Efficient Imputation for Patch-based Missing Single-cell Data via Cluster-regularized Optimal Transport

TL;DR

This work tackles patch-based missingness in single-cell sequencing data by introducing Cluster-Regularized Optimal Transport (CROT), which minimizes $L_{ ext{CROT}}(X_1,X_2) = S_p^psilon(X_1,X_2) + \alpha S_p^psilon(\mathcal{C}_1,\mathcal{C}_2)$ to fuse data-level alignment with cluster-centroid regularization. By coupling entropic optimal transport with a clustering-consistent term, CROT preserves cell-type structure while imputing missing modalities. Across Citeseq, Multiome, and PBMC datasets, CROT demonstrates superior numerical recovery (higher PCC, lower RMSE/MAE) and clustering quality (higher ARI, Purity) with substantially lower runtimes than a range of baselines. The approach holds broad practical impact for large-scale multimodal single-cell analyses and structured missing data problems, enabling robust downstream analyses such as clustering and visualization.

Abstract

Missing data in single-cell sequencing datasets poses significant challenges for extracting meaningful biological insights. However, existing imputation approaches, which often assume uniformity and data completeness, struggle to address cases with large patches of missing data. In this paper, we present CROT, an optimal transport-based imputation algorithm designed to handle patch-based missing data in tabular formats. Our approach effectively captures the underlying data structure in the presence of significant missingness. Notably, it achieves superior imputation accuracy while significantly reducing runtime, demonstrating its scalability and efficiency for large-scale datasets. This work introduces a robust solution for imputation in heterogeneous, high-dimensional datasets with structured data absence, addressing critical challenges in both biological and clinical data analysis. Our code is available at Anomalous Github.

Figures (6)

• Figure 1: Runtime comparison on three datasets. Calculated as the total time of model initialization, model training, and inference on the dataset (if the method is model-dependent), or the total time of iterative interpolation on the target dataset (if the method is not model-dependent). The final results are truncated to integers.
• Figure 2: An illustration of our framework. Assume that all modality 1 data from batch 3 is missing (where "modality" may vary by dataset). The process begins by initializing the missing data and using observed data from batches 1 and 2 to determine an optimal number of clusters. The following iterative optimization procedure is then applied. In each iteration, clustering with $k$ clusters is performed to assign a class label to each row in $X_1$ and $X_2$, respectively. Next, centroids $C_1$ and $C_2$ are calculated by averaging the rows belonging to each class. Subsequently, the Sinkhorn divergence between ($X_1, X_2$) and ($C_1, C_2$) is computed to form the total loss. This procedure continues until the total loss converges.
• Figure 3: UMAP visualizations comparing clustering quality across different imputation methods. Better distinct clusters of UMAP plots helps with further analysis of single-cell data, such as the presence of rare cell types or intermediate states between well-defined populations.
• Figure 4: Numerical value of RMSE, PCC and ARI on one missing setting of Citeseq during iterative imputation process.
• Figure 5: UMAP visualizations showing clusters of different iterations during imputation. Better distinct clusters of UMAP plots helps with further analysis of single-cell data, such as the presence of rare cell types or intermediate states between well-defined populations.