Background

Characterization of intratumoral heterogeneity is critical to precision cancer therapy, as diverse cell populations usually enable relapse and resistance to treatment [1]. Conventional bulk RNA-seq technology reveals the average gene expression of a collection of cells, and subsequently many methods have been developed to inference tumor evolution using data from bulk-sequencing of tumor samples [2, 3]. These approaches require deconvolution of the mixed signals of the underlying tumor subpopulations, which are often ambiguous [4].

Recently, single-cell RNA-Seq (scRNA-seq) quantifies the expression of diverse cellular populations and enables researchers to analyze the difference among cells [5–7]. A full characterization of the transcriptional landscape of individual cell holds enormous potential for detection of clinically important tumor subpopulations, understanding of tumor heterogeneity and further clinical applications [8, 9]. Clustering of single-cell expression data provides an intuitive way for identification of cell types from a mass of heterogeneous cells, which can be used in diverse downstream expression analysis [10–12].

Due to noise, high dimensionality and data heterogeneity, newly produced scRNA-seq data pose a grand challenge for traditional clustering algorithms, such as K-means, hierarchical clustering, and spectral clustering [13]. One feasible strategy is to first reduce the high dimensional data into a lower dimensional subspace and apply traditional clustering to the dimension-reduced data. The widely used dimension reduction methods include principal component analysis (PCA) [14] or t-Distributed Stochastic Neighbor Embedding algorithm (t-SNE) [15]. Meanwhile, a number of methods which specifically designed for scRNA-seq analysis have been introduced, including Seurat [16], CIDR [17], SNN-cliq [18], SINCERA [19] and SC3 [20]. These advanced methods have greatly improved the capability of scRNA-seq data analysis. However, as clustering methods are mostly sensitive to noise and initial parameters, how to accurately cluster scRNA-seq data across different environments and revealing biological insights is still a substantial challenge [21].

Here, we proposed a consensus clustering model, conCluster, for cancer subtype identification from single-cell RNA-seq data. Specifically, conCluster first obtains a set of basic partitions using tSNE+K-means clustering with different initial parameters, and then fuses these different partitions into consensus clusters. Our conCluster method can also be easily extended to ensemble the clustering results of different clustering methods. We applied conCluster to real cancer scRNA-seq datasets, and further constructed the co-expression networks for the identified cancer subtypes to analyze their difference. The experimental results demonstrate the effectiveness and robustness of conCluster compared with five widely used clustering methods.

Methods

Overview of the conCluster model

To identify subtypes from a collection of cancer cells, we developed conCluster to ensemble multiple clustering results. Let E N∗G denotes a single-cell gene expression matrix, in which rows correspond to different cells and columns correspond to genes. Each element of E ij corresponds to the expression of gene j in the ith cell. Our conCluster takes the expression matrix E as input, through four steps, finally partition the N cells into K clusters, represented as C={Ck|k=1,2,⋯,K}. Figure 1 shows the overview of the proposed conCluster model. In the following, we will elaborate each step in detail.

Fig. 1
figure 1

The schematic workflow of conCluster

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Step1 Filter genes

To focus on the intrinsic transcriptomic signatures of these tumor cells, we filtered out rare and ubiquitous genes and identified the most variable genes across the single-cell dataset. Firstly, as the rare and ubiquitous genes are usually not useful for clustering, we filtered out genes that are either expressed in less than r% of cells (rare genes) or expressed in at least (100-r)% of cells (ubiquitous genes). As in the previous study [22], r is set as 6. Next, we identified the gene set that was the most v% variable across these single-cells, by controlling the relationship between mean expression and variability.

Step 2 Reduce dimension using t-SNE

To further reduce the dimensionality, we adopted the widely used t-SNE to reduce the high dimensional data into a lower dimensional subspace. Detailedly, perplexity is an important parameter of t-SNE, which is used as a smooth measure of the effective number of neighbors. Previous studies indicate that performance of t-SNE is fairly robust with changes in the perplexity between 5 and 50. Here, we set perplexity as 30 and used t-SNE to reduce the filtered scRNA expression data into two dimensions.

Step3 Partition cells in multiple ways

Based on the transformed two-dimensional data matrices, we performed K-means clustering with different initial parameters T times to obtain different basic partitions for these single cells. In this step, we can also utilize other basic clustering methods. For each individual clustering result, we derived a binary matrix B N∗Kt, which was constructed based the corresponding cluster labels of N cells, where Kt (t=1,2,⋯,T) is the cluster number in the tth basic partition. For each row of B N∗Kt, only one element is 1, others are 0.

Step4 Consensus clustering

After gaining the T different partitions, we concatenated all those binary matrices into a larger binary matrix B={BN∗Kt|t=1,2,⋯,T}. Furthermore, we performed K-means clustering based on the merged binary matrix. Here, Calinski-Harabaz Index [22] is utilized to decide the number of clusters. Then we fused the results of each individual clustering result into a consensus one [23].

Evaluation Metrics

When cell labels are available in the dataset, we adopted the adjusted rand index (ARI) to measure the accuracy of clustering [24]. For a set of N cells and two different partitions of these cells, the overlap between the two partitions can be summarized in a contingency table, in which each entry denotes the number of objects in common between the two partitions. The ARI is then calculated as:

$$ ARI=\frac{\sum\limits_{ij}{{n_{ij}} \choose {2}} -\left[\sum\limits_{i} {{a_{i}} \choose {2}} \sum\limits_{j} {{b_{i}} \choose {2}} \right]/{{n} \choose {2}}}{\left[\sum\limits_{i} {{a_{i}} \choose {2}} +\sum\limits_{j} {{b_{i}} \choose {2}} \right]/2-\left[\sum\limits_{i} {{a_{i}} \choose {2}} \sum\limits_{j} {{b_{i}} \choose {2}} \right]/{{n} \choose {2}}} $$
(1)

where (.) denotes a binomial coefficient, nij is the element from the contingency table, ai is the sum of the ith row of the contingency table, bj is the sum of the jth column of the contingency table.

Datasets

Single-cell expression data from two recent scRNA-seq studies were selected from the data repository NCBI Gene Expression Omnibus (GSE72056 [25], GSE73727 [26]).

As they contained the cell types in the original publications, it can be used to further validate the clustering results of different methods. In these studies, cell types were determined through a multi-stage process involving additional information such as cell-type molecular signatures. The first dataset contains a collection of cells from human melanoma tumor, consisted of 4645 single cells isolated from 19 patients; and the second dataset is from human pancreatic islet, containing 6 known human islet cell types. To ensure good data quality, samples with a library size less than 10,000 were excluded. Data sets transformed by logTPM were used as inputs of different methods.

Results

Performance evaluation on single cell RNA-seq data

To fully evaluate the performance, we compared conCluster with five widely used scRNA-seq data clustering methods, including spectral clustering, tSNE+K-means, SNN-Cliq, CIDR and SC3. Specifically, spectral clustering is an efficient traditional clustering method; tSNE+K-means is K-means clustering combined with the nonlinear dimensionality reduction technique tSNE; SNN-Cliq adopts a shared nearest neighbours approach to calculate similarities between cells and performs single cell clustering using a graph-theoretical model; CIDR uses an imputation approach to alleviate the impact of dropouts in scRNA-seq data in a principled manner; and SC3 transforms a cell-to-cell distance matrix from individual K-means clustering to get a consensus partitions. To run the main SC3 method, the parameter ks is required to set. For CIDR, there are two parameters (nPC and nCluster). SNN-cliq relies on four paramters (k, distance r and m). We tried different values of these parameters and selected those values which obtain the highest ARI. Here, we selected two single cell RNA-seq datasets [GSE72056 and GSE73727], as they contained preexisting cluster structures that can be used for validation.

Figure 2 shows the clustering performance of different algorithms as measured by the adjusted rand index (ARI). For dataset GSE73727 with 6 clusters, these methods achieve better performance when the cluster number is close to 6. For dataset GSE72056 with 2 clusters (malignant and benign tumor), the performance is the best when k equals to 2. Overall, the proposed conCluster identifies the subtypes of these single cells more correctly, as reflected by an adjusted rand index close to 0.9, which is higher than those of the five compared methods for both the datasets. Some methods such as SNN-cliq and SC3 can get comparable performance to conCluster. However, their performance is not stable for different datasets and clusters. The ARI of traditional clustering method such as spectral clustering is relative lower than other methods. Although the performance of tSNE+K-means is not so good and K-means exhibits the stochasticity in the clustering structures due to the random initialization, our conCluster based on multiple tSNE+K-means gains better solutions than other methods. Its performance suggests that the ensemble of multiple partitions of the data helps to merge clusters together in a sensible way.

Fig. 2
figure 2

Performance evaluation of conCluster and five widely-used scRNA-data clustering methods. Adjusted Rand Index (ARI) is employed to measure the similarity between inferred and true cluster labels

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Identification of cancer subtypes

Further, we applied conCluster and the five compared algorithms on the malignant melanoma tumor cells in GSE72056. In this dataset, there are 1257 malignant cells after excluding benign tumor cells. Determining the number of clusters is known to be difficult in clustering. As there is not ground truth of the clusters for these malignant cells, we utilized Calinski-Harabaz Index [22] to determine the number of clusters. conCluster managed to identify six clusters in the dataset. As shown in Fig. 3, conCluster displays five more clearly recognizable clusters than the compared methods. SNN-cliq, tSNE+K-means and SC3 also get relatively clear clusters, whereas spectral clustering and CIDR did not perform well in differentiating these clusters.

Fig. 3
figure 3

Identification of subtypes from the human melanoma scRNA-seq data set. The different colors denote the clusters output by each algorithm (Clusters numbers k = 6)

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Next, to identify the regulatory genes of each subtype of the malignant melanoma, we conducted gene co-expression network analysis. A co-expression network identifies which genes have a tendency to show a coordinated expression pattern in specific subtype. This co-expression network can be represented as a gene¨Cgene similarity matrix. Here, we identified genes having significant expression difference among cells by applying a 5% FDR. These genes were used to reconstruct the subtype specific co-expression network and identify a number of modules of high co-expression genes. we utilized WGCNA to construct co-expression modules, which is a widely used tool for co-expression analysis. Figure 4 shows the co-expression network for each melanoma subtype. We noticed that different subtypes include the distinct co-expression gene subsets. These genes with the highest degree of connectivity usually are expected to be drivers which are required for signaling pathways of essential function.

Fig. 4
figure 4

The co-expression networks are visualized for six different subtypes of human malignant melanoma tumor. Node represents gene, Edge weight indicates the statistical significance of co-expression relationship

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We computed the network degree for each gene in the co-expression networks of different melanoma subtypes, and identify genes with the most connections. To examine the potential functions of those genes, we performed systematic gene ontology enrichment analysis using DAVID tools and summarized the key biological processes and pathways [27]. The most highly connected genes in each network and the corresponding gene ontology enrichment analysis are listed in Table 1. Overall, these modules are significantly enriched for biologically important processes that are relevant to melanoma, including response to light stimulus, antigen processing and regulation of cell death. For example, in subtypes 1, the most connected gene was involved in translation initiation (RPL12, RPL38, RPS24, RPS3); in subtypes 2, the set of most highly connected genes included genes involved in cellular response to stimulus response (FOS, DUSP1,JUN, FOSB); in subtypes 3, genes sets including B2M, HLA-A, HLA-B, are related with antigen processing and presentation.

Table 1 Significant genes and GO analysis of the co-expression networks of different melanoma subtypes
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Conclusions

Cancers usually exhibit substantial tumor heterogeneity in virtually all distinguishable phenotypic features, such as cellular morphology, gene expression and metabolism. In order to analyze tumor heterogeneity, it is important to correctly group cell population into different subtypes based on single-cell expression data. Due to the unavoidable biological and technical variations, these scRNA-seq dataseta are noisy and high dimensional, which poses great challenges to the computational methods. In this paper, we proposed, conCluster, an unsupervised consensus clustering method to overcome these limitation and provide robust clustering. Specifically, our conCluster fuses many basic partitions to a consensus one, this procedure may reduce the impact that the performances of individual clustering method tend to affected by noises and different initial parameters. Moreover, data preprocessing steps such as dimensionality reduction is important in scRNA-seq data analysis. The experimental result indicates that the proposed conCluster can more accurately detect cancer subtypes than the compared widely used scRNA-seq clustering methods. The performance improvement of conCluster will be of interest to researchers in the field of scRNA-seq data analysis.