Benchmarking spatial and single-cell transcriptomics integration methods for transcript distribution prediction and cell type deconvolution.

Spatial transcriptomics approaches have substantially advanced our capacity to detect the spatial distribution of RNA transcripts in tissues, yet it remains challenging to characterize whole-transcriptome-level data for single cells in space. Addressing this need, researchers have developed integration methods to combine spatial transcriptomic data with single-cell RNA-seq data to predict the spatial distribution of undetected transcripts and/or perform cell type deconvolution of spots in histological sections. However, to date, no independent studies have comparatively analyzed these integration methods to benchmark their performance. Here we present benchmarking of 16 integration methods using 45 paired datasets (comprising both spatial transcriptomics and scRNA-seq data) and 32 simulated datasets. We found that Tangram, gimVI, and SpaGE outperformed other integration methods for predicting the spatial distribution of RNA transcripts, whereas Cell2location, SpatialDWLS, and RCTD are the top-performing methods for the cell type deconvolution of spots. We provide a benchmark pipeline to help researchers select optimal integration methods to process their datasets.

WEDGE: imputation of gene expression values from single-cell RNA-seq datasets using biased matrix decomposition.

The low capture rate of expressed RNAs from single-cell sequencing technology is one of the major obstacles to downstream functional genomics analyses. Recently, a number of imputation methods have emerged for single-cell transcriptome data, however, recovering missing values in very sparse expression matrices remains a substantial challenge. Here, we propose a new algorithm, WEDGE (WEighted Decomposition of Gene Expression), to impute gene expression matrices by using a biased low-rank matrix decomposition method. WEDGE successfully recovered expression matrices, reproduced the cell-wise and gene-wise correlations and improved the clustering of cells, performing impressively for applications with sparse datasets. Overall, this study shows a potent approach for imputing sparse expression matrix data, and our WEDGE algorithm should help many researchers to more profitably explore the biological meanings embedded in their single-cell RNA sequencing datasets. The source code of WEDGE has been released at https://github.com/QuKunLab/WEDGE.

Single-cell data clustering based on sparse optimization and low-rank matrix factorization.

Unsupervised clustering is a fundamental step of single-cell RNA-sequencing (scRNA-seq) data analysis. This issue has inspired several clustering methods to classify cells in scRNA-seq data. However, accurate prediction of the cell clusters remains a substantial challenge. In this study, we propose a new algorithm for scRNA-seq data clustering based on Sparse Optimization and low-rank matrix factorization (scSO). We applied our scSO algorithm to analyze multiple benchmark datasets and showed that the cluster number predicted by scSO was close to the number of reference cell types and that most cells were correctly classified. Our scSO algorithm is available at https://github.com/QuKunLab/scSO. Overall, this study demonstrates a potent cell clustering approach that can help researchers distinguish cell types in single- scRNA-seq data.

Spectral Mesh Segmentation via l0 Gradient Minimization.

Mesh segmentation is a process of partitioning a mesh model into meaningful parts - a fundamental problem in various disciplines. This paper introduces a novel mesh segmentation method inspired by sparsity pursuit. Based on the local geometric and topological information of a given mesh, we build a Laplacian matrix whose Fiedler vector is used to characterize the uniformity among elements of the same segment. By analyzing the Fiedler vector, we reformulate the mesh segmentation problem as a l0 gradient minimization problem. To solve this problem efficiently, we adopt a coarse-to-fine strategy. A fast heuristic algorithm is first devised to find a rational coarse segmentation, and then an optimization algorithm based on the alternating direction method of multiplier (ADMM) is proposed to refine the segment boundaries within their local regions. To extract the inherent hierarchical structure of the given mesh, our method performs segmentation in a recursive way. Experimental results demonstrate that the presented method outperforms the state-of-the-art segmentation methods when evaluated on the Princeton Segmentation Benchmark, the LIFL/LIRIS Segmentation Benchmark and a number of other complex meshes.

Diffusion equations over arbitrary triangulated surfaces for filtering and texture applications.

In computer graphics, triangular mesh representations of surfaces have become very popular. Compared with parametric and implicit forms of surfaces, triangular mesh surfaces have many advantages, such as easy to render, convenient to store and the ability to model geometric objects with arbitrary topology. In this paper, we are interested in data processing over triangular mesh surfaces through PDEs (partial differential equations). We study several diffusion equations over triangular mesh surfaces, and present corresponding numerical schemes to solve them. Our methods work for triangular mesh surfaces with arbitrary geometry (the angles of each triangle are arbitrary) and topology (open meshes or closed meshes of arbitrary genus). Besides the flexibility, our methods are efficient due to the implicit/semi-implicit time discretization. We finally apply our methods to several filtering and texture applications such as image processing, texture generating and regularization of harmonic maps over triangular mesh surfaces. The results demonstrate the flexibility and effectiveness of our methods.