Neighborhood Graph Research Articles

On Spectral Portraits of Incidence Matrices of Nearest Neighbor Graphs

On Spectral Portraits of Incidence Matrices of Nearest Neighbor Graphs

Multi-omics integration for both single-cell and spatially resolved data based on dual-path graph attention auto-encoder.

Single-cell multi-omics integration enables joint analysis at the single-cell level of resolution to provide more accurate understanding of complex biological systems, while spatial multi-omics integration is benefit to the exploration of cell spatial heterogeneity to facilitate more comprehensive downstream analyses. Existing methods are mainly designed for single-cell multi-omics data with little consideration of spatial information and still have room for performance improvement. A reliable multi-omics integration method designed for both single-cell and spatially resolved data is necessary and significant. We propose a multi-omics integration method based on dual-path graph attention auto-encoder (SSGATE). It can construct the neighborhood graphs based on single-cell expression profiles or spatial coordinates, enabling it to process single-cell data and utilize spatial information from spatially resolved data. It can also perform self-supervised learning for integration through the graph attention auto-encoders from two paths. SSGATE is applied to integration of transcriptomics and proteomics, including single-cell and spatially resolved data of various tissues from different sequencing technologies. SSGATE shows better performance and stronger robustness than competitive methods and facilitates downstream analysis.

Diffusion on PCA-UMAP Manifold: The Impact of Data Structure Preservation to Denoise High-Dimensional Single-Cell RNA Sequencing Data.

Single-cell transcriptomics (scRNA-seq) is revolutionizing biological research, yet it faces challenges such as inefficient transcript capture and noise. To address these challenges, methods like neighbor averaging or graph diffusion are used. These methods often rely on k-nearest neighbor graphs from low-dimensional manifolds. However, scRNA-seq data suffer from the 'curse of dimensionality', leading to the over-smoothing of data when using imputation methods. To overcome this, sc-PHENIX employs a PCA-UMAP diffusion method, which enhances the preservation of data structures and allows for a refined use of PCA dimensions and diffusion parameters (e.g., k-nearest neighbors, exponentiation of the Markov matrix) to minimize noise introduction. This approach enables a more accurate construction of the exponentiated Markov matrix (cell neighborhood graph), surpassing methods like MAGIC. sc-PHENIX significantly mitigates over-smoothing, as validated through various scRNA-seq datasets, demonstrating improved cell phenotype representation. Applied to a multicellular tumor spheroid dataset, sc-PHENIX identified known extreme phenotype states, showcasing its effectiveness. sc-PHENIX is open-source and available for use and modification.

Multi-view subspace clustering based on multi-order neighbor diffusion

Multi-view subspace clustering (MVC) intends to separate out samples via integrating the complementary information from diverse views. In MVC, since the structural information in the graph is crucial to the graph learning, most of the existing algorithms construct the superficial graph from the original data by directly measuring the similarity between the first-order complementary nearest neighbors. However, the information provided by the superficial graph structure would be influenced by contaminated or absent samples. To address this problem, in the proposed method, the higher-order complementary neighbor graphs are exploited to discover the latent structural information between the samples, and fusing the latent structural information across different orders to achieve the MVC. Specifically, the higher-order neighbor graphs under different views are leveraged to estimate the missing samples. Then, to integrate the neighbor graphs of different orders, the multi-order neighbor diffusion fusion is proposed. Nevertheless, the above problem of diffusion fusion is an intractable non-convex issue. Thus, to address it, the multi-order neighbor diffusion fusion is considered as a combination problem of the solution under different order, and the heuristic algorithm is leveraged to solve it. In this way, not only the data representation under different view and also the neighbor structure under different order can be diffused under a joint optimization framework, thus the consistency and integral information among various perspectives and orders can be utilized effectively and simultaneously. Experiments on both incomplete and complete multi-view dataset demonstrate the convincingness of the high-order neighborhood structure based subspace clustering scheme by comparing with the existing approaches.

Few-shot bearing fault diagnosis by semi-supervised meta-learning with graph convolutional neural network under variable working conditions

Aiming at the problems of low accuracy and weak generalization ability in fault diagnosis caused by complex working conditions and limited fault samples of bearings, a few-shot bearing fault diagnosis method by semi-supervised meta-learning with simplifying graph convolutional neural network (semi-meta-sgc) is proposed. Firstly, the time domain signal is converted into the frequency domain by fast Fourier transform (FFT). Secondly, considering each spectrum sample as a node, a k-nearest neighbor (KNN) graph is constructed according to the adjacencies between nodes, thus transforming the bearing fault classification into a graphical node classification. Then, relying on meta-learning, graph convolutional neural network, and semi-supervised learning, a high-accuracy node classifier is obtained by using a small number of training samples to achieve the classification of bearing faults under variable working conditions. Finally, the proposed method is verified by four cases and compared with other methods. The results show that this method has higher recognition accuracy and generalization performance.

Density peaks clustering based on Gaussian fuzzy neighborhood with noise parameter

Density peak clustering (DPC) is an effective clustering method known for its robustness, non-iterative nature, and hybrid approach. However, it is not without limitations: (a) the determination of the cutoff distance (dc) relies on human experience, which can significantly impact the clustering outcome; (b) DPC does not take into account the local structure of the data when computing local densities; (c) it employs a crisp kernel for density computation; (d) the performance of DPC is affected by chain reactions; and (e) DPC often struggles to handle noisy data. In order to address these limitations, this paper proposes a novel approach called DPC based on Gaussian fuzzy neighborhood with noise parameter (DPC-GFNN). The proposed method leverages a Gaussian fuzzy kernel to enhance the separation between clusters and mitigates the influence of outliers through an adjustable noise parameter (λ). DPC-GFNN utilizes a k-nearest neighbor graph based on density to label highly dense regions. This technique effectively avoids chain reactions by assigning accurate labels to points in border areas, enabling proper clustering of data with diverse shapes and densities. To evaluate the effectiveness of DPC-GFNN, a series of experiments are conducted on both real-world and synthetic datasets. The experimental results demonstrate that DPC-GFNN exhibits superior robustness and clustering accuracy compared to other modified variants of DPC including DPC based on k-nearest neighbors (DPC-KNN), improved DPC (IDPC), DPC based on density backbone and fuzzy neighborhood (DPC-DBFN), and DPC based on fuzzy weighted k-nearest neighbors (FKNN).

SPRITE: improving spatial gene expression imputation with gene and cell networks.

Spatially resolved single-cell transcriptomics have provided unprecedented insights into gene expression in situ, particularly in the context of cell interactions or organization of tissues. However, current technologies for profiling spatial gene expression at single-cell resolution are generally limited to the measurement of a small number of genes. To address this limitation, several algorithms have been developed to impute or predict the expression of additional genes that were not present in the measured gene panel. Current algorithms do not leverage the rich spatial and gene relational information in spatial transcriptomics. To improve spatial gene expression predictions, we introduce Spatial Propagation and Reinforcement of Imputed Transcript Expression (SPRITE) as a meta-algorithm that processes predictions obtained from existing methods by propagating information across gene correlation networks and spatial neighborhood graphs. SPRITE improves spatial gene expression predictions across multiple spatial transcriptomics datasets. Furthermore, SPRITE predicted spatial gene expression leads to improved clustering, visualization, and classification of cells. SPRITE can be used in spatial transcriptomics data analysis to improve inferences based on predicted gene expression. The SPRITE software package is available at https://github.com/sunericd/SPRITE. Code for generating experiments and analyses in the manuscript is available at https://github.com/sunericd/sprite-figures-and-analyses.

Fokker-Planck diffusion maps of multiple single cell microglial transcriptomes reveals radial differentiation into substates associated with Alzheimer's pathology.

The identification of microglia subtypes is important for understanding the role of innate immunity in neurodegenerative diseases. Current methods of unsupervised cell type identification assume a small noise-to-signal ratio of transcriptome measurements that would produce well-separated cell clusters. However, identification of subtypes is obscured by gene expression noise, diminishing the distances in transcriptome space between distinct cell types and blurring boundaries. Here we use Fokker-Planck (FP) diffusion maps to model cellular differentiation as a stochastic process whereby cells settle into local minima, corresponding to cell subtypes, in a potential landscape constructed from transcriptome data using a nearest neighbor graph approach. By applying critical transition fields, we identify individual cells on the verge of transitioning between subtypes, revealing microglial cells in inactivated, homeostatic state before radially transitioning into various specialized subtypes. Specifically, we show that cells from Alzheimer's disease patients are enriched in a microglia subtype associated to antigen presentation and T-cell recruitment.

MvG-NRLMF: Multi-view graph neighborhood regularized logistic matrix factorization for identifying drug–target interaction

Traditional methods for predicting drug–target interactions (DTIs) have significant room for improvement in terms of time period and monetary overhead. At present, machine learning-based approaches are commonly used in the drug discovery field. In this study, a multi-view graph neighborhood regularized logical matrix factorization (MvG-NRLMF) model was proposed to predict unknown DTIs. Multiple similarity matrices (kernels) were constructed from the space of drugs and targets, the corresponding Laplacian matrices were generated, and these were fused. Finally, the MvG-NRLMF model was adjusted using an alternating gradient ascent procedure for training. On the four benchmark datasets, our method was competitive, and on some datasets, our method even outperformed existing models.

Server Saturation in Skewed Networks

We use bipartite graphs to model compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. We prove that servers with skewed graph neighborhoods saturate with tasks in a limiting regime. The neighborhood of a server is skewed if it contains a diverging number of dispatchers with uniformly bounded degrees.

Discriminative Subspace Learning With Adaptive Graph Regularization

Abstract Many subspace learning methods based on low-rank representation employ the nearest neighborhood graph to preserve the local structure. However, in these methods, the nearest neighborhood graph is a binary matrix, which fails to precisely capture the similarity between distinct samples. Additionally, these methods need to manually select an appropriate number of neighbors, and they cannot adaptively update the similarity graph during projection learning. To tackle these issues, we introduce Discriminative Subspace Learning with Adaptive Graph Regularization (DSL_AGR), an innovative unsupervised subspace learning method that integrates low-rank representation, adaptive graph learning and nonnegative representation into a framework. DSL_AGR introduces a low-rank constraint to capture the global structure of the data and extract more discriminative information. Furthermore, a novel graph regularization term in DSL_AGR is guided by nonnegative representations to enhance the capability of capturing the local structure. Since closed-form solutions for the proposed method are not easily obtained, we devise an iterative optimization algorithm for its resolution. We also analyze the computational complexity and convergence of DSL_AGR. Extensive experiments on real-world datasets demonstrate that the proposed method achieves competitive performance compared with other state-of-the-art methods.

Quasi-Laplacian energy of fractal graphs

Graph energy is a measurement of determining the structural information content of graphs. The first Zagreb index can be handled with its connection to graph energy. In this paper, a novel and significant application of the first Zagreb index to composite graphs based on fractal graphs is revealed, and by the relation between quasi-Laplacian energy and the vertex degrees of a graph, we derive closed-form formulas for the quasi-Laplacian energy of fractal graphs or namely R-graphs, R-vertex and edge join, R-vertex and edge corona, R-vertex and edge neighborhood graphs in terms of the corresponding energy, the first Zagreb indices, number of vertices and edges of the underlying graphs.

Structure Suture Learning-Based Robust Multiview Palmprint Recognition.

Low-quality palmprint images will degrade the recognition performance, when they are captured under the open, unconstraint, and low-illumination conditions. Moreover, the traditional single-view palmprint representation methods have been difficult to express the characteristics of each palm strongly, where the palmprint characteristics become weak. To tackle these issues, in this article, we propose a structure suture learning-based robust multiview palmprint recognition method (SSL_RMPR), which comprehensively presents the salient palmprint features from multiple views. Unlike the existing multiview palmprint representation methods, SSL_RMPR introduces a structure suture learning strategy to produce an elastic nearest neighbor graph (ENNG) on the reconstruction errors that simultaneously exploit the label information and the latent consensus structure of the multiview data, such that the discriminant palmprint representation can be adaptively enhanced. Meanwhile, a low-rank reconstruction term integrating with the projection matrix learning is proposed, in such a manner that the robustness of the projection matrix can be improved. Particularly, since no extra structure capture term is imposed into the proposed model, the complexity of the model can be greatly reduced. Experimental results have proven the superiority of the proposed SSL_RMPR by achieving the best recognition performances on a number of real-world palmprint databases.

A single-cell multiomics analysis of IRF4 in mediating treatment resistance in ibrutinib-treated chronic lymphocytic leukemia (CLL).

7051 Background: The Bruton tyrosine kinase (BTK) inhibitor ibrutinib (ibr) has revolutionized the treatment of CLL, showing efficacy in the majority of patients. Nevertheless, resistance occurs in a subset of patients, often with dismal clinical outcomes. Ibr resistance occurs through several mechanisms, including mutations affecting BTK or PLCG2, or upregulation of alternative survival pathways. We investigated at the single-cell level the molecular mechanisms that underlie ibr resistance in CLL cells and their interactions with non-malignant tumor microenvironment (TME) cell populations. Methods: We retrospectively identified 7 CLL patients with ibr resistance (as second line therapy). Samples were obtained before ibr treatment and at progression. Chromium Single Cell Multiome ATAC + Gene Expression (GEX) (10x Genomics) was applied to a mixture of CD19+CD5+ and CD19- cells to jointly analyze DNA accessibility and gene expression in the same single nuclei of CLL B and TME cells. An average of 4,800 cells (range 2,600-15,000) per sample was retained after QC filtering. Principal component analysis (PCA) was performed on GEX counts. ATAC peaks were called with MACS2, and latent semantic indexing was used for dimensionality reduction. We then computed a weighted nearest neighbour graph, identified clusters using the SLM algorithm and performed cell type assignment with established marker genes. Results: We identified 28 distinct cell clusters, representing CLL B-cells or cell types that constitute the TME, including CD4+ and CD8+ T cells, monocytes, dendritic and NK cells. CLL B-cell clusters were patient and timepoint-specific, while TME clusters were occupied by cells from multiple patients. Five patients showed multiple distinct CLL B-cell clusters pre-treatment or at progression, reflecting cellular heterogeneity within the tumor compartment. Interestingly, some clusters that were dominated by post-treatment CLL B-cells also included cells from pre-treatment samples, suggesting pre-existence of the clone giving rise to the relapse. For each patient, we performed pairwise differential expression between CLL B-cell clusters. Gene ontology analysis revealed increased activation of IRF4 and MHC-related pathways in CLL B-cells at progression compared to pre-treatment in 6 and 4 out of 7 patients, respectively. The elevated IRF4 pathway activity was underpinned by increased chromatin accessibility in IRF4 signature genes. Conclusions: Differential blockade of B-cell receptor signaling by ibr has been reported to downregulate activity of IRF4, a key transcription factor in B-cell activation. Our results suggest that CLL B-cells that are resistant to ibrutinib have re-activated IRF4 activity beyond pre-treatment levels, implying a potential role for IRF4 in ibrutinib resistance.

Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering

Subspace clustering algorithms have demonstrated remarkable success across diverse fields, including object segmentation, gene clustering, and recommendation systems. However, they often face challenges, such as omitting cluster information and the neglect of higher-order neighbor relationships within the data. To address these issues, a novel subspace clustering method named Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering is proposed. This method seamlessly embeds Markov transition probability information into the self-expression, leveraging a fine-grained neighbor matrix to uncover latent data structures. This matrix preserves crucial high-order local information and complementary details, ensuring a comprehensive understanding of the data. To effectively handle complex nonlinear relationships, the method learns the underlying manifold structure from a cross-order local neighbor graph. Additionally, connectivity constraints are applied to the affinity matrix, enhancing the group structure and further improving the clustering performance. Extensive experiments demonstrate the superiority of this novel method over baseline approaches, validating its effectiveness and practical utility.

SpaNCMG: improving spatial domains identification of spatial transcriptomics using neighborhood-complementary mixed-view graph convolutional network.

The advancement of spatial transcriptomics (ST) technology contributes to a more profound comprehension of the spatial properties of gene expression within tissues. However, due to challenges of high dimensionality, pronounced noise and dynamic limitations in ST data, the integration of gene expression and spatial information to accurately identify spatial domains remains challenging. This paper proposes a SpaNCMG algorithm for the purpose of achieving precise spatial domain description and localization based on a neighborhood-complementary mixed-view graph convolutional network. The algorithm enables better adaptation to ST data at different resolutions by integrating the local information from KNN and the global structure from r-radius into a complementary neighborhood graph. It also introduces an attention mechanism to achieve adaptive fusion of different reconstructed expressions, and utilizes KPCA method for dimensionality reduction. The application of SpaNCMG on five datasets from four sequencing platforms demonstrates superior performance to eight existing advanced methods. Specifically, the algorithm achieved highest ARI accuracies of 0.63 and 0.52 on the datasets of the human dorsolateral prefrontal cortex and mouse somatosensory cortex, respectively. It accurately identified the spatial locations of marker genes in the mouse olfactory bulb tissue and inferred the biological functions of different regions. When handling larger datasets such as mouse embryos, the SpaNCMG not only identified the main tissue structures but also explored unlabeled domains. Overall, the good generalization ability and scalability of SpaNCMG make it an outstanding tool for understanding tissue structure and disease mechanisms. Our codes are available at https://github.com/ZhihaoSi/SpaNCMG.

Three-way graph convolutional network for multi-label classification in multi-label information system

The Graph Convolutional Neural Networks (GCNs) have demonstrated a powerful capacity for relation processing. To improve the representation learning capability of GCNs, numerous studies have begun to excavate latent topological graphs based on node features, aiming to obtain richer representations of nodes. However, these graph mining methods based on global metrics, such as Euclidean distance, lack descriptions of uncertainty and fine granularity, leading to the loss of structural information, which affects the final representation of nodes. Therefore, this paper proposes the Three-way Graph Convolutional Neural Network (TW-GCN), which is based on multi-granularity and three-way decision. First, from the perspective of multi-granularity, each attribute is analyzed as a granule, and we establish relations of advantage, disadvantage, and uncertainty for objects under each attribute granule. Three-way relation captures the complex connections between nodes from multiple perspectives, improves the comprehensive understanding of graph data, and avoids the information loss caused by traditional two-way processing. Second, a three-way graph convolutional layer is constructed to capture uncertainty and ambiguity by performing graph convolution on different topological graphs. The final node representation is obtained through message passing on the node’s neighbor graph, which considers not only the global structure, but also effectively captures local structural features. Finally, we employ the TW-GCN for multi-label classification within information systems to validate the model’s validity based on multiple indicators.

Abstract PR004: Spatial proteomics and transcriptomics reveal an altered immune cell landscape in bladder cancer patients unresponsive to BCG treatment

Abstract Introduction: Patients with high-risk non-muscle invasive bladder cancer (NMIBC) are recommended treatment with Bacillus Calmette-Guérin (BCG). The therapeutic effect of BCG is highly dependent on the host immune system and the tumor microenvironment (TME). The cellular composition and the functional status of the TME have been shown to play crucial roles for treatment efficacy. However, much is still unknown regarding the cellular interactions and mechanisms of BCG. Using spatial proteomics and transcriptomics, we investigated the immune cell landscape in a cohort of BCG treated patients. Materials and methods: A total of 183 tumors from 111 patients with NMIBC treated with BCG were included on a tissue microarray (TMA). The TMA included paired pre- and post-BCG tumors. We analyzed the tumor tissue using Imaging Mass Cytometry (IMC; StandardBioTools) for simultaneous detection of 35 immune and tumor-related proteins at single cell resolution. Ilastik was used to generate probability maps and DeepCell Mesmer was used for cell segmentation. Markers were quantified for the mean intensity per cell. GeoMX Digital Spatial Profiling (DSP) was used for spatial proteomics and transcriptomics profiling of tumor and stromal areas, targeting 63 protein targets and whole transcriptome amplification, respectively. Results: We identified a total of 364,504 cells in the tumor tissue using IMC. After computing a neighborhood graph using the log normalised and z-scaled signal and embedding it using UMAP, leiden clustering was performed to detect communities of unique cell types by interrogating the presence of phenotypic markers. We identified major lineages such as macrophages, CD8 T cells, dendritic cells (DCs), NK cells and neutrophils in the TME of analyzed tumors. Specifically, we observed more CD8 T cells after BCG (p=0.015), especially in females (p=0.048). Females also had higher levels of DCs and macrophages after treatment compared to males (p=0.024 and p=0.048). Patients who progressed to MIBC after BCG had higher numbers of CD8 T cells and NK cells prior to BCG (p=0.039 and p=0.021). Prolonged exposure to interferons has been associated with immune evasion and tumor cell proliferation. In concordance, we found high pretreatment protein expression of IFNα and IFNγ in tumor regions from patients with a pronounced signature of CD8 T cell exhaustion after BCG treatment using GeoMX DSP proteomic analysis. Data analysis is currently ongoing, and additional results will be presented at the conference. Conclusion: The composition and functional status of the TME is associated with clinical and biological features such as immune cell abundance, CD8 T cell exhaustion, sex and progression. A greater understanding of the TME may help identify patients unresponsive to BCG earlier and improve the understanding of biological differences in tumor development and aggressiveness. This may ultimately improve patient outcomes. Citation Format: Trine Strandgaard, Tine Ginnerup Andreasen, Tessa Jane Divita, Liina Salminen, Sean Houghton, Kasper Thorsen, Iver Nordentoft, Iyinyeoluwa Okulate, Alexander Schmitz, Søren Riis Paludan, John Sfakianos, Amir Horowitz, Jørgen Bjerggaard Jensen, Lars Dyrskjøt. Spatial proteomics and transcriptomics reveal an altered immune cell landscape in bladder cancer patients unresponsive to BCG treatment [abstract]. In: Proceedings of the AACR Special Conference on Bladder Cancer: Transforming the Field; 2024 May 17-20; Charlotte, NC. Philadelphia (PA): AACR; Clin Cancer Res 2024;30(10_Suppl):Abstract nr PR004.

DPC-DNG: Graph-based label propagation of [formula omitted]-nearest higher-density neighbors for density peaks clustering

Density peaks clustering (DPC) algorithm is a novel density-based clustering approach that effectively determines cluster centers from a decision graph and groups objects by assigning non-center objects to the same cluster as their nearest higher-density neighbor. Although DPC can allocate clusters of arbitrary shapes, its single-chain label propagation mechanism has the risk of “chain error”, where an object assigned an incorrect label causes its subordinates to also be assigned the same incorrect label. Hence, DPC is unable to effectively group objects that are located in overlapping areas between clusters, which leads to unsatisfactory clustering results. To address this issue, this study proposes the graph-based label propagation of k-nearest higher-density neighbor for density peaks clustering (DPC-DNG). DPC-DNG extends the single-chain label propagation of DPC to a graph-based multi-chain label propagation that assigns labels to objects from their k-nearest higher-density neighbors. First, based on k-nearest higher-density neighbors and the selected cluster centers, a symmetric density-based neighbor graph (DNG) is constructed. Second, to assign labels to objects, a classic graph-based label propagation mechanism is utilized in conjunction with DNG. To validate our method, we carry out comprehensive experiments on 6 synthetic and 12 real datasets. Statistically speaking, the results show that our method has improved the clustering performance of DPC and exhibits promising performance over other state-of-the-art DPC-related methods.

Mechanical Fault Diagnosis of High-Voltage Circuit Breakers with Dynamic Multi-Attention Graph Convolutional Networks Based on Adaptive Graph Construction

With the rapid development of deep learning, its powerful capabilities make it possible to perform mechanical fault diagnosis of high-voltage circuit breakers (HVCBs). Among deep learning approaches, the convolutional neural network is widely used. However, while it can extract features effectively, it also has some limitations. Specifically, it depends on a large number of training data and only takes data information into account without considering structural information. These shortcomings lead to unused information and unsatisfactory model results. To address these shortcomings, this paper proposes AKNN-DMGCN, a novel dynamic multi-attention graph convolutional network based on an adaptively constructed graph, which can achieve high accuracy and robust mechanical fault diagnosis of HVCBs. First, a novel adaptive k-nearest neighbor (AKNN) graph construction method is proposed to construct informative graphs. The AKNN method can mine the relationship between the original data samples and utilize the data and label information. Thus, it has high fault tolerance to noise signals and can construct a structure graph with rich and accurate information, which can improve the overall model performance. Then, a dynamic multi-attention graph convolutional network (DMGCN) is applied for mechanical fault diagnosis of HVCBs. DMGCN fully utilizes structural and numerical information representing HVCB signals to perform classification. DMGCN has a dynamic multi-attention mechanism with strong expressive ability, which allows it to achieve high diagnostic accuracy. The experimental results indicate that the accuracy of AKNN-DMGCN reaches 97.22% on a balanced dataset and 95.01% on an imbalanced dataset, which demonstrates that the proposed method is effective for both balanced and imbalanced samples.