Deep clustering of single-cell RNA-seq using adversarial graph contrastive learning

Abstract

Single-cell technologies enable the exploration of biological insights at cellular resolution. One of the crucial tasks in the analysis of single-cell RNA sequencing (scRNA-seq) data is to classify cells into groups of cell types. Recent developments in scRNA-seq clustering methods utilize the strength of contrastive learning and graph-based deep learning to learn high-quality representations which are beneficial for classifying cells. However, the unique characteristics of the scRNA-seq data still pose many computational challenges. This study proposes a novel method for clustering scRNA-seq data using adversarial graph contrastive learning, called scAGCL. The proposed algorithm creates a cell-cell graph and then generates a meaningful representation for clustering based on a contrastive learning process with the support of an adversarial attack on both the graph structures and node features. In addition, a subgraph sampling technique is used to increase the scalability of the method. Experiments on real scRNA-seq datasets demonstrate that the proposed method outperforms seven state-of-the-art algorithms. Furthermore, scAGCL also shows the ability to support the identification of marker genes for cell types. The source code of the proposed method and all datasets used in this paper can be downloaded at https://github.com/levinhcntt/scAGCL.

Introduction

Cells are the basic biological units of all living organisms. Understanding cellular biology from transcriptional profiling benefits different fields such as life sciences and clinical applications [1]. Traditional methods such as microarrays or bulk RNA sequencing provide only a measurement of average gene expression levels across a population of cells. The development of single-cell RNA sequencing (scRNA-seq) technologies [2] overcomes the limitation by allowing the ability to analyze gene expression at cellular level, which can reveal heterogeneity and diversity across cells.

One of the crucial tasks in an scRNA-seq data analyzing workflow is to classify cells with similar transcriptome files into the same clusters. The clustering results support the identification of cell subpopulations as well as other downstream analysis steps. Due to the unique properties of scRNA-seq data, cell clustering still remains highly challenging despite the improvement of scRNA sequencing technologies or advances in machine learning methods. In particular, the high dimensionality and high sparsity of the data cause difficulty in distinguishing cells [3, 4]. Moreover, many scRNA-seq datasets that contain extremely large numbers of cells also pose computational challenges [3].

Several clustering methods for single-cell analysis have been proposed in recent years. Early methods for scRNA-seq clustering such as RaceID [5], SINCERA [6] directly use traditional clustering methods in their classification process. While RaceID computes Pearson’s correlation coefficients between cells serving as input for the -means algorithm, SINCERA is a pipeline for analyzing scRNA-seq data using a hierarchical clustering technique. Dealing with the high dimensionality of data, SC3 [7] uses the Principal Component Analysis algorithm for feature extraction before performing consensus clustering techniques to classify cells. Another method, SNN-Cliq [8] constructs a share nearest-neighbor graph where each node is a cell, and then finds quasi-cliques in the graph to produce clusters.

Recent advances of deep learning offer opportunities to enhance clustering performance of scRNA-seq data. Due to the high dimensionality and sparsity of scRNA-seq data, most current deep clustering based methods perform techniques to train an encoder for reducing data dimensionality as well as extracting meaningful representation of data. A category of methods, i.e. scMAE [9], and scDeepCluster [10], use an autoencoder model which sequentially adds a decoder to the encoder and optimizes a reconstruction loss in their training process. scDeepCluster utilizes ZINB model-based autoencoder and incorporates with random Gaussian noise to improve the embedded feature representation. Meanwhile, scMAE is based on a masked autoencoder in which scRNA-seq data are shuffled and masked to support autoencoder training. Besides, scVI [11], and autoCell [12] are based on variational autoencoder networks to deal with noises and generate embedded data. Another group of methods, such as contrastive-sc [13], and scNAME [14], applies contrastive learning techniques that learn meaningful representations of data by pulling similar samples closer, as well as increasing the distance between dissimilar ones in the embedding space. Those algorithms utilize data augmentation strategies to generate different sample views of original data and use them to train an encoder. Depending on specific behaviors of each learning paradigm, scDeepCluster, and scNAME perform a fine-tuning step to align the latent embeddings of data with clustering targets using Kullback–Leibler divergence loss or soft -means loss. On the other hand, scMAE and contrastive-sc use clustering algorithms such as -means, or spectral clustering to classify cells on latent space.

A different branch of deep learning methods for scRNA-seq data clustering are based on graph neural networks which can utilize structural information between cells. With the same objective of training a graph encoder, those methods build a cell-to-cell graph (AttentionAE-sc [15], and scGAC [16] ) or cell-to-gene graph (graph-sc [17], and scGPCL [18]). While graph-sc only uses graph convolutional network (GCN) as a core of an autoencoder, AttentionAE-sc and scGAC additionally employ attention mechanisms to improve the quality of data representation. Additionally, scGPCL uses contrastive learning on graphs to cluster scRNA-sq data and applies feature marking on subgraph to generate augmented views.

Graph contrastive learning strategies bring a promising solution for the clustering of scRNA-seq data. However, a major challenge is how to generate meaningful augmented samples to support the contrastive learning process. One of the techniques used to make reliable augmented samples which could be hard enough for the training task is adversarial attack [19]. Some works in other fields [20, 21] have applied adversarial training to enhance the performance of contrastive learning processes.

Inspired by the recent studies above, we propose a novel clustering method for scRNA-seq data, called scAGCL (i.e. single-cell Adversarial Graph Contrastive Learning). The proposed method performs a process to train an encoder that extracts low-dimensional embeddings from gene expression data for clustering using graph contrastive learning. Different from existing studies, this work employs a new graph-based contrastive learning with the support of adversarial training to generate reliable augmented samples. Additionally, a subgraph sampling technique is applied to produce a scalability ability to analyze large datasets. Experimental results on real scRNA-seq datasets demonstrate the strength of scAGCL compared with state-of-the-art methods.

Materials and methods

The framework of scAGCL

Given a gene expression matrix , where and denote the number of cells and genes, respectively. The objective of scAGCL is to classify cells into clusters of cell types using the gene expression features. Figure 1 presents the general framework of the proposed method. Additionally, the detailed algorithm of scAGCL is provided in Supplementary Algorithm 1. scAGCL consists of two phases of training and clustering. In the training phase, after a cell-to-cell graph is constructed, different graph views are generated by augmentation and adversarial attack techniques. Adversarial graph contrastive learning is then applied to produce embeddings for the clustering phase.

Figure 1.

The overall architecture of scAGCL.

Cell-to-cell graph construction

First of all, an attributed cell-to-cell graph is constructed, where is an adjacency matrix, and is the gene expression matrix, which is used as node features. A -nearest neighbors algorithm is applied to generate the adjacency matrix. The algorithm requires a distance matrix that measures the similarity between cells. Given two cells, represented by two vectors and , this work calculates the distance between the two cells based on Pearson’s correlation coefficient as follows:

(1)

in which, and are the mean of the elements of vectors and , respectively.

Graph augmentation and adversarial attack

The first step in a contrastive learning process is to generate views of the original data. In this work, two graphs and are generated from using edge dropping and feature (or gene) masking augmentation techniques [21]. Given the adjacency matrix , a masking matrix is generated randomly following the Bernoulli distribution with probability independently. A modified matrix (i.e. or ) is created as follows:

(2)

in which, , and represents element-wise multiplication. Additionally, in order to generate and , this work also uses the Bernoulli distribution to generate a dropout mask which determines the genes to be kept or dropped from the original node feature .

In order to enhance the robustness of the graph contrastive learning framework, the proposed method uses an adversarial attack technique, which allows the model to learn more discriminative representations. Two adversarial samples , and are generated from the two augmented graphs , and , respectively. This work uses a projected gradient descent (PGD) attack method that performs simultaneously on graph structures [22], and node features [23]. The PGD attack is one of the effective techniques for adversarial training because it offers a balance between perturbation strength and computational efficiency. It is considered a universal first-order adversary that is strong enough to generate meaningful perturbations to enhance the model robustness. Additionally, the technique can generate adversarial samples efficiently during each training iteration, ensures its applicability even to large-scale datasets. Given a graph , an adversarial sample is generated as follows.

We firstly calculate the supplement matrix of , , where is an identity matrix. Define , the perturbed adjacency matrix is calculated as follows:

(3)

where is a learnable perturbation matrix, and is responsible as a constraint matrix to ensure that the perturbations only effect valid edges of the graph.

In addition, the perturbed gene expression matrix can be calculated as:

(4)

in which, is a perturbation on the gene expression matrix. The PGD method updates the perturbation and through an optimization process aiming to maximize contrastive loss defined in equation (8). It is noted that is chosen as the anchor for the adversarial attack. Let , and be the values of and at iteration , they can be calculated as follows:

(5)

(6)

where and are two projection operations onto the constraint set and , respectively [22, 23]. and are the corresponding step sizes for the adjacency and the feature perturbation. Furthermore, in each step is relaxed to a convex hull for ease of optimization.

Adversarial graph contrastive learning

The objective of graph contrastive learning with the support of adversarial training in this work is to learn an encoder to generate node representation. The encoder is built on top of a two-layer GCN [24]. All created graphs and are treated as different augmentation views of the original graph in the contrastive learning. Given a graph , the embedded feature matrix for can be computed as follows:

(7)

where is a symmetrically normalized adjacency matrix, is a matrix with self-connections, and is a degree matrix.

As presented in Fig. 1, in order to guide the learning process, the proposed method computes contrastive loss between two pairs of graph views (, and . Given two graph views , , their node representation in latent space are . A projection head constructed by a two-layer multilayer perceptron is used to map , and into a projection space. We denote , . Let be the two corresponding feature vectors of node of and in the latent space. This means that and are the row vectors of and , respectively. The contrastive loss between the two views is as follows:

(8)

where is a pairwise objective to measure the similarity between two node feature vectors [21].

(9)

in which, is temperature parameter, and is the cosine similarity function between two node feature vectors. In this case, every pair of graph view , , respectively, is considered as a positive pair, and is treated as the anchor. In contrast, other pairs of the two graph views and of the same graph view are negative pairs. In addition, because any two views are symmetric, is defined for the case where is the anchor.

Consequently, four embedded feature matrices are produced from the generated graph views , respectively, and equation (8) is used to compute the total loss function of the proposed method as follows:

(10)

in which, is a loss weight to control the contribution of the adversarial contrastive loss.

Besides, to increase the scalability of the proposed method, this study applies a subgraph sampling technique, which has been shown to not only reduce computational cost, but may also help improve the accuracy of contrastive learning methods [21, 25]. Instead of generating graph views directly using the original graph , the views are augmented and adversarial attacked from a subgraph of . With a predefined subgraph size , a subgraph is generated by randomly selecting nodes from and the edges between the selected nodes.

Clustering phase

After performing an adversarial contrastive learning process, the trained encoder corresponding to the best loss is used to generate cell embedding in the latent space. The embedded data are then normalized using L2 normalization and formed as input for the - means algorithm [26] to classify the cells into clusters.

Evaluation metrics

In order to evaluate the quality performance of clustering methods, this work uses two commonly-used metrics including Adjusted Rand Index (ARI) [27] and Normalized Mutual Information (NMI) [28]. ARI is a statistical tool to measure the similarity between clustering results and the ground truth while accounting for the possibility of random chance. In particular, the ARI is calculated as follows:

(11)

in which, is the number of shared cells assigned to cluster of the ground truth and cluster of clustering results, is the number of cells belonging to cluster of the ground truth, and is the number of cells belonging to cluster of the clustering results. On the other hand, NMI is a metric derived from information theory. It quantifies the amount of information shared between the true and predicted clusters, and applies a normalization to scale the results between 0 and 1. Denote be the ground truth clustering assignment, and be a clustering assignment result, the NMI metric is stated as follows:

(12)

where is the mutual information between and , and is an entropy function. Both the ARI and NMI indicate a perfect agreement in clustering when they get value 1.

Benchmark settings

Datasets and data preprocessing

The clustering performance of scAGCL and baseline methods is evaluated on 15 real datasets which are used in previous studies [9, 29–31]. The details of the datasets are provided in Supplementary Table S1. The datasets are generated from different tissues by different sequencing platforms, e.g. Smart-seq2, Drop-seq, 10 and others. The sizes of the datasets are from 90 cells to 48 266 cells with numbers of cell types from 4 to 18. Additionally, seven datasets are randomly generated from a large dataset (Mouse Brain dataset by 10 Genomics [32]) used to evaluate the computational efficiency of the methods.

Before performing the training process, scAGCL applies a similar technique as previous works [13, 33] to preprocess input raw gene expression matrix using the scanpy package [34]. Firstly, all genes that are not expressed in any cells are discarded. In order to account for differences in library sizes, values of the matrix are then normalized to make sure that every cell has the same total count. The proposed method continues to do a logarithmic transformation to the data matrix, and select the most variable genes (top 2000) used for training tasks.

Baseline methods

There are seven baseline methods evaluated and compared with the proposed method, including SC3 [7], DESC [35], scDeepCluster [10], AttentionAE-sc [15], contrastive-sc [13], scNAME [14], and scMMN [36]. Among them, SC3 is a traditional clustering method. DESC and scDeepCluster are deep learning method used autoencoder model. AttentionAE-sc is a graph neural network based method. scNAME and contrastive-sc utilize contrastive learning techniques. The remaining method, scMMN, uses a graph contrastive learning algorithm. For a fair comparison, the preprocessing task and hyperparameter settings are conducted as the guidelines provided in the studies. Because contrastive-sc returns two ARI and two NMI values for the case of using k-means or Leiden algorithm, respectively, we only get results from the better one using k-means.

Hyperparameter settings

In the proposed algorithm, the number of neighbors used in the -nearest neighbors algorithm to build the cell graph is set automatically as , where is the number of cells and is the number of clusters. is also limited to be in the range of 5 and 15. Meanwhile, we use the same set of hyperparameters for scAGCL for all the tested datasets, in which the temperature parameter is 0.5, step size for the adjacency perturbation is 100, step size for the feature perturbation is 0.01, subgraph size is 400, and adversarial contrastive loss weight is 1.0. Additionally, scAGCL model is trained through 500 epochs for its main process, and 10 iterations for adversarial training. The Adam optimizer is used to train with the learning rate set to 0.001. These hyperparameters are evaluated in Ablation study section and Supplementary Fig. S8. Otherwise, to ensure the reliability of experimental results, we run the proposed method and the baseline methods five times with different random seeds: 1, 12, 123, 1234, 12 345. After obtaining 5 ARI and NMI values from the number of runs, we calculate average results and report them as the performance of each method.

Results and discussion

Results on real datasets

The ARI values of scAGCL and seven baseline methods on the 15 real datasets are presented in Fig. 2. It can be seen in the heatmap that the proposed method outperforms the remaining clustering approaches on the datasets. For more details, scAGCL achieves the highest number of best results with 8/15 cases. Compared separately with each method, scAGCL produces better results for most datasets. Especially, the proposed method has higher ARI scores compared with scDeepCluster for all cases and higher than those of the 4 remaining methods from 10/15 to 14/15 tested cases.

Figure 2.

The ARI scores of scAGCL and seven baseline methods on 15 real datasets where rank 1 indicates the best results.

Figure 3 presents the average ARI scores and NMI scores of the seven methods. The two bar charts in the figure show that scAGCL achieves the best both average ARI and NMI values on the real datasets. In particular, scAGCL has from 3.43% to 24.19% average ARI values, and from 3.18% to 10.29% average NMI values higher than the baseline methods. The details of the results are provided in Supplementary Tables S2 and S3.

Figure 3.

The average ARI and NMI scores of scAGCL and seven baseline methods on 15 real datasets.

Additionally, to deeply understand of the clustering ability of the methods, their cell embeddings and labeling for Limb_Muscle dataset are visualized using UMAP. The dataset contains cells from 6 cell types. UMAP pictures of the embeddings generated by DESC, AttentionAE-sc, scDeepCluster, and scAGCL for the dataset are presented in Fig. 4. The other embeddings from SC3, scName, contrastive-sc, and scMMN are provided in Supplementary Fig. S1. The embeddings are colored based on predicted and ground truth labels. Random seed value used in this experiment is 12 345. It can be seen from the Fig. 4 that the embedding generated from the proposed method provides clearly separated clusters, which makes the clustering algorithm (-means in this case) classify easily. Compared with the ground truth cell types, scAGCL correctly assigns six clusters to six cluster labels. In the case of DESC and AttentionAE-sc, some ground truth clusters are separated into different parts and result in an incorrect cluster assignment. The embedding from scDeepCluster contains six separated components, but many cells from different cell types are put into the same clusters.

Figure 4.

UMAP visualization of the embeddings for Limb_Muscle dataset by DESC, AttentionAE-sc, scDeepCluster, and scAGCL. They are colored according to predicted labels and ground truth labels.

Considering the computational efficiency of scAGCL, other experimental results on seven datasets randomly generated from the Mouse Brain dataset are presented in Supplementary Figs S5–S7 and Supplementary Table S4. The experiments show that the proposed method achieves the best training time among the tested methods. Furthermore, scAGCL and contrastive-sc have the best efficiency GPUs usage, and are the only two methods able to work with two large-scale datasets in the case of using the GPUs available in our system.

Ablation study

The contribution of adversarial training

This section analyzes the contribution of adversarial training and the overall adversarial contrastive learning module to the proposed method. We create two variants of scAGCL called and . is the variant that uses only the normal contrastive loss , and do not use adversarial training process (adversarial contrastive loss weight ). is for the case of only using -means algorithm and not using adversarial contrastive learning module.

The experiments are conducted on four datasets (Pollen, Melanoma, Tosches, and Diaphragm). Figure 5 presents the results of scAGCL and its two variants on the datasets. It can be seen in the bar charts that scAGCL achieves higher ARI and NMI values than the two variants on all the tested cases. In particular, the proposed method returns and higher average ARI values than , and on the datasets, respectively. The two variants also get and lower average NMI values than scAGCL, respectively. The results show a significant contribution of the adversarial training to the proposed method.

Figure 5.

The performance of scAGCL and its two variants (, and ) on four datasets (Pollen, Melanoma, Tosches, and Diaphragm).

For deeper understanding of the contribution of each module, we analyze the UMAP embeddings of the methods on the four datasets for the case of using a random seed of 12 345. The embeddings generated by the three methods with the coloring labels for predicting results and the ground truth in the case of Tosches dataset (consisting of 15 clusters) are presented in Fig. 6. The cases of Pollen, Melanoma, and Diaphragm datasets are presented in Supplementary Figs S2–S4. The visualization shows that the embeddings generated from scAGCL have a better separation than the ones from , and . That is the reason why scAGCL achieves better clustering results than the two variants.

Figure 6.

UMAP visualization of the embeddings for Tosches dataset by scAGCL and its two variants (, and ). They are colored according to predicted labels and ground truth labels.

Furthermore, the effect of the adversarial training task on the overall performance of scAGCL is evaluated using different values of . This experiment carried on Pollen and Diaphragm datasets with being set to gradually increase from 0.2 to 1.8, while other hyperparameters are fixed. The line charts in Fig. 7 present ARI and NMI values of the proposed method on the two datasets. It can be seen from the charts that scAGCL produces stable results with different values of for the two datasets. For the case , the proposed method returns slightly better ARI and NMI scores compared to other values of .

Figure 7.

The performance of scAGCL with different values of on Pollen and Diaphragm datasets.

The effect of subgraph size on the proposed method

Considering the effect of the subgraph size on the quality and computational performance of scAGCL, we tested the method with different values of from 70 to 780 on Diaphragm dataset, while other hyperparameters were fixed. The line charts in Fig. 8 show that scAGCL achieves similar ARI and NMI values for different subgraph sizes. The case of , in which the model is trained on a whole graph, requires the highest training time, but does not help improve ARI or NMI scores compared to other cases. Conversely, the cases trained with smaller graph sizes demonstrate that the subgraph technique not only reduces computing costs, but also achieves similar clustering results.

Figure 8.

The results and training time of scAGCL with different subgraph sizes on Diaphragm dataset.

Biological analysis

One of the significant functions of single-cell analysis tools is to identify marker genes in each cluster. In this experiment, gene expression matrix and predicted labels are used to calculate top 50 differentially expressed genes (DEGs) in each cluster using Wilcoxon Rank Sum test for Limb_Muscle dataset (with six cell types). Figure 9 presents the similarity of the top DEGs generated by four deep learning-based methods (contrastive-sc, scDeepCluster, scName, and scAGCL) and true cell types (B cell, T cell, endothelial cell, macrophage, mesenchymal stem cell, skeletal muscle satellite cell). Each row of the heatmap presents a cluster predicted by the clustering methods, while each column expresses a true cell type from the ground truth. A heatmap cell shows the percentage of the top DEGs that overlap between a cluster and a true cell type. Using the heatmap, we label each cluster by the cell type that has the highest similarity level with it. As a result, it has failed to assign a label to cluster 4 from clustering result of scName, and there are two cell types having the same top DEGs overlapping percentage with cluster 1. In addition, there are no clusters overlapped with mesenchymal stem cell. In the case of scDeepCluster, two clusters 2 and 5 are assigned to endothelial cell, and do not have any clusters labeled as B cells. All clusters produced by scAGCL and contrastive-sc can be assigned to a unique true cell type. However, scAGCL achieves a higher similarity level than contrastive-sc for the assignment to macrophage cell type (83.3% compared with 82.1%, respectively).

Figure 9.

Overlap of top 50 DEGs in clusters that are detected by contrastive-sc, scDeepCluster, scName, and scAGCL with true cell types for Limb_Muscle dataset.

Utilizing the annotated clusters, we continue to find the top 2 DEGs in cell types which can be candidates as marker genes for corresponding cells. Figure 10 presents that the DEGs also get highest mean expression in their cluster labeled by a cell type compared to the remaining clusters. A list of marker genes are discovered for the cell types as B cell (Cd79a, Cd74), T cell (Cd3d, Cd3g), endothelial cell (Fabp4, Cdh5), macrophage (Tyrobp, Fcer1g), mesenchymal stem cell (Gsn, Dcn), and skeletal muscle satellite cell (Chodl, Des). All the marker genes are correctly the same as the ones from the ground truth. We search the all top 2 DEGs on CellMarker 2.0 [37] and Mouse Cell Atlas 3.0 [38] to assess the validity of the marker genes. We found that all the cell types are available on the cell-type lists matching to the discovered marker genes in the two databases. Most of the cell types are at the top of the lists.

Figure 10.

Matrix plot of top 2 DEGs in each cell type detected by scAGCL from the case of Limb_Muscle dataset.

Conclusion

In this study, we propose a novel deep learning-based clustering method for scRNA-seq data. The proposed method performs an effective training process for an encoder to generate a meaningful latent representation of data with the support of adversarial graph contrastive learning and subgraph sampling techniques. The utilization of adversarial training to generate reliable augmented graph views is demonstrated to strengthen clustering performance. The subgraph technique used is also a strength of the proposed method when it helps reduce much computation time while still keeping a competitive clustering accuracy compared with the case of using a whole graph. The proposed method demonstrates to be able to get better results than seven other state-of-the-art clustering algorithms on 15 real datasets. It also shows the ability to correctly support the identification of marker genes in datasets.

With the usage of k-means algorithm in the clustering phase, scAGCL still needs a given number of clusters. However, in real-world project, the information may be not available. Thus, the detection of cluster numbers in datasets automatically should be considered in future works to better support practical applications. Additionally, other adversarial and augmentation techniques could be used to improve the performance of the proposed method. Furthermore, considering the ability to handle batch effects in the data is also an interesting research direction.

Key Points

• scAGCL is a novel clustering algorithm for scRNA-seq data that employs a new graph-based contrastive learning with the support of adversarial training to generate reliable augmented samples.

• A subgraph sampling technique is applied to improve the scalability of scAGCL in analyzing large-scale datasets.

• Experiments on real scRNA-seq datasets demonstrate that scAGCL outperforms other state-of-the-art clustering methods. Experimental results also show the significant contribution of adversarial training to the effectiveness of the proposed method.

• scAGCL demonstrates the ability to support the identification of marker genes in scRNA-seq datasets.

Author contributions

L.V.V. proposed the idea for the algorithm. L.V.V., T.V.H., and T.N.Q. equally contributed to the design of the method and experiments. L.V.V., L.H.H., and P.N.P. developed and conducted the experiments. All authors wrote and reviewed the manuscript.

Conflict of interest: No competing interest is declared.