Graph Clustering Research Articles

An improved Nyström spectral graph clustering using k-core decomposition as a sampling strategy for large networks

Clustering on graphs (networks) is becoming intractable due to increasing sizes. Nyström spectral graph clustering (NSC) is a popular method to circumvent the problem. However, NSC currently faces two issues: (1) how to efficiently obtain representative samples for large networks; (2) the NSC is irrational for the mapping of nodes. To address the issues, in this paper, we propose an improved Nyström spectral graph clustering based on k-core decomposition sampling for large networks. In the proposed method, we first employ k-core decomposition as a sampling method, then use the samples to conduct the NSC to acquire the clusters of the sample nodes and the nodes connected with the samples, and finally utilize the proposed label propagation algorithm to group the remaining nodes into previously found clusters. To evaluate the performance, we use spectral clustering and NSC as baselines and compare our algorithm with the baselines on 9 small networks. Moreover, the proposed method is applied to 5 large networks. The proposed method can achieve a Modularity of 0.355 and cost 1234.95 s for a large network with approximately 120 million edges, which demonstrates that the proposed method has higher accuracy than NSC and higher efficiency than spectral clustering.

Attributed graph clustering with multi-task embedding learning

Attributed graph clustering is challenging as it needs to effectively combine both graph structure and node feature information to accomplish node clustering. Recent studies mostly adopt graph neural networks to learn node embeddings, then apply traditional clustering methods to obtain clusters. However, their node embeddings are not specifically designed for clustering. Moreover, most of their loss functions only rely on either structure or feature information, making both kinds of information not fully retained in node embeddings. In this paper, we propose a multi-task embedding learning method (MTEL) for attributed graph clustering, which constructs two prediction tasks in terms of structure and feature based adjacency matrices respectively. To make the node embeddings helpful for the downstream clustering, in each task, we predict the minimum hop number between each pair of nodes in the adjacency matrix, so that the correlation degrees among nodes can be encoded into node embeddings. To improve the performance of the prediction task, we regularize the model parameters in these two tasks via ℓ2,1 norm, through which the model parameters can be jointly learned. Experiments on real attributed graphs show that MTEL is superior for attributed graph clustering over state-of-the-art methods.

Graph analysis and clustering of proteins linked with COVID-19

A remarkable number of scientific initiatives are in practice to encounter the new coronavirus epidemic (COVID-19). One of the biggest challenges faced by the COVID-19 researchers in the therapeutic field is the knowledge about the biological functions in disease-human interacting proteins. The detection of COVID-19 protein complexes, a group of proteins that possess the same biological functions, helps in better understanding of the biological processes in our body. The main contribution of this work is to cluster proteins that perform the same biological functions to increase the knowledge about the COVID-19 disease-human interacting proteins. The authors investigated proteins linked with COVID-19 disease by creating a disease-human protein-protein interaction graph. Topological means of graph analysis and graph clustering have been employed to group proteins that possess the same biological functions. These clusters will be the protein complexes that work together to carry out a specific biological function in a human cell. Moreover, through the cluster analysis, we can uncover previously unknown COVID-19 disease-human protein links that are beneficial for promising knowledge discovery. Also, the authors evaluated how the Markov Cluster algorithm, a graph-based algorithm finds interesting patterns of similar features from COVID-19 disease-human protein-protein interaction graph. The Markov Cluster algorithm results in six statistically significant protein clusters, including cluster (A): keratinization (3.50E-71), (B): regulation of cellular process (6.62E-05), (C): regulation of cell cycle (1.31E-27), (D): mitotic cell cycle (1.66E-06), (E): regulation of phosphoprotein phosphatase activity (1.15E-09), and (G): G2/M transition of mitotic cell cycle (3.03E-07).

Graph Clustering With Graph Capsule Network.

Graph clustering, which aims to partition a set of graphs into groups with similar structures, is a fundamental task in data analysis. With the great advances made by deep learning, deep graph clustering methods have achieved success. However, these methods have two limitations: (1) they learn graph embeddings by a neural language model that fails to effectively express graph properties, and (2) they treat embedding learning and clustering as two isolated processes, so the learned embeddings are unsuitable for the subsequent clustering. To overcome these limitations, we propose a novel capsule-based graph clustering (CGC) algorithm to cluster graphs. First, we construct a graph clustering capsule network (GCCN) that introduces capsules to capture graph properties. Second, we design an iterative optimization strategy to alternately update the GCCN parameters and clustering assignment parameters. This strategy leads GCCN to learn cluster-oriented graph embeddings. Experimental results show that our algorithm achieves performance superior to that of existing graph clustering algorithms in terms of three standard evaluation metrics: ACC, NMI, and ARI. Moreover, we use visualization results to analyze the effectiveness of the capsules and demonstrate that GCCN can learn cluster-oriented embeddings.

Online author name disambiguation in evolving digital library

Name ambiguity is a prevalent problem in digital library domain where mapping of bibliographic records to authors is a major issue. The unprecedented growth of the bibliographic records and absence of unique identifiers are further exacerbating the problem. Specifically, name ambiguity affects various bibliometric analysis tasks that include record management as well as scientific assessment of the authors thereby necessitating the name disambiguation. The name disambiguation task is to assign the records, possibly with the ambiguous authorship, to corresponding authors. While existing techniques are good at extracting abstract features from set of records with a common author name that can be subsequently used for clustering the records based on unique author identities, however, such techniques usually perform poorly in disambiguating isolated individual record entries that arrive continuously. Disambiguation of only newly arrived records, rather than the whole records of the digital library is challenging, however, computationally rewarding and thus, not only preferable but becoming the necessity due to tremendous growth in the number of bibliographic records with the time, which is likely to continue. In this regard, we propose an online author name disambiguation approach for evolving digital library. Our approach involves representation learning of records in an online manner in evolving (academic networks) digital library using dynamic graph embedding and clustering of latent representation of records. We show the use of our online name disambiguation method in batch setting (for static or initial records of digital library) and incremental setting (for new records of digital library). Significant improvement, over existing state-of-the-art methods in terms of various evaluation metrics, has been observed which indicates the effectiveness of the proposed approach.

FRAMEWORK TO BUILD AN ADVANCED ANALYTICS MATURITY ASSESSMENT MODEL: QUESTIONNAIRE DESIGN

INTRODUCTION
 Every minute of every day, a huge amount of data is created – social media, email communication, any device connected to the internet, google search. The future of digitalisation and internet of things promises a further generation of new data volumes. New advanced analytical approaches are required to deal with and make sense of large volumes of unstructured and structured data.
 Data-driven business environment is a competitive advantage for any organisation. To ensure faster and smarter decision-making, organisations are forced to use advanced analytics to analyse the past, understand the present behaviour and predict and influence future events, actions, decisions and behaviour. Assessment of the advanced analytics ecosystem is crucial for further development, competitions in the market and to reach the strategic goals of the organisation. The assessment and understanding of the investments needed and next steps is critical to make the digitalisation process productive.
 Advanced analytics can be described as a process of turning huge volumes of structured or unstructured data, statistical and predictive analytics into decision-making with a value to business. In addition, time after time it is accepted as predictive analytics, big data analytics, data mining and similar. This is a forward-looking technique that can provide insights from huge unstructured or structured data volumes. The techniques used include data mining, machine learning, forecasting, visualisation, semantic analysis, sentiment analysis, network and cluster analysis, multivariate statistics, graph analysis, simulation, neural networks and others.
 MATERIALS AND METHODS
 The questionnaire developed by the author is based on an academic literature review, reports and publications shared by the analytics sector, industry experts and the author’s professional experience in the advanced analytics industry. The questionnaire design is developed based on 4 models with disclosed or semi-disclosed information to obtain data for modelling: 1) Analytics Maturity Quotient Framework (AMQ), Authors: Aryng, Data Science consulting, training and advising company; 2) DELTA Plus Model, Authors: International Institute for Analytics (IIA, Davenport); 3) Defining analytics maturity indicators (DAMI), Authors: Jasmien Lismont, Jan Vanthienen, Bart Baesens, Wilfried Lemahieu; 4) TDWI Analytics Maturity Model, Authors: TDWI (Transforming data with intelligence) training company.
 RESULTS
 The outcome is a questionnaire with 40 questions – single choice, multiple choice, text entry, matrix table, constant sum type questions allowing one to collect wide ranging and structured information. The main blocks are Demographics, Data management, Analytics, Process around data and analytics, People, Technologies, Culture, Leadership, Success drivers, Barriers. The questionnaire was launched on 20 December 2021 and now the field work is at the final stage. The author developed the new questionnaire, adjusted it for 2022, and localised it for Latvia.
 DISCUSSION
 Considering the increasing demand for advanced analytics including automated decision-making based on data, the significance of understanding the advanced analytics ecosystem maturity level in the organisations of Latvia is topical. The outcome is a core phase of the research paper “Challenges of Advanced Analytics Adoption in the Organisations of Latvia” with the research goal to develop the Advanced Analytics Ecosystem Assessment and Recommendation Tool based on ‘self-assessment’ to improve the results of the organisation in accordance with the strategic goals of the organisation. The questionnaire design of the quantitative survey is the most significant step in building an assessment model that allows one to collect core data material to obtain the initial model. The domains and factors which determine the maturity of advanced analytics will be identified based on quantitative survey data using proper analysis such as clustering, factor analysis, correlation analysis and other relevant analytical methods.
 CONCLUSIONS
 The challenge was to create a questionnaire in Latvian because of missing relevant terminology in Latvian, thus, leading to the identification of potential new terminology to be developed and implemented in Latvian.

Possibility results for graph clustering: A novel consistency axiom

Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg’s Consistency axiom, and the impossibility result. Namely, we describe a clustering algorithm, Morse Clustering, inspired by Morse Theory in Differential Topology, which satisfies Kleinberg’s original axioms with Consistency replaced by Monotonic Consistency. Morse clustering uncovers the underlying flow structure on a set or graph and returns a partition into trees representing basins of attraction of critical vertices. We also generalise Kleinberg’s axiomatic approach to sparse graphs, showing an impossibility result for Consistency, and a possibility result for Monotonic Consistency and Morse clustering.

Spectral clustering with anchor graph based on set-to-set distances for large-scale hyperspectral images

ABSTRACT Since labelled samples of hyperspectral images (HSIs) may be unavailable in practical remote sensing applications, large-scale HSI clustering is very important. Due to the huge amount of data brought by the rich spectral and spatial information in large-scale HSIs, HSI clustering is still a challenging task. Among the methods designed for large-scale HSIs clustering, the anchor graph-based methods simultaneously inherit the merits of graph-based clustering and reduce the computational complexity by introducing anchor samples to graph construction. However, the affinity matrix computed by inaccurate distances between anchor samples and other HSI samples can hardly obtain satisfactory clustering performance. To solve this problem, we propose a novel approach for large-scale HSI clustering, namely, spectral clustering with anchor graph based on set-to-set distances (SCAG-SSD) derived from local covariance matrix representation (LCMR). First, superpixels and LCMR features of HSI are obtained via the entropy rate superpixel algorithm and maximum noise fraction, respectively. Second, pure and anomalous samples of each superpixel are distinguished via the distances of LCMR features, and then anchor samples are selected via statistics of the distances between pure samples in each superpixel. In this way, selected anchor samples are representative enough to link all the HSI samples. Third, pure samples in each superpixel, anomalous and anchor samples with their corresponding nearest neighbouring samples are all regarded as different sets. The set-to-set distance is achieved by weighting the LCMR-based distances between samples of two sets. Finally, fast anchor graph clustering is conducted based on set-to-set distances to obtain final clustering maps. Extensive experiments conducted on three publicly available benchmark HSIs demonstrate that the proposed method achieves state-of-the-art clustering accuracy with comparable efficiency.

Deep linear graph attention model for attributed graph clustering

Attributed graph clustering is an important task for grouping the nodes in a graph. In recent years, the algorithms based on graph convolutional networks (GCN) have achieved promising performance. However, almost all existing methods ignore that the nonlinearity between two consecutive GCN layers is unnecessary for improving the performance of attributed graph clustering, and may even harm the efficiency of the model. In this paper, we propose a novel deep linear graph attention model for attributed graph clustering (DLGAMC), which consists of an attention-based aggregation module and a similarity preserve module. Specifically, we simply exploit cosine similarity to construct the attention for aggregation, which does not need to learn extra attention parameters. It is worth noting that the attention we designed not only explicitly considers the similarity of attribute information, but also implicitly takes into account the local graph structure. To select the proper order of aggregation, we propose an adaptive strategy to evaluate the smoothness of node representations, where intra-cluster distance and inter-cluster distance are the key indicators in this process. To learn node representations for clustering, we design a similarity preserve module to preserve local similarity and global dissimilarity of the smooth features obtained by multiple aggregations, which is different from the ideas in reconstruction-based methods. Finally, k-means is performed on the learned representations to obtain the cluster partition. Experiments on several datasets show that our algorithm achieves great performance in attributed graph clustering tasks.

Studying the Wikipedia Math Essential Pages using Graph Theory Metrics

Abstract COVID-19 pandemic enforced students in schools and universities all around the world to study using the online and blinded learning. In these learning models, students depend on the Internet for information searching of different scientific essentials to improve their skills and to overcome the gap of facing instructors. One of the most popular sources of information is Wikipedia. In this work, we attempt to study the relations of different math essential pages of Wikipedia to find the relation between these topics. A graph has been constructed for these pages. The graph theoretical metrics, such as, centrality, edge weights and clustering coefficient have been extracted of the constructed graph. The extracted values have been investigated to gain more insights of the math topics that should be studied first. The extracted results show that the in-degree property of the articles and the betweenness value of these articles are correlated. Moreover, there is no relation between the in /out-degree of the pages. Finally, the constructed graph has a small average shortest path and a high global cluster coefficient. This proves that the constructed graph follows the small world phenomenon. Keywords: Graph metrics, Math essentials, Gephi, Small world phenomenon, Directed graph

Graph clustering via generalized colorings

We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges between the clusters, as it is motivated by some earlier observations, e.g. in the structure of networks in ecology and economics and by applications of discrete tomography. Mathematically special colorings and chromatic numbers of graphs are studied.

Collaborative learning of graph generation, clustering and classification for brain networks diagnosis

Purpose: Accurate diagnosis of autism spectrum disorder (ASD) plays a key role in improving the condition and quality of life for patients. In this study, we mainly focus on ASD diagnosis with functional brain networks (FBNs). The major challenge for brain networks modeling is the high dimensional connectivity in brain networks and limited number of subjects, which hinders the classification capability of graph convolutional networks (GCNs). Method: To alleviate the influence of the limited data and high dimensional connectivity, we introduce a unified three-stage graph learning framework for brain network classification, involving multi-graph clustering, graph generation and graph classification. The framework combining Graph Generation, Clustering and Classification Networks (GraphCGC-Net) enhances the critical connections by multi-graph clustering (MGC) with a supervision scheme, and generates realistic brain networks by simultaneously preserving the global consistent distribution and local topology properties. Results: To demonstrate the effectiveness of our approach, we evaluate the performance of the proposed method on the Autism Brain Imaging Data Exchange (ABIDE) dataset and conduct extensive experiments on the ASD classification problem. Our proposed method achieves an average accuracy of 70.45% and an AUC of 72.76% on ABIDE. Compared with the traditional GCN model, the proposed GraphCGC-Net obtains 9.3%, and 10.64% improvement in terms of accuracy and AUC metrics, respectively. Conclusion: The comprehensive experiments demonstrate that our GraphCGC-Net is effective for graph classification in brain disorders diagnosis. Moreover, we find that MGC can generate biologically meaningful subnetworks, which is highly consistent with the previous neuroimaging-derived biomarker evidence of ASD. More importantly, the promising results suggest that applying generative adversarial networks (GANs) in brain networks to improve the classification performance is worth further investigation.

Multi-granularity Decomposition of Componentized Network Applications Based on Weighted Graph Clustering

With the development of mobile communication and network technology, smart network applications are experiencing explosive growth. These applications may consume different types of resources extensively, thus calling for the resource contribution from multiple nodes available in probably different network domains to meet the service quality requirements. Task decomposition is to set the functional components in an application in several groups to form subtasks, which can then be processed in different nodes. This paper focuses on the models and methods that decompose network applications composed of interdependent components into subtasks in different granularity. The proposed model characterizes factors that have important effects on the decomposition, such as dependency level, expected traffic, bandwidth, transmission delay between components, as well as node resources required by the components, and a density peak clustering (DPC) -based decomposition algorithm is proposed to achieve the multi-granularity decomposition. Simulation results validate the effect of the proposed approach on reducing the expected execution delay and balancing the computing resource demands of subtasks.

Import and Export Trade Prediction Algorithm of Belt and Road Countries Based on Hybrid RVM Model

Due to the large fluctuation of import and export volume and many influencing factors, it is difficult for the general prediction algorithm to obtain more accurate prediction results. To solve this problem, a trade forecasting method based on the Particle Swarm Optimization (PSO) optimization hybrid Relevance Vector Machine (RVM) model is proposed. The method firstly finds out the indexes that affect the import and export trade and extracts the principal factors of the indexes as the input data of the model through principal component analysis. Then, based on the single-kernel RVM model training with multiple different kernel functions, the multikernel weighting method was used to construct the hybrid kernel RVM model according to the prediction error of the single-kernel RVM model. Finally, the parameters of the hybrid kernel model were optimized by PSO to improve the prediction accuracy. Close trade will strengthen the dependence between countries, and under this premise, it becomes particularly important to study the frequency of trade between countries. In this paper, the countries along the Belt and Road are classified by the method of high-order directed graph clustering, and the trade transactions between the countries are represented by a small network subgraph. Then, the 65 trading countries are classified by cutting graph and K-means clustering method, and the classification results are obtained by running relevant codes in MATLAB. The results are represented by the lattice graph.

A FAST OVERLAPPING COMMUNITY DETECTION ALGORITHM BASED ON LABEL PROPAGATION AND SOCIAL NETWORK GRAPH CLUSTERING COEFFICIENT

Detecting community structure on social network has been an important and interesting issue on which many researchers have paid much attention and developed applications. Many graph clustering algorithms have been applied to find disjoint communities, i.e each node belongs to a single community. However, for social network in particular, public communication network in general, most of communities are not completely detached but they may be embedding, overlapping or crossing, that means certain nodes can belong to more than one community. Overlapping node plays a role of interface between communities and it is really interesting to study the community establishment of these nodes because it reflects dynamic behaviuor of participants.This article introduces the algorithm to find overlapping communities on huge social network. The proposed COPACN algorithm has been developed on the basis of label propagation, using advanced clustering coefficient to find overlapping communities on social network. Exprermental results on a set of popular, standard social networks and certain real network have shown the high speed and high effiency in finding overlapping structures.

Network Representation Learning Algorithm Based on Community Folding

<p>Network representation learning is a machine learning method that maps network topology and node information into low-dimensional vector space, which can reduce the temporal and spatial complexity of downstream network data mining such as node classification and graph clustering. This paper addresses the problem that neighborhood information-based network representation learning algorithm ignores the global topological information of the network. We propose the Network Representation Learning Algorithm Based on Community Folding (CF-NRL) considering the influence of community structure on the global topology of the network. Each community of the target network is regarded as a folding unit, the same network representation learning algorithm is used to learn the vector representation of the nodes on the folding network and the target network, then the vector representations are spliced correspondingly to obtain the final vector representation of the node. Experimental results show the excellent performance of the proposed algorithm.</p> <p> </p>

Visual Analysis of Evolutionary Patterns in Judicial Judgment Documents

Existing analysis of judicial data is mainly based on traditional statistical charts, and can not better relate to the internal information of judicial document nor satisfy the requirement of judicial data analysis. A visual analysis approach is proposed to analyze the judicial judgment document data by interactively presenting the evolution of judicial data. First, the approach consists of a hierarchical structure based evolution view to analyze the overall changes of judicial judgment document data. Second, the approach combines matrix view, word network view, topic clustering graph, and word cloud to carry out a refined analysis of internal multiple information. The triplet information of the case is further extracted and the key entities are visualized with constraint layout to help locate and grasp the contents of the case quickly. Based on a large-scale judicial judgment documents, case analysis is conducted on the evolution of case dispute types and the internal relations of the case, and quantitative user research and evaluation for multiple view tasks combined with the scoring method are carried out. The average score of all questions is larger than 3.5, which provides a potential solution for the subsequent visual analysis of judicial document data.

Network Clustering Algorithm Based on Fast Detection of Central Node

Based on scale-free and density-based complex networks and numerical clustering algorithm, a graph clustering algorithm based on fast detection of central nodes is proposed. Through the calculation of local density and comprehensive clustering of nodes in the network, the clustering center in the network can be found quickly and noncentral nodes can be divided into the clustering center according to the nearest neighbor principle, thus avoiding parameter limitations such as the number of clustering to be set in advance using conventional classic social network detection algorithm. The experimental comparison and analysis in the real network indicate that the graph clustering algorithm based on fast detection of the central node is highly effective and efficient.

Extract Descriptors for Point Cloud Registration by Graph Clustering Attention Network

Extracting geometric descriptors in 3D vision is the first step. It plays an important role in 3D registration, 3D reconstruction, and other applications. The success of many 3D tasks is closely related to whether the geometric descriptor has accurate characteristics. Today, the main methods are divided into manual production and neural network learning. The applicability of descriptors is limited to a low-level point, corner, edge, and fixed neighborhood features. For this, we use the class attention of the point cloud. In order to extract class attention, the graph clustering approach is utilized. It can collect points with similar structures and divide regions dynamically. While maintaining rotation invariance, features can enhance their fit to the original data. Point attention and edge attention are used to describe the structural characteristics of point clouds. We combine the three attentions indicated before to improve the features obtained by the PointNet decoder. This feature can dynamically reflect the structure of the point cloud, which includes both soft shape information and rich detail information. Finally, the 3D descriptors are extracted with the FoldingNet decoder. Our method is validated on both indoor and outdoor datasets. The accuracy of the final result is improved by two percentage points.

Latent structure blockmodels for Bayesian spectral graph clustering

Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated from a latent position model. Furthermore, the presence of communities within the network might generate community-specific submanifold structures in the embedding, but this is not explicitly accounted for in most statistical models for networks. In this article, a class of models called latent structure block models (LSBM) is proposed to address such scenarios, allowing for graph clustering when community-specific one-dimensional manifold structure is present. LSBMs focus on a specific class of latent space model, the random dot product graph (RDPG), and assign a latent submanifold to the latent positions of each community. A Bayesian model for the embeddings arising from LSBMs is discussed, and shown to have a good performance on simulated and real-world network data. The model is able to correctly recover the underlying communities living in a one-dimensional manifold, even when the parametric form of the underlying curves is unknown, achieving remarkable results on a variety of real data.