The presence of interference, where the outcome of an individual may depend on the treatment assignment and behavior of neighboring nodes, can lead to biased causal effect estimation. Current approaches to network experiment design focus on limiting interference through cluster-based randomization, in which clusters are identified using graph clustering, and cluster randomization dictates the node assignment to treatment and control. However, cluster-based randomization approaches perform poorly when interference propagates in cascades, whereby the response of individuals to treatment propagates to their multi-hop neighbors. When we have knowledge of the cascade seed nodes, we can leverage this interference structure to mitigate the resulting causal effect estimation bias. With this goal, we propose a cascade-based network experiment design that initiates treatment assignment from the cascade seed node and propagates the assignment to their multi-hop neighbors to limit interference during cascade growth and thereby reduce the overall causal effect estimation error. Our extensive experiments on real-world and synthetic datasets demonstrate that our proposed framework outperforms the existing state-of-the-art approaches in estimating causal effects in network data.
Graph clustering is a fundamental problem in machine learning. Deep learning methods achieve the state-of-the-art results in recent years, but they still cannot work without predefined cluster numbers. Such limitation motivates us to pose a more challenging problem of graph clustering with unknown cluster number. We propose to address this problem from a fresh perspective of graph information theory (i.e., structural information). In the literature, structural information has not yet been introduced to deep clustering, and its classic definition falls short of discrete formulation and modeling node features. In this work, we first formulate a differentiable structural information (DSI) in the continuous realm, accompanied by several theoretical results. By minimizing DSI, we construct the optimal partitioning tree where densely connected nodes in the graph tend to have the same assignment, revealing the cluster structure. DSI is also theoretically presented as a new graph clustering objective, not requiring the predefined cluster number. Furthermore, we design a neural LSEnet in the Lorentz model of hyperbolic space, where we integrate node features to structural information via manifold-valued graph convolution. Extensive empirical results on real graphs show the superiority of our approach.
Current graph clustering methods emphasize individual node and edge con nections, while ignoring higher-order organization at the level of motif. Re cently, higher-order graph clustering approaches have been designed by motif based hypergraphs. However, these approaches often suffer from hypergraph fragmentation issue seriously, which degrades the clustering performance greatly. Moreover, real-world graphs usually contain diverse motifs, with nodes participating in multiple motifs. A key challenge is how to achieve precise clustering results by integrating information from multiple motifs at the node level. In this paper, we propose a multi-order graph clustering model (MOGC) to integrate multiple higher-order structures and edge connections at node level. MOGC employs an adaptive weight learning mechanism to au tomatically adjust the contributions of different motifs for each node. This not only tackles hypergraph fragmentation issue but enhances clustering accuracy. MOGC is efficiently solved by an alternating minimization algo rithm. Experiments on seven real-world datasets illustrate the effectiveness of MOGC.
Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. Moreover, we show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a vertex of maximum degree in an auxiliary graph and forming a cluster around it. One of these algorithms relies on solving a linear program. Our final contribution is to design a new and purely combinatorial approach for doing so that is far more scalable in theory and practice.
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their extension to directed graphs remains relatively underexplored due to the additional complexity introduced by edge directions. In this paper, we leverage statistical inference on stochastic block models to guide the development of a spectral clustering algorithm for directed graphs. Specifically, we study the maximum likelihood estimation under a widely used directed stochastic block model, and derive a global objective function that aligns with the underlying community structure. We further establish a theoretical upper bound on the misclustering error of its spectral relaxation, and based on this relaxation, introduce a novel, self-adaptive spectral clustering method for directed graphs. Extensive experiments on synthetic and real-world datasets demonstrate significant performance gains over existing baselines.
Clustering holds profound significance in data mining. In recent years, graph convolutional network (GCN) has emerged as a powerful tool for deep clustering, integrating both graph structural information and node attributes. However, most existing methods ignore the higher-order structural information of the graph. Evidently, nodes within the same cluster can establish distant connections. Besides, recent deep clustering methods usually apply a self-supervised module to monitor the training process of their model, focusing solely on node attributes without paying attention to graph structure. In this paper, we propose a novel graph clustering network to make full use of graph structural information. To capture the higher-order structural information, we design a graph mutual infomax module, effectively maximizing mutual information between graph-level and node-level representations, and employ a trinary self-supervised module that includes modularity as a structural constraint. Our proposed model outperforms many state-of-the-art methods on various datasets, demonstrating its superiority.
Over the last few years, various multi-view graph clustering methods have shown promising performances. However, we argue that these methods can have limitations. In particular, they are often unnecessarily complex, leading to scalability problems that make them prohibitive for most real-world graph applications. Furthermore, many of them can handle only specific types of multi-view graphs. Another limitation is that the process of learning graph representations is separated from the clustering process, and in some cases these methods do not even learn a graph representation, which severely restricts their flexibility and usefulness. In this paper we propose a simple yet effective linear model that addresses the dual tasks of multi-view attributed graph representation learning and clustering in a unified framework. The model starts by performing a first-order neighborhood smoothing step for the different individual views, then gives each one a weight corresponding to its importance. Finally, an iterative process of simultaneous clustering and representation learning is performed w.r.t. the importance of each view, yielding a consensus embedding and partition of the graph. Our model is generic and can deal with any type of multi-view graph. Finally, we show through extensive experimentation that this simple model consistently achieves competitive performances w.r.t. state-of-the-art multi-view attributed graph clustering models, while at the same time having training times that are shorter, in some cases by orders of magnitude.
Attributed graphs are used to model a wide variety of real-world networks. Recent graph convolutional network-based representation learning methods have set state-of-the-art results on the clustering of attributed graphs. However, these approaches deal with clustering as a downstream task while better performances can be attained by incorporating the clustering objective into the representation learning process. In this paper, we propose, in a unified framework, an objective function taking into account both tasks simultaneously. Based on a variant of the simple graph convolutional network, our model does clustering by minimizing the difference between the convolved node representations and their reconstructed cluster representatives. We showcase the efficiency of the derived algorithm against state-of-the-art methods both in terms of clustering performance and computational cost on thede facto benchmark graph clustering datasets. We further demonstrate the usefulness of the proposed approach for graph visualization through generating embeddings that exhibit a clustering structure.
Functional MRI (fMRI) research, employing naturalistic stimuli like movies, explores brain network interactions in complex cognitive processes such as empathy. The empathy network encompasses multiple brain areas, including the Insula, PFC, ACC, and parietal regions. Our novel processing pipeline applies graph learning methods to whole-brain timeseries signals, incorporating high-pass filtering, voxel-level clustering, and windowed graph learning with a sparsity-based approach. The study involves two short movies shown to 14 healthy volunteers, considering 54 regions extracted from the AAL Atlas. The sparsity-based graph learning consistently outperforms, achieving over 88% accuracy in capturing emotion contagion variations. Temporal analysis reveals a gradual induction of empathy, supported by the method's effectiveness in capturing dynamic connectomes through graph clustering. Edge-weight dynamics analysis underscores sparsity-based learning's superiority, while connectome-network analysis highlights the pivotal role of the Insula, Amygdala, and Thalamus in empathy. Spectral filtering analysis emphasizes the band-pass filter's significance in isolating regions linked to emotional and empathetic processing during empathy HIGH states. Key regions like Amygdala, Insula, and Angular Gyrus consistently activate, supporting their critical role in immediate emotional responses. Strong similarities across movies in graph cluster labels, connectome-network analysis, and spectral filtering-based analyses reveal robust neural correlates of empathy. These findings advance our understanding of empathy-related neural dynamics and identify specific regions in empathetic responses, offering insights for targeted interventions and treatments associated with empathetic processing.
Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This significantly limits their applicability in practice, since real-world graphs exhibit a structural disparity and cannot simply be classified as homophily and heterophily. Thus, a principled way to handle practical graphs is urgently needed. To fill this gap, we provide a novel solution with theoretical support. Interestingly, we find that most homophilic and heterophilic edges can be correctly identified on the basis of neighbor information. Motivated by this finding, we construct two graphs that are highly homophilic and heterophilic, respectively. They are used to build low-pass and high-pass filters to capture holistic information. Important features are further enhanced by the squeeze-and-excitation block. We validate our approach through extensive experiments on both homophilic and heterophilic graphs. Empirical results demonstrate the superiority of our method compared to state-of-the-art clustering methods.
Conventional fair graph clustering methods face two primary challenges: i) They prioritize balanced clusters at the expense of cluster cohesion by imposing rigid constraints, ii) Existing methods of both individual and group-level fairness in graph partitioning mostly rely on eigen decompositions and thus, generally lack interpretability. To address these issues, we propose iFairNMTF, an individual Fairness Nonnegative Matrix Tri-Factorization model with contrastive fairness regularization that achieves balanced and cohesive clusters. By introducing fairness regularization, our model allows for customizable accuracy-fairness trade-offs, thereby enhancing user autonomy without compromising the interpretability provided by nonnegative matrix tri-factorization. Experimental evaluations on real and synthetic datasets demonstrate the superior flexibility of iFairNMTF in achieving fairness and clustering performance.
Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first algorithm uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to rapidly compute a SymNMF of the approximation. The second algorithm uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. We prove theoretically that leverage score sampling can approximately solve nonnegative least squares problems to a chosen accuracy with high probability. Additionally, we prove sampling complexity results for previously proposed hybrid sampling techniques which deterministically include high leverage score rows. This hybrid scheme is crucial for obtaining speeds ups in practice. Finally we demonstrate that both methods work well in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.
Learning positional information of nodes in a graph is important for link prediction tasks. We propose a representation of positional information using representative nodes called landmarks. A small number of nodes with high degree centrality are selected as landmarks, which serve as reference points for the nodes' positions. We justify this selection strategy for well-known random graph models and derive closed-form bounds on the average path lengths involving landmarks. In a model for power-law graphs, we prove that landmarks provide asymptotically exact information on inter-node distances. We apply theoretical insights to practical networks and propose Hierarchical Position embedding with Landmarks and Clustering (HPLC). HPLC combines landmark selection and graph clustering, where the graph is partitioned into densely connected clusters in which nodes with the highest degree are selected as landmarks. HPLC leverages the positional information of nodes based on landmarks at various levels of hierarchy such as nodes' distances to landmarks, inter-landmark distances and hierarchical grouping of clusters. Experiments show that HPLC achieves state-of-the-art performances of link prediction on various datasets in terms of HIT@K, MRR, and AUC. The code is available at \url{https://github.com/kmswin1/HPLC}.
Privacy, scalability, and reliability are significant challenges in unmanned aerial vehicle (UAV) networks as distributed systems, especially when employing machine learning (ML) technologies with substantial data exchange. Recently, the application of federated learning (FL) to UAV networks has improved collaboration, privacy, resilience, and adaptability, making it a promising framework for UAV applications. However, implementing FL for UAV networks introduces drawbacks such as communication overhead, synchronization issues, scalability limitations, and resource constraints. To address these challenges, this paper presents the Blockchain-enabled Clustered and Scalable Federated Learning (BCS-FL) framework for UAV networks. This improves the decentralization, coordination, scalability, and efficiency of FL in large-scale UAV networks. The framework partitions UAV networks into separate clusters, coordinated by cluster head UAVs (CHs), to establish a connected graph. Clustering enables efficient coordination of updates to the ML model. Additionally, hybrid inter-cluster and intra-cluster model aggregation schemes generate the global model after each training round, improving collaboration and knowledge sharing among clusters. The numerical findings illustrate the achievement of convergence while also emphasizing the trade-offs between the effectiveness of training and communication efficiency.
Speaker diarization, the task of segmenting an audio recording based on speaker identity, constitutes an important speech pre-processing step for several downstream applications.The conventional approach to diarization involves multiple steps of embedding extraction and clustering, which are often optimized in an isolated fashion. While end-to-end diarization systems attempt to learn a single model for the task, they are often cumbersome to train and require large supervised datasets. In this paper, we propose an end-to-end supervised hierarchical clustering algorithm based on graph neural networks (GNN), called End-to-end Supervised HierARchical Clustering (E-SHARC). The embedding extractor is initialized using a pre-trained x-vector model while the GNN model is trained initially using the x-vector embeddings from the pre-trained model. Finally, the E-SHARC model uses the front-end mel-filterbank features as input and jointly optimizes the embedding extractor and the GNN clustering module, performing representation learning, metric learning, and clustering with end-to-end optimization. Further, with additional inputs from an external overlap detector, the E-SHARC approach is capable of predicting the speakers in the overlapping speech regions. The experimental evaluation on benchmark datasets like AMI, Voxconverse and DISPLACE, illustrates that the proposed E-SHARC framework provides competitive diarization results using graph based clustering methods.
Open-vocabulary 3D instance segmentation is cutting-edge for its ability to segment 3D instances without predefined categories. However, progress in 3D lags behind its 2D counterpart due to limited annotated 3D data. To address this, recent works first generate 2D open-vocabulary masks through 2D models and then merge them into 3D instances based on metrics calculated between two neighboring frames. In contrast to these local metrics, we propose a novel metric, view consensus rate, to enhance the utilization of multi-view observations. The key insight is that two 2D masks should be deemed part of the same 3D instance if a significant number of other 2D masks from different views contain both these two masks. Using this metric as edge weight, we construct a global mask graph where each mask is a node. Through iterative clustering of masks showing high view consensus, we generate a series of clusters, each representing a distinct 3D instance. Notably, our model is training-free. Through extensive experiments on publicly available datasets, including ScanNet++, ScanNet200 and MatterPort3D, we demonstrate that our method achieves state-of-the-art performance in open-vocabulary 3D instance segmentation. Our project page is at https://pku-epic.github.io/MaskClustering.
We introduce a highly efficient method for panoptic segmentation of large 3D point clouds by redefining this task as a scalable graph clustering problem. This approach can be trained using only local auxiliary tasks, thereby eliminating the resource-intensive instance-matching step during training. Moreover, our formulation can easily be adapted to the superpoint paradigm, further increasing its efficiency. This allows our model to process scenes with millions of points and thousands of objects in a single inference. Our method, called SuperCluster, achieves a new state-of-the-art panoptic segmentation performance for two indoor scanning datasets: $50.1$ PQ ($+7.8$) for S3DIS Area~5, and $58.7$ PQ ($+25.2$) for ScanNetV2. We also set the first state-of-the-art for two large-scale mobile mapping benchmarks: KITTI-360 and DALES. With only $209$k parameters, our model is over $30$ times smaller than the best-competing method and trains up to $15$ times faster. Our code and pretrained models are available at https://github.com/drprojects/superpoint_transformer.
Attributed graph clustering is an unsupervised task that partitions nodes into different groups. Self-supervised learning (SSL) shows great potential in handling this task, and some recent studies simultaneously learn multiple SSL tasks to further boost performance. Currently, different SSL tasks are assigned the same set of weights for all graph nodes. However, we observe that some graph nodes whose neighbors are in different groups require significantly different emphases on SSL tasks. In this paper, we propose to dynamically learn the weights of SSL tasks for different nodes and fuse the embeddings learned from different SSL tasks to boost performance. We design an innovative graph clustering approach, namely Dynamically Fusing Self-Supervised Learning (DyFSS). Specifically, DyFSS fuses features extracted from diverse SSL tasks using distinct weights derived from a gating network. To effectively learn the gating network, we design a dual-level self-supervised strategy that incorporates pseudo labels and the graph structure. Extensive experiments on five datasets show that DyFSS outperforms the state-of-the-art multi-task SSL methods by up to 8.66% on the accuracy metric. The code of DyFSS is available at: https://github.com/q086/DyFSS.
Graph clustering algorithms with autoencoder structures have recently gained popularity due to their efficient performance and low training cost. However, for existing graph autoencoder clustering algorithms based on GCN or GAT, not only do they lack good generalization ability, but also the number of clusters clustered by such autoencoder models is difficult to determine automatically. To solve this problem, we propose a new framework called Graph Clustering with Masked Autoencoders (GCMA). It employs our designed fusion autoencoder based on the graph masking method for the fusion coding of graph. It introduces our improved density-based clustering algorithm as a second decoder while decoding with multi-target reconstruction. By decoding the mask embedding, our model can capture more generalized and comprehensive knowledge. The number of clusters and clustering results can be output end-to-end while improving the generalization ability. As a nonparametric class method, extensive experiments demonstrate the superiority of \textit{GCMA} over state-of-the-art baselines.