scMVAF: a multi-view adaptive fusion clustering approach for single-cell RNA-sequencing data.

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Learn more: PMC Disclaimer | PMC Copyright Notice Brief Bioinform . 2026 May 31;27(3):bbaf169. doi: 10.1093/bib/bbaf169 scMVAF: a multi-view adaptive fusion clustering approach for single-cell RNA-sequencing data Jinfeng Wang 1 , Qixiong Long 2, ✉ , Deyu Tang 3 , Jin Deng 4 , Yong Liang 5 Author information Article notes Copyright and License information 1 College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China 2 College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China 3 College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China 4 College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China 5 Peng Cheng Laboratory, No. 6001 Shahe West Road, 518055 Shenzhen, China ✉ Corresponding author. College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China. E-mail: 2272734687@qq.com Received 2024 Sep 12; Revised 2025 Mar 13; Accepted 2025 Mar 23; Collection date 2026 May. © The Author(s) 2026. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License ( https://creativecommons.org/licenses/by-nc/4.0/ ), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com. PMC Copyright notice PMCID: PMC13222525  PMID: 42218719 Abstract Single-cell RNA-sequencing (scRNA-seq) can excavate cellular heterogeneity and distinguish different types of cells. Clustering cells into subpopulations is essential in analyzing scRNA-seq data as it can help subsequent downstream analysis. However, scRNA-seq data are high-dimensional, sparse, and contain erroneous zero counts, which poses a great challenge for clustering. Although various methods have emerged in recent years, they cannot fully grasp the information of cells by characterizing scRNA-seq data from a single perspective, resulting in poor learned embedding representation and poor clustering performance. In this paper, we propose a multi-view clustering framework scMVAF for scRNA-seq data, which can learn more discriminative embedding representations by integrating feature information from multiple cell views. First, to comprehensively capture the data information, we generate multiple diverse views by down-sampling features, and then scMVAF learns a strong embedding representation for each cell view using an autoencoder based on a denoising zero-inflated negative binomial model. Next, to explore the correlation between cells in different views, a multi-view fusion module is introduced to fuse the embeddings from different views into a unified feature space. Concurrently, the fused embeddings are clustered to generate pseudo labels to improve the embedding process, and finally updating the embedding features and pseudo-labels in turn to obtain better clustering performance. Experiments are implemented on 16 real datasets and verify that scMVAF is superior to the other eight advanced technologies. Our code script can be obtained at https://github.com/LQXLE/scMVAF/ Keywords: scRNA-seq data, multi-view clustering, autoencoder, fusion Introduction Live creatures are composed mostly of cells, which are also responsible for ensuring that live organisms develop and operate properly [ 1 ]. Traditional RNA sequencing (Bulk RNA-seq) sequences all cells in a sample simultaneously at the tissue level. However, it fails to reveal cellular heterogeneity. In recent years, the development of single-cell sequencing (scRNA-seq) has enabled us to analyze tens of thousands of cells at single-cell resolution. It is an important tool for studying cellular heterogeneity [ 2 ] and plays an important role in studying complex diseases [ 3 ], exploring biological development processes [ 4 ], and assisting drug development [ 5 ]. In the early days, single-cell sequencing technology mainly focused on low-throughput sequencing methods. With the maturity of next-generation sequencing technology, the emergence of high-throughput sequencing platforms has greatly increased data output [ 6 ]. Due to the limited transcript coverage of each cell during the sequencing process, the expression values of a large number of genes were zero. Additionally, polymerase chain reaction amplification bias and sequencing errors can also interfere with the detection of true biological signals [ 7 ]. Compared with bulk RNA-seq data, scRNA-seq data are characterized by high noise [ 8 ] and sparseness. These characteristics impact downstream analysis and make cell grouping extremely difficult. Therefore, it becomes extremely important to develop a clustering model that can cope with these challenges. In recent years, clustering has received widespread attention in the analysis of single-cell RNA sequencing (scRNA-seq) data. As a key analytical tool, clustering aims to divide cells into different subpopulations based on their gene expression characteristics, thereby revealing the diversity of cell types and identifying new cell populations. This is of great significance for understanding complex biological systems and disease mechanisms. In order to cluster scRNA-seq data, some classic clustering methods have been proposed. For instance, K-means [ 9 ] clustering is a widely used unsupervised machine learning algorithm. CIDR [ 10 ] is a typical hierarchical clustering method that incorporates an implicit zeroing method into distance calculation to provide stable cell-to-cell distance estimates. SIMLR [ 11 ] is a clustering method that combines spectral clustering with multiple kernel similarity measures. Seurat [ 12 ] is a popular community detection-based method that constructs a k-nearest neighbor graph by selecting genes with large variations, and finally uses a community detection algorithm to complete clustering. While these methods offer distinct benefits, they also come with some drawbacks. For example, several methods are not suitable for small sample data, which are usually sparser and noisier in single-cell sequencing, and these methods cannot handle the noise in the data well, resulting in poor performance in feature selection and clustering. Furthermore, some of these methods have high complexity and cannot be scaled to large datasets. There are analysis-relevant factors in scRNA-seq data. A key technical challenge is the occurrence of missing values in the data. In a gene expression matrix, zero values may be due to technical reasons that the gene is not expressed or detected, a situation often referred to as false zero [ 13 ]. This implies that gene expression values are unobserved due to factors such as low capture efficiency or inadequate sequencing depth [ 14 ]. Deep learning models have attracted widespread attention because they can reduce the impact of technical factors in single-cell data. scGMAI [ 15 ] is a Gaussian mixture model that first reconstructs the data using an autoencoder, then reduces the dimensionality, and finally performs clustering using a Gaussian mixture model. DCA [ 16 ] applied two different noise models combined with an autoencoder to infer distribution parameters to better characterize scRNA-seq data. scDeepCluster [ 17 ] simultaneously learns feature representation and clustering through generative explicit modeling by projecting the original data space into a zero-inflated negative binomial (ZINB) distribution and combining DCA to impute missing values. Contrast-sc [ 18 ] extracts features by comparing the similarities between cells. scDCCA [ 19 ] not only learns the similarity of samples but also takes into account the characteristics of the data itself by using dual contrastive learning to obtain the pairwise similarity of cells. Clustering methods based on deep learning perform well in capturing complex data patterns, but a single model has limitations in dealing with data diversity. To overcome this limitation, recent studies have adopted ensemble learning methods to integrate the results of multiple deep learning models to comprehensively mine data. scDFC [ 20 ] effectively integrates the attribute and structure information of scRNA-seq data by combining the attribute feature clustering module and the structure-attention feature clustering module. SC3 [ 21 ] is an ensemble-based clustering method that first applies PCA and Laplace transform to reduce the dimensionality of genetic data, calculates pairwise distances between cells, and constructs a consensus matrix, which is then used as input for hierarchical clustering. SAFE [ 22 ] is another ensemble-based method that integrates the results of four clustering algorithms: SC3, CIDR, Seurat, and t-SNE [ 23 ] + K-means, and applies three hypergraph-based segmentation algorithms to fuse the clustering solutions of each method to generate the final clustering results. scMVFI [ 24 ] is a multi-view clustering method that integrates multiple perspectives to reveal potential biological patterns that are difficult to capture with a single perspective, helping to discover new cell types. However, it ignores the redundant information between perspectives and the differences in the contributions of perspectives to clustering, which affects clustering accuracy. Given the constraints of current approaches, this paper proposes a multi-view clustering framework called scMVAF. The proposed method first generates multiple views by down-sampling the original data several times and then learns the embedding representations of each view using a ZINB-based denoising autoencoder. This scheme can not only reduce the problem of data sparsity, but also better fill in the missing information and reduce the impact of single-view data noise through comprehensive analysis of multiple views. Next, we design a multi-view feature fusion module which can capture the differences between different views and dynamically assign weights to each view. Finally, the fusion view is used to generate a unified target distribution to guide the optimization of the autoencoder, thereby mining an embedded representation with higher discriminative information to identify cell types. Our model is multiple compared on 16 real datasets, and the experimental results show that the proposed model scMVAF outperforms the other 8 baseline models and shows excellent performance in cell clustering. Materials and methods Datasets and data preprocessing Sixteen real single-cell datasets were collected from public platforms for experiments and compared with other baseline methods. All datasets have a credible real label, and the label information of the cell type is annotated by its author. The details of these datasets are shown in Table 1 . Table 1. Dataset information including cell types, source, and reference Datasets Cells Genes Cell types Cell source Reference Yan 90 20 214 6 Human [ 26 ] Goolam 124 41 480 5 Mouse [ 27 ] Deng 268 22 431 6 Mouse [ 28 ] Camp 777 19 020 7 Mouse [ 29 ] QS_Limb_Muscle 1090 23 341 6 Mouse [ 30 ] QS_Trachea 1350 23 341 4 Mouse [ 30 ] Qx_Bladder 2500 23 341 4 Mouse [ 30 ] Qx_Limb_Muscle 3909 23 271 6 Mouse [ 30 ] QS_Heart 4365 23 341 8 Mouse [ 30 ] QxSpleen 9552 23 341 5 Mouse [ 30 ] PBMC-Zheng4k 4340 33 694 8 Human [ 31 ] PBMC-Ding 7111 20 428 10 Human [ 31 ] PBMC-A 11 432 14 504 8 Human [ 31 ] PBMC-C 11 989 14 222 8 Human [ 31 ] PBMC-B 12 261 14 473 8 Human [ 31 ] AD-brain 13 214 10 850 8 Human [ 31 ] Open in a new tab For the original dataset, our preprocessing is as follows. First, datasets with sample sizes >50 were log-transformed (base 2), and then cells in which >95% of the cells had a gene expression value of 0 were removed. We then normalized the data based on library size by calculating the size factor. Specifically, the library size of a specific cell is denoted by , the library size of all cells is denoted by , and the size factor for cell is expressed as the ratio , where represents the median of . Finally, the python package SCANPY [ 25 ] was used to screen out 2000 genes with large variations from the original data. By selecting genes with large variations between cells, the impact of technical noise can be effectively reduced, making it possible to better distinguish different cell types because these genes show significant expression differences between different cell types, thereby improving the accuracy and stability of clustering. The framework of scMVAF Figure 1 shows the framework diagram of scMVAF. It consists of two key modules. Specifically, the preprocessed expression matrix is first sampled at a fixed sampling rate of 0.9 to generate multiple views. Then multiple views are input into multiple denoising ZINB distributed autoencoders, respectively, and projected into the latent space to obtain multiple independent single-view latent features. Considering that multiple views are generated in different scenarios and there may be diversity between them, simple fusion may ignore the cell consensus information learned from multiple views. Therefore, this paper proposes an adaptive weighted fusion module that can dynamically perceive the importance of each view and perform feature fusion of multiple views, which helps to combine multi-view information for comprehensive prediction of cell types. Finally, the fused views are used to obtain a unified target distribution and each view encoder obtains a soft cluster distribution. The private soft distribution of each view and the unified target distribution of the fused view optimize each other, thereby guiding each view encoder to obtain better discriminative information. Figure 1. Open in a new tab Illustration of scMVAF framework. (A) The overall framework. The preprocessed is first generated by multiple times down-sampling to generate views, each of which is independently fed into the ZINB-based model for denoising projection to obtain the embedding features of a single view, followed by adaptive weighted fusion. A uniform target distribution is obtained by the clustering algorithm on the fused features and is the soft clustering distribution for each view. Finally, the uniform objective distribution is used to guide the view of private soft distribution for clustering optimization. (B) Adaptive weighted fusion Module. Generate cell views Due to technical limitations in the scRNA-seq process, there are missing values in the data, also known as dropout events. This blurs the relationship between genes and greatly affects downstream analysis. Recently, ensemble learning has been used for dropout imputation in scRNA-seq [ 32 , 33 ], which can achieve better prediction performance by integrating the classification results of multiple weak classifiers [ 34 ]. For ensemble clustering, the first task is to generate multiple base cluster partitions. A common approach is to repeatedly sample a certain number of gene features from the preprocessed data [ 35 ]. In this study, in order to eliminate possible redundant features and generate a robust view, the original data were repeatedly sampled multiple times using a fixed sampling rate to generate multiple subsets. Multiple random subsampled submatrices can reveal different patterns and variabilities within the data. Training with several distinct views helps mitigate the noise effects of any single view, thereby enhancing the model’s generalization ability. Additionally, random subsampling helps prevent overfitting associated with using a single view (the complete data matrix), particularly when dealing with sparse and noisy scRNA-seq data. Specifically, these subsets have the same number of cells as the original data but only contain a subset of genes. The preprocessed expression matrix is represented as , and scMVAF randomly samples features of to generate multiple cell views . Each cell view is obtained by sampling the original expression matrix, and the generated multiple cell views are input to the ZINB-based denoising multi-view autoencoder to learn multiple independent feature embeddings. Denoising multi-view autoencoder Autoencoder is a popular neural network model used for feature learning and data compression in unsupervised learning. It consists of two parts: an encoder and a decoder. The basic idea is to compress the input data into low-dimensional representations in the latent space through the encoder and reconstruct these representations into outputs as close to the original input as possible through the decoder. However, scRNA-seq data are highly sparse and contain numerous zero values and noise due to dropout events, potentially leading to features learned by the autoencoder that lack robustness and generalizability. To mitigate the impact of noise and dropout, this paper adopts a ZINB-based denoising autoencoder to map data from different cell views into multiple embedding spaces and perform feature fusion. Denoising autoencoders can recover undamaged data from noisy input data, which helps to alleviate the impact of noise [ 36 ]. Compared with simple reconstruction methods, the ZINB distribution model can provide more accurate estimates of gene expression levels by considering the zero-inflated nature of the data, thereby improving the performance of downstream analysis. Specifically the cell view data are , each cell view data are first corrupted by random Gaussian noise to obtain : (1) the noise can be passed to any layer of the encoder. We define as the learning parameter of the encoder, and the encoder function is defined as: (2) where denotes the encoder function parameterized by , represents the potential representation obtained after being processed by the encoder function . Subsequently, the decoder reconstructs the hidden mapping, is the learning parameter of the decoder, and the decoder function is : (3) where is the result obtained by decoder. The encoder and decoder consist of fully connected neural networks using rectified linear units as their activation function, and the minimization loss function during the learning process of the denoising autoencoder is expressed as: (4) Denoising Autoencoder Based on ZINB Distribution consists of an encoder and three decoders. The encoder compresses high-dimensional gene expression data into a low-dimensional embedding space. The three decoders are used to predict the mean ( ), discrete value ( ), and zero-inflated probability ( ), respectively. The ZINB denoising model uses as the interpolated gene expression value. For zero values in the data, the model will determine the source of the zero value based on the value. If it is introduced by technical noise, the value will be used for interpolation. The value captures the overdispersion of scRNA-seq data by adjusting the variance of the negative binomial distribution, and combines it with the zero-inflation part to deal with excess zero values, so that the ZINB model can more accurately reflect the true characteristics of single-cell gene expression data. It is expressed as follows: (5) (6) During the reconstruction process, the ZINB model estimates the parameters , , and . The estimation process can be defined as follows: (7) (8) (9) (10) where stands for the last layer of the decoder, three independent fully connected layers attached after . , , the probability estimation matrices for the mean, discrete, and lost probabilities, respectively. , , and are learnable parameter matrices of , , and , respectively. The loss of the ZINB-based autoencoder uses a negative log-likelihood, and the loss function for pretraining on a single-cell view and the minimized loss function during learning are defined as follows: (11) (12) Adaptive weighted fusion module In multi-view learning, each view contain different information, and there may be correlations and differences between these information. Equally weighted view fusion ignores the differences between views, and the fusion result is more sensitive to noise and outliers, which reduces the robustness and stability of the model. The attention mechanism has achieved remarkable results in capturing the differences between views, which can dynamically perceive the differences between views and assign weights to them. Therefore, this paper designs a module that automatically perceives the weights of each view. It assigns different weights to the embedded representation of each view based on the improved attention mechanism, and makes full use of the information of different unit views for fusion. Specifically, for the views in a cell sample, the embedding representation , . The global information is captured by computing the correlation between different views. The core is to calculate the weight matrix to perceive the importance of different views. Calculate the importance score for each cell view, which can be defined as: (13) where represents the bias term. Then, the importance score of each view is normalized and converted into view weight. These weights reflect the relative importance of each view in the current clustering task. It can be defined as: (14) where represents the weight coefficient of the view in the sample. Finally, the comprehensive feature of each sample is calculated by weighted summing the features of multiple views. Specifically, for each sample, its features under different views are weighted and summed according to the calculated weights to obtain the final feature vector of the sample. For samples, the feature vector of each sample is a weighted combination of its multiple view features. The fusion of a specific sample can be defined as: (15) where , is the embedding representation learned for the view in the sample. Multi-view self-supervised learning module In multi-view learning, the complementarity of views can improve performance [ 37 ], and the additional information provided by different views helps to distinguish cell subpopulations more accurately. Since the information learned in these views is related, each view may contain information that other views cannot capture. The complementary information provided by different views can effectively reduce the noise and bias in the data. However, existing multi-view clustering algorithms for scRNA-seq data do not fully consider the complementarity between views. To address these limitations, this paper introduces a multi-view self-supervised learning module to promote information complementarity between views. It enhances information fusion and consistency of feature representation between views by narrowing the difference between the distribution of individual views and the fused view. Specifically, the centroid of is first initialized by the K-means method, and then the soft distribution is obtained using the Student distribution to generate the target distribution. The soft distribution and the target distribution can be expressed as follows: (16) (17) Each cell view obtains a soft label through K-means. Define as the probability that the cell in the cell view belongs to the cluster, which can be expressed as: (18) where denotes the cluster center of mass of the cell view and represents the sample in the view. Finally, the relative entropy between the target distribution obtained from the fused representation and the private distribution learned for each cell view is used to guide the encoder training, which can be expressed as: (19) In order to better learn robust embedding features, the model jointly optimizes the autoencoder reconstruction loss and Kullback–Leibler (KL) loss to learn more discriminative features to better cluster cells. The overall loss function that minimizes the training process is defined as follows: (20) where is the correlation coefficient of KL loss. Results Parameter setting scMVAF is run in pytorch based on Python 3.9. The encoding layer size of each view encoder is (256, 64), the bottleneck layer is 32, and the decoding layer size is (64, 256). The view encoder uses a ZINB-based denoising autoencoder, which is pretrained for 90 epochs using the optimizer AdamW [ 38 ] with a pretraining learning rate of 0.001. Experimental verification shows that when the number of view encoders reaches 9 and the sampling rate is 0.9, the fusion effect is the best. scMVAF down-sampled the preprocessed cell count matrix using a fixed sampling rate of 0.9 to generate nine views. During the training phase, the optimizer Adadelta [ 39 ] was used, and the learning rate was adjusted to 0.001. The model was trained for 150 epochs. The batch size is 256 in both the pretraining and training stages. All experiments are performed on NVIDIA GeForce GTX 4060Ti (16G). Table 3. ARI scores for scMVAF and baseline methods across 16 datasets, with the highest values highlighted in bold Datasets K-means scDFC scGMAI scDeepCluster Seurat scDCCA SC3 SAFE Ours Yan 0.734 0.752 0.790 0.613 0.690 0.714 0.708 0.602 0.874 Goolam 0.614 0.687 0.593 0.561 0.580 0.747 0.687 0.390 0.991 Deng 0.448 0.632 0.620 0.470 0.500 0.743 0.580 0.835 0.922 Camp 0.691 0.715 0.461 0.553 0.620 0.640 0.679 0.680 0.722 QS_Limb_Muscle 0.700 0.656 0.281 0.654 0.551 0.519 0.669 0.536 0.976 QS_Trachea 0.592 0.881 0.149 0.683 0.221 0.426 0.525 0.510 0.928 Qx_Bladder 0.515 0.768 0.458 0.758 0.231 0.523 0.757 0.575 0.816 Qx_Limb_Muscle 0.698 0.804 0.507 0.746 0.479 0.742 0.926 0.740 0.989 QS_Heart 0.609 0.660 0.190 0.617 0.369 0.518 0.668 0.445 0.937 QxSpleen 0.496 – 0.192 0.431 0.231 0.614 0.317 0.051 0.946 PBMC-Zheng4k 0.610 0.445 0.100 0.634 0.581 0.626 0.643 0.729 0.839 PBMC-Ding 0.367 0.302 −0.008 0.262 0.308 0.039 0.111 0.178 0.532 PBMC-A 0.543 – 0.261 0.609 0.496 0.672 0.146 – 0.742 PBMC-C 0.569 – 0.287 0.556 0.491 0.626 0.118 – 0.785 PBMC-B 0.640 – 0.281 0.568 0.471 0.603 0.084 – 0.783 AD-brain 0.357 – 0.194 0.392 0.344 0.560 0.107 – 0.550 Open in a new tab Clustering performance This study uses ACC (clustering accuracy) [ 40 ], ARI (adjusted random index) [ 41 ], and NMI (normalized mutual information) [ 42 ] as evaluation indicators. The definitions of these three evaluation metrics are provided in Section A of the Supplementary Material . To assess the performance of scMVAF, we tested it on 16 real-world scRNA-seq datasets and compared its results with those of eight leading methods, where K-means and Seurat are traditional clustering methods, and scDeepCluster, scGMAI, scDFC, and scDCCA are deep clustering methods, SC3, and SAFE are integrated methods. To ensure fairness, scMVAF and all baseline methods were run five times using default parameters, and the mean and standard deviation of the results were calculated. After multiple experimental verifications, our model shows excellent performance in all three evaluation indicators, as shown in Tables 2 – 4 . Some values are missing in some positions in the table because SAFE and scDFC have too high time complexity or cannot run on some datasets due to the biological complexity of the dataset. In contrast, scMVAF shows excellent performance in almost all tasks. Supplementary Tables S1–S3 list the standard deviations of the ACC, ARI, and NMI scores for all methods across the five runs. Table 2. ACC scores for scMVAF and baseline methods across 16 datasets, with the highest values highlighted in bold Datasets K-means scDFC scGMAI scDeepCluster Seurat scDCCA SC3 SAFE Ours Yan 0.762 0.800 0.773 0.687 0.689 0.769 0.756 0.644 0.858 Goolam 0.700 0.758 0.653 0.658 0.710 0.815 0.758 0.629 0.965 Deng 0.538 0.705 0.701 0.554 0.649 0.745 0.629 0.761 0.938 Camp 0.773 0.804 0.608 0.610 0.660 0.693 0.786 0.726 0.852 QS_Limb_Muscle 0.751 0.740 0.532 0.735 0.667 0.621 0.738 0.635 0.990 QS_Trachea 0.781 0.956 0.464 0.814 0.343 0.625 0.642 0.582 0.955 Qx_Bladder 0.606 0.834 0.625 0.773 0.312 0.639 0.771 0.665 0.864 Qx_Limb_Muscle 0.735 0.819 0.628 0.759 0.553 0.762 0.935 0.794 0.994 QS_Heart 0.681 0.747 0.383 0.718 0.474 0.672 0.724 0.554 0.926 QxSpleen 0.723 – 0.530 0.666 0.412 0.755 0.744 0.145 0.966 PBMC-Zheng4k 0.696 0.615 0.418 0.743 0.650 0.739 0.762 0.856 0.879 PBMC-Ding 0.553 0.458 0.277 0.430 0.457 0.317 0.361 0.256 0.690 PBMC-A 0.669 – 0.491 0.776 0.633 0.794 0.521 – 0.785 PBMC-C 0.649 – 0.492 0.699 0.588 0.734 0.499 – 0.793 PBMC-B 0.656 – 0.488 0.671 0.574 0.737 0.417 – 0.759 AD-brain 0.536 – 0.328 0.567 0.485 0.641 0.53 – 0.682 Open in a new tab Table 4. NMI scores for scMVAF and baseline methods across 16 datasets, with the highest values highlighted in bold Datasets K-means scDFC scGMAI scDeepCluster Seurat scDCCA SC3 SAFE Ours Yan 0.827 0.815 0.840 0.740 0.663 0.824 0.831 0.628 0.881 Goolam 0.775 0.857 0.749 0.697 0.740 0.761 0.776 0.523 0.968 Deng 0.689 0.803 0.784 0.696 0.662 0.787 0.743 0.691 0.879 Camp 0.800 0.842 0.633 0.742 0.726 0.765 0.802 0.758 0.819 QS_Limb_Muscle 0.766 0.816 0.399 0.806 0.668 0.668 0.760 0.655 0.958 QS_Trachea 0.641 0.857 0.297 0.725 0.399 0.457 0.535 0.415 0.872 Qx_Bladder 0.634 0.790 0.490 0.806 0.370 0.618 0.704 0.505 0.814 Qx_Limb_Muscle 0.787 0.852 0.507 0.846 0.624 0.775 0.909 0.753 0.976 QS_Heart 0.766 0.798 0.351 0.746 0.556 0.643 0.712 0.551 0.892 QxSpleen 0.604 – 0.230 0.544 0.352 0.568 0.346 0.198 0.870 PBMC-Zheng4k 0.715 0.603 0.108 0.744 0.614 0.689 0.660 0.770 0.826 PBMC-Ding 0.527 0.464 0.020 0.383 0.466 0.065 0.232 0.366 0.626 PBMC-A 0.665 – 0.361 0.676 0.629 0.696 0.320 – 0.726 PBMC-C 0.629 – 0.362 0.671 0.571 0.653 0.281 – 0.732 PBMC-B 0.706 – 0.364 0.675 0.551 0.644 0.230 – 0.752 AD-brain 0.559 – 0.343 0.589 0.477 0.622 0.244 – 0.649 Open in a new tab scMVAF consistently maintains the top two results in the comparison with all other baseline methods. In terms of ACC score, scMVAF improves ACC by 21.1% on the QxSpleen dataset compared with the second-best algorithm. In terms of ARI score, our method improves the second-best result by 11%, 25.9%, and 26.9% on the PBMC-Zheng4k, QS_Limb_Muscle, and QS_Heart datasets, respectively. In terms of NMI score, except for Camp, which ranks second, all other datasets rank first in NMI score. For the Camp dataset, which ranks second, scMVAF performs similarly to the other eight methods. The experimental results show that our model has stronger generalization ability than other baseline methods on most datasets. This may be due to the significant advantages of multi-view clustering in enhancing cell heterogeneity identification and improving clustering accuracy. It can better handle the uncertainty in the data and effectively integrate information from different perspectives, thereby reducing the noise and bias of a single perspective. In addition, data from different perspectives can provide different levels of biological information. Multi-view clustering can reveal complex biological relationships that cannot be discovered from a single view. Multi-view learning promotes cell clustering Most methods cluster data from a single view, which may not be comprehensive enough to capture valuable information. In contrast, multi-view learning addresses the limitations of single-view learning and enhances the feature expressiveness. In scMVAF, one of the views can be optimized by the guidance of the other views, and each view learns a robust representation of cell clustering. To verify the contribution of scMVAF in multi-view cell clustering, we conducted a comparative experiment of single-view and multi-view learning on the QS_Heart dataset. In the experiment, we selected single-view, three-view, five-view, nine-view, and eleven-view settings, and visualized the corresponding embedding representations. The colors in the figures correspond to distinct cell types. As shown in Fig. 2 , in the embedded representation obtained using a single view, the boundaries between different clusters are blurred, the overlap between clusters is high, and it is difficult to clearly distinguish different types of cell populations. One possible reason is that single-view learning only uses reconstruction loss to learn representations, which may fail to fully capture the complex correlations and heterogeneity between cells. The multi-view method learns rich features from multiple views and then integrates the complementary information of multiple views. In contrast, the model can effectively reduce the impact of noise and finally separate cells belonging to different clusters to form clear boundaries. Therefore, in the visualization using multi-view clustering, the boundaries between different clusters are clearer and the data points within the cluster are more densely distributed. Figure 2. Open in a new tab Comparing embedded representations for single-view learning and multi-view learning on the QS_Heart dataset. Additional comparison with scDeepCluster in real datasets To further verify the effectiveness of the scMVAF method, we compared scMVAF with the scDeepCluster method combined with Dropout Layer. Dropout Layer, as a regularization technique, helps reduce the overfitting of the model by randomly dropping neurons during training. In this experiment, we selected eight real datasets from different scales to evaluate the performance of the two methods, as shown in Fig. 3 and Supplementary Table S4 . The experimental results show that scMVAF outperforms the method combining scDeepCluster with Dropout Layer in multiple evaluation indicators, further verifying the effectiveness of our method. By building multiple sub-models and keeping the model structure clear, scMVAF outperforms the method combining scDeepCluster and Dropout Layer in performance, proving that scMVAF is a superior clustering method. Figure 3. Open in a new tab Comparison of ARI scores between scMVAF and the method combining scDeepCluster and Dropout Layer on datasets of different sizes. The impact of hyperparameters The number of views is a crucial parameter in our scMVAF model, as it determines the number of distinct views for each cell and significantly impacts clustering performance [ 43 ]. In this experiment, our method is performed with different numbers of views to analyze its impact on performance. To ensure the reliability of the scMVAF results, we set 5 random seeds 1234, 3333, 2222, 142, 42, and performed 5 independent runs. Then, we calculated the median ARI score under different views as a metric to evaluate its performance. Figure 4 and Supplementary Table S5 shows the ARI results of our method using different numbers of views on the datasets Goolam, QS_Heart, Qx_Bladder, PBMC-Ding, and PBMC-Zheng4k. It can be seen that in most cases, when the number of views is set to 9, the model achieves better clustering performance. Taking the PBMC-Ding dataset as an example, when the number of views is <9, the increase in the number of views improves the performance. The possible reason is that as the number of views increases, cells can be characterized from more different angles and better results can be obtained in the identification of cell types. When the number of views is >9, the clustering performance decreases. Too many cell views may lead to redundant views, which will harm the performance of the model. Therefore, the number of views is set to 9 as our default parameter. Figure 5 , Supplementary Tables S6 and S7 show the running time and memory usage for five datasets with different numbers of views. Figure 4. Open in a new tab The effect of the number of views in scMVAF. Figure 5. Open in a new tab Running time and memory consumption of scMVAF in different views. (A) Running time; (B) memory consumption. The down-sampling rate controls the size of each generated unit view. To explore the impact of the down-sampling rate on model performance, our method is run with different down-sampling rates in this experiment. Figure 6 and Supplementary Table S8 present the ARI results. It can be seen that when the down-sampling rate is 0.9, our model takes satisfactory performance. In most cases, when the down-sampling rate is <0.9, the clustering performance of the model improves as the down-sampling rate increases. The possible reason is that fewer features retained lead to loss of information. As the number of features increases, the clustering performance of the model improves. When down-sampling is not performed, the model performance decreases. The possible reason is that there is redundant information in the complete data. Therefore, the down-sampling rate is set to 0.9 as the default parameter. Figure 6. Open in a new tab The effect of down-sampling rate in scMVAF. In the scMVAF model, we design a hyperparameter to balance the reconstruction loss and the KL loss. was adjusted on different datasets to explore its impact on model performance. We set the value of from 0.2 to 1 with a step size of 0.2. When = 0.2, the model relies more on the reconstruction loss, and when = 1, the reconstruction loss and KL loss are equally important. As shown in Fig. 7 and Supplementary Table S9 , there are significant differences in the sensitivity of different datasets to . Specifically, on the PBMC-Ding dataset, as the value increases, the model performance gradually improves, while in the other four datasets, the model performance remains stable under different values. Overall, when is close to 1, the model performs relatively well on the five datasets. This shows that balancing the reconstruction loss and the KL divergence loss to make full use of the information of different cell views is crucial to improving model performance. Figure 7. Open in a new tab ARI scores of scMVAF with different values. Impact of dropout rate on methods We selected three deep clustering-based baseline methods and compared the impact of dropout events on performance on four datasets of different sizes. To this end, we set the dropout rate to 15%–30% and kept other parameters at default values to simulate a “dropout” event. Each method was run five times, and the clustering performance of each method under different dropout rates was evaluated by calculating the average value of ARI. As shown in Fig. 8 and Supplementary Table S10 , the average ARI of scMVAF under different dropout rates remains stable. In particular, in the Goolam dataset, scMVAF always maintains a high stability, while the performance of other methods drops significantly with the increase of dropout rate, and only a few results drop <0.5. In the PBMC-Ding dataset, the ARI scores for all methods are relatively close and change little under different dropout rates. In the Qx_Bladder dataset, we observed that the performance of scDFC improved with the increase of dropout rate, while in the PBMC-Zheng4k dataset, the performance of scDFC and scDCCA also improved with the increase of dropout rate. This may be because the dropout simulation events removed some noise information that was not relevant to the task, which helped to improve the performance of these methods in clustering tasks. Overall, scMVAF always outperformed the other three methods at different dropout rates and maintained high stability, which shows that this method can effectively deal with the common sparsity and random loss problems in gene expression data. Even in the case of data loss, scMVAF can still maintain relatively good clustering performance. Figure 8. Open in a new tab Comparison of methods across different dropout rates Comparison of embeddings learned by different methods In order to intuitively verify whether scMVAF can obtain better embeddings compared with other deep learning-based methods, this paper visualizes the embeddings learned by three deep clustering-based methods on the Qx_Bladder and QS_Trachea datasets. The embeddings learned by all methods are visualized by t-SNE [ 23 ]. As shown in Fig. 9 , scMVAF can separate cells well compared with other methods. In Fig. 9 A, scDCCA [ 19 ] and scDeepCluster [ 17 ] tend to mix different types of cells together. The possible reason is that the multidimensional feature learning of cells is incomplete, which affects the accuracy of clustering. In Fig. 9 B, the cell distribution of scDCCA [ 19 ] shows a high degree of overlap, which indicates that it has certain limitations in distinguishing different cell populations. In contrast, scMVAF can separate cell populations more clearly and show clearer cluster boundaries. In contrast, our method shows better performance. This may be due to the adoption of a multi-view learning strategy. The fusion module integrates data from multiple views to achieve multi-view analysis of samples. Each view provides partial information of the sample, and the fusion module effectively captures the complementary relationship between views by learning a shared embedding space, thereby significantly improving the clustering performance. Figure 9. Open in a new tab Visual analysis of the three deep learning methods applied on the two datasets using t-SNE.(A) Qx_Bladder dataset; (B) Trachea dataset. Marker gene identification Marker genes can be used to distinguish different types of cells and identify the functional state of cells. To further test the ability of scMVAF in identifying specific genes, for the embryonic dataset Yan containing 90 cells, we used the non-parametric Wilcoxon rank sum test to identify the top 3 differentially expressed genes in each predicted cluster and used them as marker genes for the cluster. In addition, to ensure the accuracy of the statistical test results, we averaged the repeated ranks. Figure 10 shows the expression levels of the top 3 marker genes in each cluster identified from the Yan dataset. As shown in Fig. 10 , the expression of the selected specific genes in each cell population is significantly different, indicating that scMVAF can better distinguish cell types. For example, in cluster 2, the top two marker genes identified are DUX4L2 and DUX4. DUX4L2 is a gene related to embryonic development. DUX4 activates a series of genes related to the 2-cell embryonic stage. Studies have shown that DUX4L2 and DUX4 are marker genes for 2-cell stage cells [ 44 ]. In addition, although some expressed genes do not match the expressed genes in existing studies. As shown in Fig. 10 , they are highly expressed in specific clusters, which may help discover new marker genes. Figure 10. Open in a new tab Expression dot plot for the Yan dataset (The color of the dot represents the average gene expression level within each cluster, while the dot size reflects the proportion of cells expressing the gene in each group) Ablation experiments scMVAF mainly consists of an adaptive weighted fusion module and a self-supervised learning module. In order to verify the contribution of these two modules to the model performance, this paper proposes two scMVAF variants. The two variants are scMVAF-FK (the adaptive fusion module and the self-supervised learning module are deleted) and scMVAF-K (only the adaptive fusion module is retained). As shown in Fig. 11 and Supplementary Table S11 , this paper selects eight real datasets of different sizes for ablation experiments. Figure 11. Open in a new tab ARI scores of scMVAF-FK, scMVAF-K, and scMVAF. The results show that scMVAF achieves the first place in all eight datasets, and scMVAF always outperforms scMVAF-K, which indicates that multi-view self-supervised learning can improve clustering performance. As shown in Fig. 11 , compared with its two variants, scMVAF performs the best and scMVAF-FK performs the worst. This result shows that it is crucial to obtain consistency between cell views, which helps to more accurately capture the relationship between cells from different angles. In addition, individual cell views show differences, and the adaptive weighted fusion module can effectively capture these differences, resulting in better discriminative features. In the PBMC-Ding and PBMC-Zheng4k datasets, the clustering performance of scMVAF-K is significantly better than that of scMVAF-FK, which further verifies the effectiveness of the weighted fusion module. Overall, scMVAF achieves the best performance in all cases, which shows that our network is efficient and robust and can handle datasets of various sizes well. Conclusion Single-cell sequencing can reveal cellular heterogeneity from a molecular perspective. Over the past decade, scRNA-seq datasets have grown exponentially, leading to the development of various cell clustering approaches to identify cell types. However, these methods consider cells from only a single perspective, failing to fully capture the differences and complex relationships between cells from multiple perspectives. This limitation leads to poor results in cell subtype clustering. In this paper, a novel multi-view clustering framework for single-cell data is proposed to enhance feature diversity by fusing features from multiple views to facilitate the identification of cell subtypes. The adaptive fusion of different views enhances the representation learning of data, and the complementarity between views helps to more comprehensively capture the diversity and complexity of data, thereby improving the robustness of clustering. Experimental results show that our method outperforms other baseline methods on 16 real datasets. In the future, feature selection methods are planned to be added to further improve the method. Since interactions between genes may enhance feature representation, gene–gene pairwise interactions can be used to promote learning of low-dimensional data, thereby improving the robustness of the network. In addition, the complexity of the model can be further reduced by studying lightweight models. Key Points Observing cells from different perspectives is crucial to understanding their characteristics. The integration of multi-perspective data can more comprehensively capture the differences and complex relationships between cells. We fuse cell features learned from different perspectives to help improve the accuracy of cell clustering. This feature fusion can more accurately reveal the intrinsic structure of cell populations. We integrated the multi-view adaptive fusion module and the self-supervision module into scMVAF to enhance the ability to distinguish cell diversity. Experimental results show that our proposed model performs well on 16 datasets, outperforming all other baseline methods. Supplementary Material bbaf169_supplementary_materials_scMVAF bbaf169_supplementary_materials_scmvaf.docx (147.6KB, docx) Acknowledgements The authors acknowledge Qiong Huang for supervision and funding support. The authors thank all editors and reviewers for the suggestions and comments. Contributor Information Jinfeng Wang, College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China. Qixiong Long, College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China. Deyu Tang, College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China. Jin Deng, College of Mathematics and Informatics, South China Agricultural University, No. 483 Wushan Road, 510642 Guangzhou, China. Yong Liang, Peng Cheng Laboratory, No. 6001 Shahe West Road, 518055 Shenzhen, China. Conflicts of interest None declared. Funding The work was supported by the Special Fund for Marine Economic Development (six marine industries) of Guangdong Province, China (GDNRC[2024]18) and the Fund of Southern Marine Science and Engineering Guangdong Laboratory (Zhanjiang)(ZJW-2023-04), Guangdong Provincial Education Department (2023ZDZX4002, 2021ZDZX1078), and Guangzhou Key Laboratory of Smart Agriculture (2019020-10081). Data availability QS_Limb_Muscle, QS_Trachea, Qx_Bladder, Qx_Limb_Muscle, QS_Heart, and QxSpleen can be downloaded from the Tabula Muris database, while other datasets can be downloaded for free at https://hemberg-lab.github.io/scRNA.seq.datasets/ and https://github.com/LQXLE/scMVAF/ . References 1. Artis  D, Spits  H. The biology of innate lymphoid cells. Nature 2015; 517:293–301. 10.1038/nature14189 [ DOI ] [ PubMed ] [ Google Scholar ] 2. Grosselin  K, Durand  A, Marsolier  J  et al.  High-throughput single-cell chip-seq identifies heterogeneity of chromatin states in breast cancer. 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