitability of the proposed approach.

As time evolves, communities in a social network may undergo various changes known as critical events. For instance, a community can either split into several other communities, expand into a larger community, shrink to a smaller community, remain stable or merge into another community. Prediction of critical events has attracted increasing attention in the recent literature. Learning the evolution of communities over time is a key step towards predicting the critical events the communities may undergo. This is an important and difficult issue in the study of social networks. In the work to date, there is a lack of formal approaches for modeling and predicting critical events over time. This motivates our effort to design a new statistical method for event prediction in order to make better use of histories of past changes. To this end, this paper proposes a sliding window analysis from which we develop a model that simultaneously exploits an autoregressive model and survival analysis techniques. The autoregressive model is employed here to simulate the evolution of the community structure, whereas the survival analysis techniques allow the prediction of future changes the community may undergo.

This paper proposes a statistical framework to automatically identify anomalous nodes in static networks. In our approach, we first associate to each node a neighborhood cohesiveness feature vector such that each element of this vector corresponds to a score quantifying the node's neighborhood connectivity, as estimated by a specific similarity measure. Next, based on the estimated node's feature vectors, we view the task of identifying anomalous nodes from a mixture modeling perspective, based on which we elaborate a statistical approach that exploits the Dirichlet distribution to automatically identify anomalies. The suitability of the proposed method is illustrated through experiments on both synthesized and real networks.

This paper introduces a parameterless approach named MCDA: Multidimensional Communities Detection Algorithm. MCDA adopts a local search mechanism which is inspired from the label propagation principle. To this end, we design a novel propagation rule that exploits the most frequently used interaction dimensions among neighbors as an additional constraint for membership selections. The new propagation rule allows MCDA to automatically unfold the hidden communities in a multidimensional context. The detected communities are further processed for relevant dimensions selection using an inter-class inertia-based procedure. The proposed algorithm is fully automated and does not require any parameter to be set by the user to recover communities and their associated dimensions.

This paper investigates the problem of the detection of anomalies in multidimensional networks, that is, networks where nodes are connected through multiple links (dimensions). Anomaly detection in monodimensional networks has been well studied and several approaches have been proposed. This problem, however, has been less investigated in the multidimensional setting. In this paper we deal with the lack of an effective approach for identifying anomalous nodes in multidimensional networks. Our contribution is two fold. First, we develop a novel scoring function that reflects the anomalousness degree of a node. Second, based on the estimated anomaly scores, we devise a probabilistic approach based on the beta mixture model to systematically discriminate between normal and anomalous nodes. A notable feature of our approach is that it performs anomaly detection in an automatic fashion without requesting human intervention to set an empirical detection threshold to detect anomalies, or by specifying the number of anomalous nodes to be selected. Furthermore, the approach that we propose exploits the topological structure of the multidimensional network as such, without considering any aggregation technique nor examining independently each dimension to identify anomalies. Experiments on synthetic as well as real networks illustrate the suitability of the proposed approach.

In real-world social networks, there is an increasing interest in tracking the evolution of groups of users and detecting the various changes they are liable to undergo. Several approaches have been proposed for this. In studying these approaches, we observed that most of them use a two-stage process. In the first stage, they run an algorithm to identify groups of users at each timestamp. In the second stage, a pairwise comparison based on a similarity measure is employed to track groups of users and detect changes they may undergo. While the majority of existing approaches use a two-stage process, they all run different algorithms to identify communities and rely on different similarity measures to track groups of users over time. Noting that the different approaches may perform differently depending on the dynamic social network under investigation, we decided to make a high level survey of some existing tracking approaches and then do a comparative analysis of some of them. In our analysis, we compared the algorithms in two main situations: (1) when groups of users do not overlap and (2) when the groups are overlapping. The study was done on three different testbeds extracted from the DBLP, Autonomous System (AS) and Yelp datasets.

We investigate the problem of community detection in multidimensional networks, that is, networks where entities engage in various interaction types (dimensions) simultaneously. While some approaches have been proposed to identify community structures in multidimensional networks, there are a number of problems still to solve. In fact, the majority of the proposed approaches suffer from one or even more of the following limitations: (1) difficulty detecting communities in networks characterized by the presence of many irrelevant dimensions, (2) lack of systematic procedures to explicitly identify the relevant dimensions of each community, and (3) dependence on a set of user-supplied parameters, including the number of communities, that require a proper tuning. Most of the existing approaches are inadequate for dealing with these three issues in a unified framework. In this paper, we develop a novel approach that is capable of addressing the aforementioned limitations in a single framework. The proposed approach allows automated identification of communities and their sub-dimensional spaces using a novel objective function and a constrained label propagation-based optimization strategy. By leveraging the relevance of dimensions at the node level, the strategy aims to maximize the number of relevant within-community links while keeping track of the most relevant dimensions. A notable feature of the proposed approach is that it is able to automatically identify low dimensional community structures embedded in a high dimensional space. Experiments on synthetic and real multidimensional networks illustrate the suitability of the new method.

In this paper, we view the task of identifying spammers in social networks from a mixture modeling perspective, based on which we devise a principled unsupervised approach to detect spammers. In our approach, we first represent each user of the social network with a feature vector that reflects its behaviour and interactions with other participants. Next, based on the estimated users feature vectors, we propose a statistical framework that uses the Dirichlet distribution in order to identify spammers. The proposed approach is able to automatically discriminate between spammers and legitimate users, while existing unsupervised approaches require human intervention in order to set informal threshold parameters to detect spammers. Furthermore, our approach is general in the sense that it can be applied to different online social sites. To demonstrate the suitability of the proposed method, we conducted experiments on real data extracted from Instagram and Twitter.

In real-world social networks, there is increasing interest in tracking the evolution of groups of users. Existing approaches track evolving communities, in a time-sequential way, by comparing communities in terms of nodes using a similarity measure such as the Jaccard or a modified Jaccard measure. The measure allows the use of a one-to-one comparison in order to match communities. However, tracking a given community based on this measure alone may, at the end of its lifespan yield a community that does not share any node with the community initially observed. In this paper we present a novel approach for modeling and detecting the evolution of communities. In our model, we first build a matrix that counts the number of nodes shared between two communities. The individual rows of the obtained matrix are then used to represent nodes shared by a community with all other communities over time. This effectively captures the trace of the communities that should be compared over the period of observation. We then propose a new similarity measure, named mutual transition, for tracking the communities and rules for capturing significant transition events a community can undergo. The proposed approach is general in the sense that it can be applied to different social networks. To demonstrate the suitability of the proposed method, we conducted experiments on real data extracted from the DBLP, Autonomous System and YELP.

Several approaches have been proposed for the problem of identifying authoritative actors in online communities. However, the majority of existing methods suffer from one or more of the following limitations: (1) There is a lack of an automatic mechanism to formally discriminate between authoritative and nonauthoritative users. In fact, a common approach to authoritative user identification is to provide a ranked list of users expecting authorities to come first. A major problem of such an approach is the question of where to stop reading the ranked list of users. How many users should be chosen as authoritative? (2) Supervised learning approaches for authoritative user identification suffer from their dependency on the training data. The problem here is that labeled samples are more difficult, expensive, and time consuming to obtain than unlabeled ones. (3) Several approaches rely on some user parameters to estimate an authority score. Detection accuracy of authoritative users can be seriously affected if incorrect values are used. In this article, we propose a parameterless mixture model-based approach that is capable of addressing the three aforementioned issues in a single framework. In our approach, we first represent each user with a feature vector composed of information related to its social behavior and activity in an online community. Next, we propose a statistical framework, based on the multivariate beta mixtures, in order to model the estimated set of feature vectors. The probability density function is therefore estimated and the beta component that corresponds to the most authoritative users is identified. The suitability of the proposed approach is illustrated on real data extracted from the Stack Exchange question-answering network and Twitter.

In this article, we define a knowledge-sharing community in a question-answering forum as a set of askers and authoritative users such that, within each community, askers exhibit more homogeneous behavior in terms of their interactions with authoritative users than elsewhere. A procedure for discovering members of such a community is devised. As a case study, we focus on Yahoo! Answers, a large and diverse online question-answering service. Our contribution is twofold. First, we propose a method for automatic identification of authoritative actors in Yahoo! Answers. To this end, we estimate and then model the authority scores of participants as a mixture of gamma distributions. The number of components in the mixture is determined using the Bayesian Information Criterion (BIC), while the parameters of each component are estimated using the Expectation-Maximization (EM) algorithm. This method allows us to automatically discriminate between authoritative and nonauthoritative users. Second, we represent the forum environment as a type of transactional data such that each transaction summarizes the interaction of an asker with a specific set of authoritative users. Then, to group askers on the basis of their interactions with authoritative users, we propose a parameter-free transaction data clustering algorithm which is based on a novel criterion function. The identified clusters correspond to the communities that we aim to discover. To evaluate the suitability of our clustering algorithm, we conduct a series of experiments on both synthetic data and public real-life data. Finally, we put our approach to work using data from Yahoo! Answers which represent users’ activities over one full year.

Clustering high-dimensional data has been a major challenge due to the inherent sparsity of the points. Most existing clustering algorithms become substantially inefficient if the required similarity measure is computed between data points in the full-dimensional space. To address this problem, a number of projected clustering algorithms have been proposed. However, most of them encounter difficulties when clusters hide in subspaces with very low dimensionality. These challenges motivate our effort to propose a robust partitional distance-based projected clustering algorithm. The algorithm consists of three phases. The first phase performs attribute relevance analysis by detecting dense and sparse regions and their location in each attribute. Starting from the results of the first phase, the goal of the second phase is to eliminate outliers, while the third phase aims to discover clusters in different subspaces. The clustering process is based on the k-means algorithm, with the computation of distance restricted to subsets of attributes where object values are dense. Our algorithm is capable of detecting projected clusters of low dimensionality embedded in a high-dimensional space and avoids the computation of the distance in the full-dimensional space. The suitability of our proposal has been demonstrated through an empirical study using synthetic and real datasets.

We consider the problem of identifying authoritative users in Yahoo! Answers. A common approach is to use link analysis techniques in order to provide a ranked list of users based on their degree of authority. A major problem for such an approach is determining how many users should be chosen as authoritative from a ranked list. To address this problem, we propose a method for automatic identification of authoritative actors. In our approach, we propose to model the authority scores of users as a mixture of gamma distributions. The number of components in the mixture is estimated by the Bayesian Information Criterion (BIC) while the parameters of each component are estimated using the Expectation-Maximization (EM) algorithm. This method allows us to automatically discriminate between authoritative and non-authoritative users. The suitability of our proposal is demonstrated in an empirical study using datasets from Yahoo! Answers.

Clustering samples in gene expression data has always been a major challenge because of the high dimensionality of the input space (typically in the tens of thousands) and the small number of samples (typically less than a hundred). Moreover, clusters may hide in subspaces with very low dimensionalities. Most existing clustering algorithms become substantially inefficient if the required similarity measure is computed between data points in the full-dimensional space. These challenges motivate our effort to propose a new and efficient partitional distance-based projected clustering algorithm for clustering samples in gene expression data. Our algorithm is capable of detecting projected clusters of extremely low dimensionality embedded in a high-dimensional space and avoids the computation of the distance in the full-dimensional space. The suitability of our proposal has been demonstrated through an empirical study using public microarray datasets.