Graph-based Clustering Algorithm Research Articles

Subnetworks in BlockDAG

In this article, we study the horizontal scaling of the Waterfall network or similar blockDAG networks by applying hierarchical and graph-based clustering algorithms to partition them into subnetworks. This results in a reduction of network load and an increase in potential performance parameters of the underlying protocol. We consider methods of topology construction, propose clustering algorithms, and perform a simulation of the partitioning of a network into subnetworks.

Multi-view and Multi-order Graph Clustering via Constrained [formula omitted]-norm

The graph-based multi-view clustering algorithms achieve decent clustering performance by consensus graph learning of the first-order graphs from different views. However, the first-order graphs are often sparse, lacking essential must-link information, which leads to suboptimal consensus graph. While high-order graphs can address this issue, a two-step strategy involving the selection of a fixed number of high-order graphs followed by their fusion may result in information loss or redundancy, restricting the exploration of high-order information. To address these challenges, we propose Multi-view and Multi-order Graph Clustering via Constrained l1,2-norm (MoMvGC), which mitigates the impact of graph sparsity on multi-view clustering. By innovatively designing constrained l1,2-norm, the model ingeniously integrates the selection of multi-order graphs and corresponding weight learning into a unified framework. Furthermore, MoMvGC not only enable sparse selection of multi-order graphs but also simultaneous selection of views. Afterwards, we design an efficient alternative optimization algorithm to solve the optimization problems in MoMvGC. The proposed model achieves state-of-the-art clustering performance on nine real-world datasets, with particularly notable improvements observed on the MSRC dataset, where the clustering accuracy is increased by 5.24% compared to the best baseline. Comprehensive experiments demonstrate the effectiveness and superiority of our model. The code is available at https://github.com/haonanxin/MoMvGC_code.

Local Sample-Weighted Multiple Kernel Clustering With Consensus Discriminative Graph.

Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proven to be of vital significance in applications since the unreliable distant-distance similarity estimation would degrade clustering performance. Although existing localized MKC algorithms exhibit improved performance compared with globally designed competitors, most of them widely adopt the KNN mechanism to localize kernel matrix by accounting for τ -nearest neighbors. However, such a coarse manner follows an unreasonable strategy that the ranking importance of different neighbors is equal, which is impractical in applications. To alleviate such problems, this article proposes a novel local sample-weighted MKC (LSWMKC) model. We first construct a consensus discriminative affinity graph in kernel space, revealing the latent local structures. Furthermore, an optimal neighborhood kernel for the learned affinity graph is output with naturally sparse property and clear block diagonal structure. Moreover, LSWMKC implicitly optimizes adaptive weights on different neighbors with corresponding samples. Experimental results demonstrate that our LSWMKC possesses better local manifold representation and outperforms existing kernel or graph-based clustering algorithms. The source code of LSWMKC can be publicly accessed from https://github.com/liliangnudt/LSWMKC.

Single-cell RNA sequencing reveals heterogeneity and differential expression of the maternal–fetal interface during ICP and normal pregnancy

Objective Intrahepatic cholestasis of pregnancy (ICP) can cause adverse perinatal outcomes. Previous studies have demonstrated that the placenta of an ICP pregnancy differs in morphology and gene expression from the placenta of a normal pregnancy. To date, however, the genetic mechanism by which ICP affects the placenta is poorly understood. Therefore, the aim of this study was to investigate the differences in main cell types, gene signatures, cell ratio, and functional changes in the placenta between ICP and normal pregnancy. Methods Single-cell RNA sequencing (scRNA-seq) technology was used to detect the gene expression of all cells at the placental maternal–fetal interface. Two individuals were analyzed – one with ICP and one without ICP. The classification of cell types was determined by a graph-based clustering algorithm. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analyses were performed using the R software phyper () function and DAVID website. The differentially expressed genes (DEGs) encoding transcription factors (TFs) were identified using getorf and DIAMOND software. Results We identified 14 cell types and 22 distinct cell subtypes that showed unique functional properties. Additionally, we found differences in the proportions of fibroblasts 1, helper T (Th) cells, extravillous trophoblasts, and villous cytotrophoblasts, and we observed heterogeneity of gene expression between ICP and control placentas. Furthermore, we identified 263 DEGs that belonged to TF families, including zf-C2H2, HMGI/HMGY, and Homeobox. In addition, 28 imprinted genes were preferentially expressed in specific cell types, such as PEG3 and PEG10 in trophoblasts as well as DLK1 and DIO3 in fibroblasts. Conclusions Our results revealed the differences in cell-type ratios, gene expression, and functional changes between ICP and normal placentas, and heterogeneity was found among cell subgroups. Hence, the imbalance of various cell types affects placental activity to varying degrees, indicating the complexity of the cell networks that form the placental tissue system, and this alteration of placental function is associated with adverse events in the perinatal period.

Efficient Multi-View Clustering via Unified and Discrete Bipartite Graph Learning.

Although previous graph-based multi-view clustering (MVC) algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view-consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the k -means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this article presents an efficient MVC approach via unified and discrete bipartite graph learning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view-consensus bipartite graph with adaptive weight learning. Furthermore, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view-consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.

SUMA: a lightweight machine learning model-powered shared nearest neighbour-based clustering application interface for scRNA-Seq data.

Single-cell transcriptomics (scRNA-Seq) explores cellular diversity at the gene expression level. Due to the inherent sparsity and noise in scRNA-Seq data and the uncertainty on the types of sequenced cells, effective clustering and cell type annotation are essential. The graph-based clustering of scRNA-Seq data is a simple yet powerful approach that presents data as a "shared nearest neighbour" graph and clusters the cells using graph clustering algorithms. These algorithms are dependent on several user-defined parameters.Here we present SUMA, a lightweight tool that uses a random forest model to predict the optimum number of neighbours to obtain the optimum clustering results. Moreover, we integrated our method with other commonly used methods in an RShiny application. SUMA can be used in a local environment (https://github.com/hkarakurt8742/SUMA) or as a browser tool (https://hkarakurt.shinyapps.io/suma/). Publicly available scRNA-Seq datasets and 3 different graph-based clustering algorithms were used to develop SUMA, and a large range for number of neighbours and variant genes was taken into consideration. The quality of clustering was assessed using the adjusted Rand index (ARI) and true labels of each dataset. The data were split into training and test datasets, and the model was built and optimised using Scikit-learn (Python) and randomForest (R) libraries. The accuracy of our machine learning model was 0.96, while the AUC of the ROC curve was 0.98. The model indicated that the number of cells in scRNA-Seq data is the most important feature when deciding the number of neighbours. We developed and evaluated the SUMA model and implemented the method in the SUMAShiny app, which integrates SUMA with different clustering methods and enables nonbioinformatician users to cluster and visualise their scRNA data easily. The SUMAShiny app is available both for desktop and browser use.

Changepoint detection-assisted nonparametric clustering for unsupervised temporal sign segmentation

Temporal sign segmentation aims to temporarily divide continuous sign language into category-agnostic sign segments. One of the challenges to temporal sign segmentation is the paucity of frame-level annotations for sign language videos, which restricts the applicability of supervised and semi-supervised approaches. To address this challenge, we consider temporal sign segmentation as a clustering problem defined as the grouping of semantically similar frames of a given video, which allows us to choose unsupervised clustering techniques as promising alternatives. However, most unsupervised clustering techniques are parametric. In the context of temporal sign segmentation, they assume that the number of sign segments of a given continuous sign video is predefined, which is implausible. The primary contributions of this study are as follows: (1) We propose the first nonparametric clustering algorithm for unsupervised temporal sign segmentation. The main concept is to enhance the hierarchical graph-based clustering algorithm to be nonparametric by adopting cost and penalty functions of a changepoint detection algorithm to determine the optimal number of sign segments. Experimental results show that the performance of the proposed unsupervised method is comparable to that of the latest semi-supervised sign segmentation method in terms of several metrics. Moreover, the execution time of the proposed clustering method was less than 1 s, thereby ensuring its applicability. (2) We identify that the conventional metrics for temporal sign segmentation do not sufficiently address over-segmentation. To overcome the difficulty, we propose a new main metric to evaluate the performance of temporal sign segmentation, called the adjusted MF1B.

Dual-GCN-based deep clustering with triplet contrast for ScRNA-seq data analysis

Single-cell RNA sequencing (ScRNA-seq) technology reveals gene expression information at the cellular level. The critical tasks in ScRNA-seq data analysis are clustering and dimensionality reduction. Recent deep clustering algorithms are used to optimize the two tasks jointly, and their variations, graph-based deep clustering algorithms, are used to capture and preserve topological information in the process. However, the existing graph-based deep clustering algorithms ignore the distribution information of nodes when constructing cell graphs which leads to incomplete information in the embedding representation; and graph convolutional networks (GCN), which are most commonly used, often suffer from over-smoothing that leads to high sample similarity in the embedding representation and then poor clustering performance. Here, the dual-GCN-based deep clustering with Triplet contrast (scDGDC) is proposed for dimensionality reduction and clustering of scRNA-seq data. Two critical components are dual-GCN-based encoder for capturing more comprehensive topological information and triplet contrast for reducing GCN over-smoothing. The two components improve the dimensionality reduction and clustering performance of scDGDC in terms of information acquisition and model optimization, respectively. The experiments on eight real ScRNA-seq datasets showed that scDGDC achieves excellent performance for both clustering and dimensionality reduction tasks and is high robustness to parameters.

Event-based sampled ECG morphology reconstruction through self-similarity

Background and Objective: Event-based analog-to-digital converters allow for sparse bio-signal acquisition, enabling local sub-Nyquist sampling frequency. However, aggressive event selection can cause the loss of important bio-markers, not recoverable with standard interpolation techniques. In this work, we leverage the self-similarity of the electrocardiogram (ECG) signal to recover missing features in event-based sampled ECG signals, dynamically selecting patient-representative templates together with a novel dynamic time warping algorithm to infer the morphology of event-based sampled heartbeats.Methods: We acquire a set of uniformly sampled heartbeats and use a graph-based clustering algorithm to define representative templates for the patient. Then, for each event-based sampled heartbeat, we select the morphologically nearest template, and we then reconstruct the heartbeat with piece-wise linear deformations of the selected template, according to a novel dynamic time warping algorithm that matches events to template segments.Results: Synthetic tests on a standard normal sinus rhythm dataset, composed of approximately 1.8 million normal heartbeats, show a big leap in performance with respect to standard resampling techniques. In particular (when compared to classic linear resampling), we show an improvement in P-wave detection of up to 10 times, an improvement in T-wave detection of up to three times, and a 30% improvement in the dynamic time warping morphological distance.Conclusion: In this work, we have developed an event-based processing pipeline that leverages signal self-similarity to reconstruct event-based sampled ECG signals. Synthetic tests show clear advantages over classical resampling techniques.

An efficient semi-supervised balanced cut with hard pairwise constraints and partial labels

With a small scale of prior information, including pairwise constraints and partial labels, semi-supervised clustering algorithms can improve clustering performance by imposing certain restrictions on the clustering results, and have accordingly attracted a lot of attention in recent years. Moreover, a large number of graph-based semi-supervised clustering algorithms have been proposed, since graphs are naturally suited to pairwise constraints. However, most graph-based approaches involve a two-step process and are not scalable to large-scale datasets due to their high time complexity. Additionally, they also encounter a serious problem of constraint violation. To deal with this issue, we propose a new non-parametric model to directly obtain the indicator matrix by minimizing the cut of the graph with a regularization term that corresponds to the balance of the clusters. To simultaneously support the two forms of prior information, our approach restricts the indicator matrix during optimization, while also ensuring that the clusters obtained by our approach do not violate any constraints. The computational complexity of the proposed approach is nearly linear to the data size n. Experiments show that the algorithm proposed in this paper achieves significant improvements in both clustering performance and efficiency.

CosTaL: an accurate and scalable graph-based clustering algorithm for high-dimensional single-cell data analysis.

With the aim of analyzing large-sized multidimensional single-cell datasets, we are describing a method for Cosine-based Tanimoto similarity-refined graph for community detection using Leiden's algorithm (CosTaL). As a graph-based clustering method, CosTaL transforms the cells with high-dimensional features into a weighted k-nearest-neighbor (kNN) graph. The cells are represented by the vertices of the graph, while an edge between two vertices in the graph represents the close relatedness between the two cells. Specifically, CosTaL builds an exact kNN graph using cosine similarity and uses the Tanimoto coefficient as the refining strategy to re-weight the edges in order to improve the effectiveness of clustering. We demonstrate that CosTaL generally achieves equivalent or higher effectiveness scores on seven benchmark cytometry datasets and six single-cell RNA-sequencing datasets using six different evaluation metrics, compared with other state-of-the-art graph-based clustering methods, including PhenoGraph, Scanpy and PARC. As indicated by the combined evaluation metrics, Costal has high efficiency with small datasets and acceptable scalability for large datasets, which is beneficial for large-scale analysis.

Robust and optimal neighborhood graph learning for multi-view clustering

In recent years, researchers have proposed many graph-based multi-view clustering (GMC) algorithms to solve the multi-view clustering (MVC) problem. However, there are still some limitations in the existing GMC algorithm. In these algorithms, a graph is usually constructed to represent the relationship between the samples in a view; however, it cannot represent the relationship very well since it is often preconstructed. In addition, these algorithms ignore the robustness problem of each graph and high-level information between different graphs. Then, in the paper, we propose a novel MVC method, i.e., robust and optimal neighborhood graph learning for MVC (RONGL/MVC). Specifically, we first build an initial graph for each view. However, these initial graphs cannot represent the relationship between the samples in each view well, so we look for the optimal graph with k connected components in the neighborhood of each initial graph, where k is the number of clusters. Then, to improve the robustness of RONGL/MVC, we reconstruct the optimal graph with the self-representation matrix. Furthermore, we stack all the self-representation matrices into a tensor and impose the tensor low-rank constraint, which can maximize consistent features and explore the high-order relationship between optimal graphs. In addition, we provide an optimization strategy by utilizing the Augmented Lagrange Multiplier (ALM) method. Experimental results on several datasets indicate that RONGL/MVC outperforms state-of-the-art methods.

An Effective Fuzzy Clustering of Crime Reports Embedded by a Universal Sentence Encoder Model

Crime reports clustering is crucial for identifying and preventing criminal activities that frequently happened in society. In the proposed work, named entities in a report are recognized to extract the crime-related phrases and subsequently, the phrases are preprocessed by applying stopword removal and lemmatization operations. Next, the module of the universal encoder model, called the transformer, is applied to extract phrases of the report to get a sentence embedding for each associated sentence, aggregation of which finally provides the vector representation of that report. An innovative and efficient graph-based clustering algorithm consisting of splitting and merging operations has been proposed to get the cluster of crime reports. The proposed clustering algorithm generates overlapping clusters, which indicates the existence of reports of multiple crime types. The fuzzy theory has been used to provide a score to the report for expressing its membership into different clusters, and accordingly, the reports are labelled by multiple categories. The efficiency of the proposed method has been assessed by taking into account different datasets and comparing them with other state-of-the-art approaches with the help of various performance measure metrics.

Incomplete multi-view clustering via kernelized graph learning

A fundamental assumption underpinning the recent progress in multi-view clustering is the full observation of all views, which rarely holds for real-world data as they often suffer from the absence of some instances in individual views. Such incompleteness generally disables the traditional multi-view clustering models in practical applications. This paper proposes a Kernelized Graph-based Incomplete Multi-view Clustering (KGIMC) algorithm to overcome this limitation. The key novelty of our model is that its subtasks, e.g. similarity learning, clustering analysis, and kernel completion, are optimized in a mutual reinforcement manner to achieve an overall optimal clustering result as follows: 1) Similarity learning is directed by clustering analysis to construct a graph with as many connected components just as the number of clusters. 2) The well-constructed similarity graph in the last iteration is employed to guide the process of kernel completion. 3) The updated kernels are in turn used to conduct subsequent similarity learning. We extend our model into multi-kernel settings to alleviate the difficulty of kernel selection. We provide an alternating iterative algorithm to solve KGIMC with convergence guaranteed and complexity analyzed. Extensive experiments are conducted on several popular datasets, and the results demonstrate that KGIMC outperforms the state-of-the-art approaches in general.

An automatic affinity propagation clustering based on improved equilibrium optimizer and t-SNE for high-dimensional data

Automatic clustering and dimension reduction are two of the most intriguing topics in the field of clustering. Affinity propagation (AP) is a representative graph-based clustering algorithm in unsupervised learning. However, extracting features from high-dimensional data and providing satisfactory clustering results is a serious challenge for the AP algorithm. Besides, the clustering performance of the AP algorithm is sensitive to preference. In this paper, an improved affinity propagation based on optimization of preference (APBOP) is proposed for automatic clustering on high-dimensional data. This method is optimized to solve the difficult problem of determining the preference of affinity propagation and the poor clustering effect for non-convex data distribution. First, t-distributed stochastic neighbor embedding is introduced to reduce the dimensionality of the original data to solve the redundancy problem caused by excessively high dimensionality. Second, an improved hybrid equilibrium optimizer based on the crisscross strategy (HEOC) is proposed to optimize preference selection. HEOC introduces the crisscross strategy to enhance local search and convergence efficiency. The benchmark function experiments indicate that the HEOC algorithm has better accuracy and convergence rate than other swarm intelligence algorithms. Simulation experiments on high-dimensional and real-world datasets show that APBOP has better effectiveness.

A split–merge clustering algorithm based on the k-nearest neighbor graph

Numerous graph-based clustering algorithms relying on k-nearest neighbor (KNN) have been proposed. However, the performance of these algorithms tends to be affected by many factors such as cluster shape, cluster density and outliers. To address these issues, we present a split–merge clustering algorithm based on the KNN graph (SMKNN), which is based on the idea that two adjacent clusters can be merged if the data points located in the connection layers of the two clusters tend to be consistent in distribution. In Stage 1, a KNN graph is constructed. In Stage 2, the subgraphs are obtained by removing the pivot points from the KNN graph, in which the pivot points are determined by the size of local distance ratio of data points. In Stage 3, the adjacent cluster pairs satisfying the maximum similarity are merged, in which the similarity measure of two clusters is designed with two concepts including external connection edges and internal connection edges. By the experiments on ten synthetic data sets and eight real data sets, we compared SMKNN with two traditional algorithms, two density-based algorithms, nine graph-based algorithms and four neural network based algorithms in accuracy. The experimental results demonstrate a good performance of the proposed clustering method.

A Graph-Based Clustering Algorithm for the Internet of Vehicles

In the large-scale and ultra-dense Internet of Vehicles (IoVs), constructing the simplest backbone network is an urgent problem to be solved. In fact, constructing the simplest backbone network is an NP-hard problem, and at present, there is no effective solution. In this paper, we propose a graph-based clustering algorithm to solve this problem and construct the simplest backbone network in the large-scale and ultra-dense IoV. We establish a backbone network model for the large-scale and ultra-dense IoV and optimize the backbone network by employing a novel local search iterative algorithm. Simulation results show that with the increase in node density, the number of clusters selected by the proposed algorithm tends to be stable, while the number of optimized clusters decreases by 28.87% on an average. Thus, the proposed algorithm can effectively simplify the backbone network.

Privacy protection model considering privacy-utility trade-off for data publishing of weighted social networks based on MST-clustering and sub-graph generalization

Along with the rapid development of the Internet technology, social network sites (SNSs) are increasingly emerging. As various types of datasets are easily exposed to the network, privacy security in SNS becomes the focus of the study. Anonymization techniques, such as generalization and bucketization, and data perturbation techniques are usually employed in data publishing for privacy protection. However, in the meanwhile, the privacy protection methods reduce the utility of the data. Thus, the issue of privacy-utility trade-off becomes one very real problem. By considering the privacy-utility trade-off and combining the minimum spanning tree (MST) clustering technique and the sub-graph generalization technique, a privacy protection model is proposed for data publishing in weighted social networks. The MST-based clustering method is one representative and concise graph-based clustering algorithm. Meanwhile, as one MST of an edge-weighted graph is the minimum weight spanning tree, some important properties of the graph like the shortest path are preserved in the MST. Finally, on the basis of sub-graphs (clusters) divided by the MST-clustering, three sub-graph generalization approaches are designed in one reasonable way for data publishing to guarantee the privacy-utility trade-off of the proposed method. Experiments and result analysis indicate workability of the proposed method that the proposed model offers privacy protection for the data publishing by means of the sub-graph generalization approach while it can also improve the data utility especially for occasions like data mining, machine learning, and pattern recognition.

Robust landmark graph-based clustering for high-dimensional data

High-dimensional data has attracted much attention because it contains more comprehensive information about samples. How to cluster these high-dimensional data has become a crucial topic in unsupervised learning. Existing clustering methods often show limited applicability due to their high computational complexity and low anti-noise ability. To address this issue, we propose a novel robust landmark graph-based clustering algorithm for high-dimensional data (RLGCH), which inherits the advantages of both k-means++ and graph-based clustering by using the results of k-means++ as pseudo labels for landmark graph-based clustering. In particular, RLGCH can achieve more reasonable clustering effectiveness than methods that just operate in the low-dimensional space or the original space since it performs k-means++ in the low-dimensional space and landmark graph-based spectral clustering in the original feature space. To avoid post-processing after optimization, the embedded factor matrix is constrained as an indicator matrix rather than a simple nonnegative matrix. To enhance the clustering robustness, the L2,1-norm is adopted to minimize the error of results between k-means++ and landmark graph-based clustering. To solve the model of RLGCH, we established a novel efficient optimization strategy to obtain all sample categories directly. Combining our clustering model and optimization strategy, the computational complexity is reduced to linear and insensitive to data dimensions. Extensive experiments on seven real-world datasets and sixteen noisy datasets show that compared with other state-of-the-art methods, RLGCH can improve the clustering efficiency and robustness greatly while guaranteeing comparable or even better clustering effectiveness.

Clustering Diagnoses From 58 Million Patient Visits in Finland Between 2015 and 2018.

BackgroundMultiple chronic diseases in patients are a major burden on the health service system. Currently, diseases are mostly treated separately without paying sufficient attention to their relationships, which results in the fragmentation of the care process. The better integration of services can lead to the more effective organization of the overall health care system.ObjectiveThis study aimed to analyze the connections between diseases based on their co-occurrences to support decision-makers in better organizing health care services.MethodsWe performed a cluster analysis of diagnoses by using data from the Finnish Health Care Registers for primary and specialized health care visits and inpatient care. The target population of this study comprised those 3.8 million individuals (3,835,531/5,487,308, 69.90% of the whole population) aged ≥18 years who used health care services from the years 2015 to 2018. They had a total of 58 million visits. Clustering was performed based on the co-occurrence of diagnoses. The more the same pair of diagnoses appeared in the records of the same patients, the more the diagnoses correlated with each other. On the basis of the co-occurrences, we calculated the relative risk of each pair of diagnoses and clustered the data by using a graph-based clustering algorithm called the M-algorithm—a variant of k-means.ResultsThe results revealed multimorbidity clusters, of which some were expected (eg, one representing hypertensive and cardiovascular diseases). Other clusters were more unexpected, such as the cluster containing lower respiratory tract diseases and systemic connective tissue disorders. The annual cost of all clusters was €10.0 billion, and the costliest cluster was cardiovascular and metabolic problems, costing €2.3 billion.ConclusionsThe method and the achieved results provide new insights into identifying key multimorbidity groups, especially those resulting in burden and costs in health care services.