Clustering Performance Research Articles

Error-robust multi-view subspace clustering with nonconvex low-rank tensor approximation and hyper-Laplacian graph embedding

Tensor based subspace clustering, a method aimed at partitioning multi-view data into distinct clusters through the tensor low-rank representation, has gained widespread popularity. Despite the effectiveness of tensor singular value decomposition (t-SVD) based nuclear norm in extracting high-dimensional information from multiple views, certain limitations persist. Firstly, while the commonly used l2,1 norm enhances clustering robustness, it remains susceptible to the impact of high-intensity noises. Secondly, the t-SVD based nuclear norm provides a biased estimation of tensor rank. Thirdly, existing methods either fail to preserve manifold structures from the original space or only extract binary relationships between data points. To address these challenges and enhance clustering performance in both high-intensity noisy and real-world conditions, an error-robust multi-view subspace clustering with nonconvex low-rank tensor approximation and hyper-Laplacian graph embedding (EMSC-NLTHG) method is proposed. Specifically, Cauchy loss function which reduces sensitivity to larger noises and outliers is introduced. Based on the Cauchy loss function, we develop the Cauchy pseudo norm to represent the reconstruction error in clustering to enhance the robustness. Moreover, rather than uniformly weighting all singular values in the t-SVD nuclear norm, a nonconvex tensor nuclear norm is adopted to add weights adaptively and approximate the true tensor rank. Additionally, hypergraph is embedded in the representation matrices to preserve local manifold structures and extract the complex multivariate relationships between data points. Extensive experiments demonstrate that the proposed EMSC-NLTHG method consistently outperforms state-of-the-art techniques by approximately 18% to 40% on datasets corrupted by high-intensity noises and around 1% to 27% on eight real-world datasets across six popular evaluation metrics.

Enhancing generalized spectral clustering with embedding Laplacian graph regularization

AbstractAn enhanced generalised spectral clustering framework that addresses the limitations of existing methods by incorporating the Laplacian graph and group effect into a regularisation term is presented. By doing so, the framework significantly enhances discrimination power and proves highly effective in handling noisy data. Its versatility enables its application to various clustering problems, making it a valuable contribution to unsupervised learning tasks. To optimise the proposed model, the authors have developed an efficient algorithm that utilises the standard Sylvester equation to compute the coefficient matrix. By setting the derivatives to zero, computational efficiency is maintained without compromising accuracy. Additionally, the authors have introduced smoothing strategies to make the non‐convex and non‐smooth terms differentiable. This enables the use of an alternative iteration re‐weighted procedure (AIwRP), which distinguishes itself from other first‐order optimisation algorithms by introducing auxiliary variables. The authors provide a provable convergence analysis of AIwRP based on the iteration procedures of unconstrained problems to support its effectiveness. Extensive numerical tests have been conducted on synthetic and benchmark databases to validate the superiority of their approaches. The results demonstrate improved clustering performance and computational efficiency compared to several existing spectral clustering methods, further reinforcing the advantages of their proposed framework. The source code is available at https://github.com/ZhangHengMin/LGR_LSRLRR.

The Role of Inclusive Leadership Style in Fostering Employee Performance: A Mediating Role of Workplace Dignity

Purpose- The current research aims to inspect the impact of inclusive leadership on increasing employee performance in the Hail health cluster to inspect the part of workplace dignity as a arbitrator between employees' inclusive leadership style and performance. Design/Methodology/Approach- This study took a model of 364 workers in the Hail health cluster in Saudi Arabia. A well-structured questionnaire is developed on the base of previous literature for the collection of data. SmartPLS is used for extracting the results. Findings- This study establishes that the inclusive leadership style knowingly influences employee performance in the Hail health cluster. Inclusive leadership enhances workplace dignity; the highly dignified worker feels secure and performs work more efficiently to provide quality work. Research limitation/implication- This study is limited to the health cluster of Hail which is service sector and used workplace dignity as mediator, while future study can test same model for production sector and can use workplace dignity as moderator. The finding of current study has theoretical, practical and empirical implementation not only for the service sector but for manufacturing sector. Originality/Value- The current research is unique, and the combination of these variables has never been studied. This study explains that any sector's leadership increases workers' performance by providing dignity in the workplace. Further, this workplace dignity helps to increase the performance of employees.

Digital Visual Design Reengineering and Application Based on K-means Clustering Algorithm

INTRODUCTION: The article discusses the key steps in digital visual design reengineering, with a special emphasis on the importance of information decoding and feature extraction for flat cultural heritage. These processes not only minimize damage to the aesthetic heritage itself but also feature high quality, efficiency, and recyclability.OBJECTIVES: The aim of the article is to explore the issues of gene extraction methods in digital visual design reengineering, proposing a visual gene extraction method through an improved K-means clustering algorithm.METHODS: A visual gene extraction method based on an improved K-means clustering algorithm is proposed. Initially analyzing the digital visual design reengineering process, combined with a color extraction method using the improved JSO algorithm-based K-means clustering algorithm, a gene extraction and clustering method for digital visual design reengineering is proposed and validated through experiments.RESULT: The results show that the proposed method improves the accuracy, robustness, and real-time performance of clustering. Through comparative analysis with Dunhuang murals, the effectiveness of the color extraction method based on the K-means-JSO algorithm in the application of digital visual design reengineering is verified. The method based on the K-means-GWO algorithm performs best in terms of average clustering time and standard deviation. The optimization curve of color extraction based on the K-means-JSO algorithm converges faster and with better accuracy compared to the K-means-ABC, K-means-GWO, K-means-DE, K-means-CMAES, and K-means-WWCD algorithms.CONCLUSION: The color extraction method of the K-means clustering algorithm improved by the JSO algorithm proposed in this paper solves the problems of insufficient standardization in feature selection, lack of generalization ability, and inefficiency in visual gene extraction methods.

Dual auto-weighted multi-view clustering via autoencoder-like nonnegative matrix factorization

Multi-view clustering (MVC) can exploit the complementary information among multi-view data to achieve the satisfactory performance, thus having extensive potentials for practical applications. Although Nonnegative Matrix Factorization (NMF) has emerged as an effective technique for MVC, the existing NMF-based methods still have two main limitations: 1) They solely focus on the reconstruction of original data, which can be regarded as the decoder of an autoencoder, while neglecting the low-dimensional representation learning. 2) They lack the ability to effectively capture both linear and nonlinear structures of data. To solve these problems, in this paper, we propose a Dual Auto-weighted multi-view clustering model based on Autoencoder-like NMF (DA2NMF), which enables a comprehensive exploration of both linear and nonlinear structures. Specifically, we establish an autoencoder-like NMF model that learns linear low-dimensional representations by integrating data reconstruction and representation learning within a unified framework. Moreover, the adaptive graph learning is introduced to explore the nonlinear structures in data. We further design a dual auto-weighted strategy to adaptively compute weights for different views and low-dimensional representations, thereby obtaining an enhanced consistent graph. An effective algorithm based on Multiplicative Update Rule (MUR) is developed to solve the DA2NMF with the theoretical convergence guarantee. Experimental results show that the proposed DA2NMF can effectively improve the clustering performance compared with the state-of-the-art MVC algorithms.

An auto-weighted enhanced horizontal collaborative fuzzy clustering algorithm with knowledge adaption mechanism

Among the multi-source data clustering tasks, there is a kind of frequently encountered tasks where only one of the multi-source datasets is available for sake of privacy and other reasons. The only available dataset is called local dataset, and the other are called external datasets. The horizontal collaborative fuzzy clustering (HCFC) model is a typical one that can deal with such clustering tasks. In HCFC, each external dataset is used through the knowledge mined from it rather than itself. The knowledge expressed as a knowledge partition matrix is fused into the clustering process of the local dataset. Reviewing the existing HCFC models, we can find three issues that need improvement. Firstly, the existing HCFC models quantify the collaboration contribution of each external knowledge by a hyperparameter at dataset-level, and moreover, do not distinguish the collaboration contributions of objects in the same external dataset. This may lead to counterintuitive clustering results. Focused on this issue, this paper proposes an enhanced HCFC (EHCFC) algorithm that extends the collaboration from dataset-level to object-level, and assigns different weights to objects based on the information amount provided by objects. Through EHCFC, a more flexible collaboration and a more intuitive clustering result can be reached. Secondly, the collaboration mechanisms of the existing HCFC models require that the dimensionalities of the partition matrices of external datasets and local dataset are the same, which makes the HCFC algorithms unable to work in many real situations. Focused on this limitation, a knowledge adaption mechanism based on relative entropy and spectral clustering is proposed resulting in a further refined EHCFC-KA algorithm, i.e., EHCFC with knowledge adaption. The proposed knowledge adaption mechanism makes both the HCFC algorithms and the EHCFC algorithm effective and successful in more application scenarios. Finally, we define two indexes in terms of consistency (the consistency of the clustering result with external knowledge) to evaluate the performance of collaborative clustering. Experiments on synthetic datasets and UCI public datasets demonstrate that the proposed EHCFC and EHCFC-KA algorithms outperform the existing HCFC algorithms and achieve significantly better intuitive collaborative clustering performance.

Deep Nonnegative Matrix Factorization with Joint Global and Local Structure Preservation

Deep Non-Negative Matrix Factorization (DNMF) methods provide an efficient low-dimensional representation of given data through their layered architecture. A limitation of such methods is that they cannot effectively preserve the local and global geometric structures of the data in each layer. Consequently, a significant amount of the geometrical information within the data, present in each layer of the employed deep framework, can be overlooked by the model. This can lead to an information loss and a subsequent drop in performance. In this paper, we propose a novel deep non-negative matrix factorization method, Deep Non-Negative Matrix Factorization with Joint Global and Local Structure Preservation (dubbed Dn2MFGL), that ensures the preservation of both global and local structures within the data space. Dn2MFGL performs representation learning through a sequential embedding procedure which involves both the global data structure by accounting for the data variance, and the local data relationships by utilizing information from neighboring data points. Moreover, a regularization term that promotes sparsity by utilizing the concept of the inner product is applied to the matrices representing the lower dimensions. This aims to retain the fundamental data structure while discarding less crucial features. Simultaneously, the residual matrix of Dn2MFGL is subjected to the L2,1 norm, which ensures the robustness of the model against noisy data samples. An effective and multiplicative updating process also facilitates Dn2MFGL in solving the employed objective function. The clustering performance of the proposed deep NMF method is explored across various benchmarks of face datasets. The results point to Dn2MFGL outperforming several existing classical and state-of-the-art NMF methods. The source code is available at https://github.com/FaridSaberi/Dn2MFGO.git.

Deep contrastive representation learning for multi-modal clustering

Benefiting from the informative expression capability of contrastive representation learning (CRL), recent multi-modal learning studies have achieved promising clustering performance. However, it should be pointed out that the existing multi-modal clustering methods based on CRL fail to simultaneously take the similarity information embedded in inter- and intra-modal levels. In this study, we mainly explore deep multi-modal contrastive representation learning, and present a multi-modal learning network, named trustworthy multi-modal contrastive clustering (TMCC), which incorporates contrastive learning and adaptively reliable sample selection with multi-modal clustering. Specifically, we are concerned with an adaptive filter to learn TMCC via progressing from ‘easy’ to ‘complex’ samples. Based on this, with the highly confident clustering labels, we present a new contrastive loss to learn modal-consensus representation, which takes into account not only the inter-modal similarity but also the intra-modal similarity. Experimental results show that these principles in TMCC consistently help promote clustering performance improvement.

Modified suppressed relative entropy fuzzy c-means clustering algorithm

The Fuzzy C-means (FCM) algorithm is one of the most widely used algorithms in unsupervised pattern recognition. As the intensity of observation noise increases, FCM tends to produce large center deviations and even overlap clustering problems. The relative entropy fuzzy C-means algorithm (REFCM) adds relative entropy as a regularization function to the fuzzy C-means algorithm, which has a good ability for noise detection and membership assignment to observed values. However, REFCM still tends to generate overlapping clusters as the size of the cluster increases and becomes imbalanced. Moreover, the convergence speed of this algorithm is slow. To solve this problem, modified suppressed relative entropy fuzzy c-means clustering (MSREFCM) is proposed. Specifically, the MSREFCM algorithm improves the convergence speed of the algorithm while maintaining the accuracy and anti-noise capability of the REFCM algorithm by adding a suppression strategy based on the intra-class average distance measurement. In addition, to further improve the clustering performance of MSREFCM for multidimensional imbalanced data, the center overlapping problem and the center offset problem of elliptical data are solved by replacing the Euclidean distance in REFCM with the Mahalanobis distance. Experiments on several synthetic and UCI datasets indicate that MSREFCM can improve the convergence speed and classification performance of the REFCM for spherical and ellipsoidal datasets with imbalanced sizes. In particular, for the Statlog dataset, the running time of MSREFCM is nearly one second less than that of REFCM, and the accuracy of MSREFCM is 0.034 higher than that of REFCM.

Incomplete Multiple Kernel Alignment Maximization for Clustering.

Multiple kernel alignment (MKA) maximization criterion has been widely applied into multiple kernel clustering (MKC) and many variants have been recently developed. Though demonstrating superior clustering performance in various applications, it is observed that none of them can effectively handle incomplete MKC, where parts or all of the pre-specified base kernel matrices are incomplete. To address this issue, we propose to integrate the imputation of incomplete kernel matrices and MKA maximization for clustering into a unified learning framework. The clustering of MKA maximization guides the imputation of incomplete kernel elements, and the completed kernel matrices are in turn combined to conduct the subsequent MKC. These two procedures are alternately performed until convergence. By this way, the imputation and MKC processes are seamlessly connected, with the aim to achieve better clustering performance. Besides theoretically analyzing the clustering generalization error bound, we empirically evaluate the clustering performance on several multiple kernel learning (MKL) benchmark datasets, and the results indicate the superiority of our algorithm over existing state-of-the-art counterparts. Our codes and data are publicly available at https://xinwangliu.github.io/.

Multi-view Subspace Clustering Based on Weighted Tensor Schatten-P Norm

In the era of advancing technology and continuous societal evolution, an abundance of voluminous data from various domains has become prevalent in the public domain. Managing this wealth of data necessitates a series of preprocessing procedures, encompassing tasks such as data storage, computation, and analysis, with the aim of unveiling intrinsic features and patterns contained within. Among these procedures, clustering stands out as a crucial step, with the primary goal of unveiling the hidden structures within the data and organizing data samples into meaningful clusters based on specific criteria. Early clustering efforts were based on a singleview. Real world data, however, often contains interrelated information, leading to the emergence of multi-view clustering. Multiview subspace clustering (T-SVD) has been widely used in recent years. However, the equal treatment of each singular value in this approach lacks relevance when the data is noisy or contaminated. In order to improve the robustness and clustering performance, this paper presents a T-SVD weighted tensor norm. In order to improve the robustness, a Schatten-P norm was proposed. This paper explores multi-view subspace clustering is based on the Schatten-P norm weighted tensor. Experiments are carried out on 6 benchmark data sets, and the results are compared with 4 existing ones. Experiments show that the proposed approach is better than the most advanced multi-view subspace clustering methods.

Self-Supervised Deep Multiview Spectral Clustering.

Multiview spectral clustering has received considerable attention in the past decades and still has great potential due to its unsupervised integration manner. It is well known that pairwise constraints boost the clustering process to a great extent. Nevertheless, the constraints are usually marked by human beings. To ameliorate the performance of multiview spectral clustering and alleviate the consumption of human resources, we propose self-supervised multiview spectral clustering with a small number of automatically retrieved pairwise constraints. First, the fused multiple autoencoders are used to extract the latent consistent feature of multiple views. Second, the pairwise constraints are achieved based on the commonality among multiple views. Then, the pairwise constraints are propagated through the neural network with historical memory. Finally, the propagated constraints are used to optimize the fused affinity matrix of spectral clustering. Our experiments on four benchmark datasets show the effectiveness of our proposed approach.

Study on the influencing factors and improving countermeasures of regional financial service function -- Take corporate loans as an example

Focusing on regional financial services, this paper analyzes the variables affecting non-financial businesses getting loans through the region economic services function, and then proposes countermeasures to improve it. The DPC algorithm is applied to the financial analysis in this paper because of its fast speed and high accuracy. The AD-DPC approach is suggested in this study as a solution to the issue that the computation of local density relies on the choice of the truncation length parameter dc and the clustering sites must be manually chosen. This strategy lessens the subjectivity and volatility that the fictitious label dc brings. For the DPC algorithm by using a one-step assignment strategy, i.e., assigning the labels of clustering centers to all non-clustering centroids at one time, such a strategy is poorly fault-tolerant, this paper proposes the DAS-DPC algorithm on the basis of AD-DPC. Through experiments, ADAS-DPC is optimal for ARI metrics in the dataset. Among them, the ARI indexes of ADAS-DPC algorithm are 0.832, 0.895, 0.768 and 0.757 in the datasets Iris, Wine, Seed and Sonar. It shows that the ADAS-DPC algorithm can not only handle the datasets with complex shapes, large density differences between clusters and tightly connected clusters, but also improve the clustering performance of the algorithm for high-dimensional data.

Augmented Sparse Representation for Incomplete Multiview Clustering.

Incomplete multiview data are collected from multiple sources or characterized by multiple modalities, where the features of some samples or some views may be missing. Incomplete multiview clustering (IMVC) aims to partition the data into different groups by taking full advantage of the complementary information from multiple incomplete views. Most existing methods based on matrix factorization or subspace learning attempt to recover the missing views or perform imputation of the missing features to improve clustering performance. However, this problem is intractable due to a lack of prior knowledge, e.g., label information or data distribution, especially when the missing views or features are completely damaged. In this article, we proposed an augmented sparse representation (ASR) method for IMVC. We first introduce a discriminative sparse representation learning (DSRL) model, which learns the sparse representations of multiple views as applied to measure the similarity of the existing features. The DSRL model explores complementary and consistent information by integrating the sparse regularization item and a consensus regularization item, respectively. Simultaneously, it learns a discriminative dictionary from the original samples. The sparsity constrained optimization problem in the DSRL model can be efficiently solved by the alternating direction method of multipliers (ADMM). Then, we present a similarity fusion scheme, namely, a sparsity augmented fusion of sparse representations, to obtain a sparsity augmented similarity matrix across different views for spectral clustering. Experimental results on several datasets demonstrate the effectiveness of the proposed ASR method for IMVC.

Multitask Image Clustering via Deep Information Bottleneck.

Multitask image clustering approaches intend to improve the model accuracy on each task by exploring the relationships of multiple related image clustering tasks. However, most existing multitask clustering (MTC) approaches isolate the representation abstraction from the downstream clustering procedure, which makes the MTC models unable to perform unified optimization. In addition, the existing MTC relies on exploring the relevant information of multiple related tasks to discover their latent correlations while ignoring the irrelevant information between partially related tasks, which may also degrade the clustering performance. To tackle these issues, a multitask image clustering method named deep multitask information bottleneck (DMTIB) is devised, which aims at conducting multiple related image clustering by maximizing the relevant information of multiple tasks while minimizing the irrelevant information among them. Specifically, DMTIB consists of a main-net and multiple subnets to characterize the relationships across tasks and the correlations hidden in a single clustering task. Then, an information maximin discriminator is devised to maximize the mutual information (MI) measurement of positive samples and minimize the MI of negative ones, in which the positive and negative sample pairs are constructed by a high-confidence pseudo-graph. Finally, a unified loss function is devised for the optimization of task relatedness discovery and MTC simultaneously. Empirical comparisons on several benchmark datasets, NUS-WIDE, Pascal VOC, Caltech-256, CIFAR-100, and COCO, show that our DMTIB approach outperforms more than 20 single-task clustering and MTC approaches.

STGIC: A graph and image convolution-based method for spatial transcriptomic clustering.

Spatial transcriptomic (ST) clustering employs spatial and transcription information to group spots spatially coherent and transcriptionally similar together into the same spatial domain. Graph convolution network (GCN) and graph attention network (GAT), fed with spatial coordinates derived adjacency and transcription profile derived feature matrix are often used to solve the problem. Our proposed method STGIC (spatial transcriptomic clustering with graph and image convolution) is designed for techniques with regular lattices on chips. It utilizes an adaptive graph convolution (AGC) to get high quality pseudo-labels and then resorts to dilated convolution framework (DCF) for virtual image converted from gene expression information and spatial coordinates of spots. The dilation rates and kernel sizes are set appropriately and updating of weight values in the kernels is made to be subject to the spatial distance from the position of corresponding elements to kernel centers so that feature extraction of each spot is better guided by spatial distance to neighbor spots. Self-supervision realized by Kullback-Leibler (KL) divergence, spatial continuity loss and cross entropy calculated among spots with high confidence pseudo-labels make up the training objective of DCF. STGIC attains state-of-the-art (SOTA) clustering performance on the benchmark dataset of 10x Visium human dorsolateral prefrontal cortex (DLPFC). Besides, it's capable of depicting fine structures of other tissues from other species as well as guiding the identification of marker genes. Also, STGIC is expandable to Stereo-seq data with high spatial resolution.

SinCWIm: An imputation method for single-cell RNA sequence dropouts using weighted alternating least squares

Background and objectivesSingle-cell RNA sequencing (scRNA-seq) provides a powerful tool for exploring cellular heterogeneity, discovering novel or rare cell types, distinguishing between tissue-specific cellular composition, and understanding cell differentiation during development. However, due to technological limitations, dropout events in scRNA-seq can mistakenly convert some entries in the real data to zero. This is equivalent to introducing noise into the data of cell gene expression entries. The data is contaminated, which affects the performance of downstream analyses, including clustering, cell annotation, differential gene expression analysis, and so on. Therefore, it is a crucial work to accurately determine which zeros are due to dropout events and perform imputation operations on them. MethodsConsidering the different confidence levels of different zeros in the gene expression matrix, this paper proposes a SinCWIm method for dropout events in scRNA-seq based on weighted alternating least squares (WALS). The method utilizes Pearson correlation coefficient and hierarchical clustering to quantify the confidence of zero entries. It is then combined with WALS for matrix decomposition. And the imputation result is made close to the actual number by outlier removal and data correction operations. ResultsA total of eight single-cell sequencing datasets were used for comparative experiments to demonstrate the overall superiority of SinCWIm over state-of-the-art models. SinCWIm was applied to cluster the data to obtain an adjusted RAND index evaluation, and the Usoskin, Pollen and Bladder datasets scored 94.46%, 96.48% and 76.74%, respectively. In addition, significant improvements were made in the retention of differential expression genes and visualization. ConclusionsSinCWIm provides a valuable imputation method for handling dropout events in single-cell sequencing data. In comparison to advanced methods, SinCWIm demonstrates excellent performance in clustering, visualization and other aspects. It is applicable to various single-cell sequencing datasets.

Trustworthy multi-view clustering via alternating generative adversarial representation learning and fusion

Multi-view clustering (MVC) has attached extensive attention as it provides an effective approach to deal with the unlabeled data in real-world applications. To enjoy the strong feature extraction capacity of deep learning, traditional shallow MVC methods are further extended to deep version. Though achieve superiorities in many fields, most existing deep MVC models are still limited by their lacking assurance of the trustworthiness and robustness. This drawback also leads to the possible poor clustering performance. To tackle this drawback, we propose an alternating generative adversarial learning strategy based network, termed as Alternating Generative Adversarial Representation Learning (AGARL) network for multi-view clustering, aiming to drive different views to fall into the same semantic space for the further alignment and information fusion. Various from the traditional generative adversarial learning strategy, the proposed alternating adversarial representation learning strategy successes in further aligning the distributions of the view-specific representations and exploring the cross-view consistency credited by its setting each view as the reference alternately. Then a consensus representative latent representation can be learned through an attention-like sub-network for all views. Finally, a self-supervised clustering module is employed in the proposed network to guide the learning of cluster assignment. In addition, comprehensive experiments on numerous benchmark MVC datasets have been performed to demonstrate the effectiveness of the proposed network compared to other state-of-the-art methods.

Effect of signal‐to‐noise ratio on the automatic clustering of X‐ray diffraction patterns from combinatorial libraries

AbstractHierarchical clustering algorithm has been applied to identify the X‐ray diffraction (XRD) patterns from a high‐throughput characterization of the combinatorial materials chips. As data quality is usually correlated with acquisition time, it is important to study the hierarchical clustering performance as a function of data quality in order to optimize the efficiency of high‐throughput experiments. This work investigated the effects of signal‐to‐noise ratio on the performance of hierarchical clustering using 29 distance metrics for the XRD patterns from Fe−Co−Ni ternary combinatorial materials chip. It is found that the clustering accuracies evaluated by the F1 score only fluctuate slightly with signal‐to‐noise ratio varying from 15.5 to 22.3 (dB) under the experimental condition. This suggests that although it may take 40–50 s to collect a visually high‐quality diffraction pattern, the measurement time could be significantly reduced to as low as 4 s without substantial loss in phase identification accuracy by hierarchical clustering. Among the 29 distance metrics, Pearson χ2 shows the highest mean F1 score of 0.77 and lowest standard deviation of 0.008. It shows that the distance matrixes calculated by Pearson χ2 are mainly controlled by the XRD peak shifting characteristics and visualized by the metric multidimensional data scaling.

Effect of compaction degree on the topological characteristics of force chain network (FCN) in aggregate blend

Aggregates are the main carrier to resist external loads for asphalt pavement, and the characteristics of force chain network (FCN) in aggregate blend are closely related to the skeleton performance of asphalt mixture. This study analyzed the effect of compaction degree of aggregate blend on the topological characteristics of FCN using discrete element (DEM) and complex network theory. Six types of aggregate blends with different gradations were generated and compacted using DEM software EDEM. The compaction degree was evenly divided into 7 parts from the loose to the compacted states. FCN topology graph (FCNTG) of aggregate blend at each compaction degree was built according to the contact information between aggregates and the definition of complex network. The features of each FCNTG were quantified using the indicators characterizing complex network (including degree, vertex strength, clustering coefficient, and path length). The effect of compaction degree on the characteristics of FCN was analyzed. The results showed that complex network theory is a feasible method for investigating aggregate blend FCN. Each topological feature indicator in complex network method can be used to analyze the internal structural features of aggregate blend. With increasing compaction degree, the average degree and the average vertex strength of aggregate blend FCN and different size particles increase gradually, the clustering performance of particles becomes better gradually, and the average path length of FCN decreases gradually. There is a good linear relationship between the compaction degree and each topology indicator except the vertex strength. The compaction can reduce the dispersion degree of the contact forces between particles in aggregate blend and make it more uniform. It can also shorten the path length between two particles, which is important to improve the efficiency of transferring the external load.