BinSpect is a multi-stage analysis tool to identify spatially variable genes (SVGs), based on statistical enrichment of binarized expression levels in neighboring cells within the spatial network. It first constructs the binary or weighted spatial neighborhood network, where nodes are cells or spots and edges are defined by k-nearest neighbors or radial distance cutoff. Then, for each gene, it dichotomizes expression counts using k-means clustering or top percentage rank thresholding. Last, it builds a contingency by counting the different combinations of binarized expression value pairs between neighboring cells and conducts a Fisher exact test to test their independence. BinSpect outputs p-values for selecting SVGs.

MERINGUE is a density-agnostic method to identify spatial gene expression heterogeneity using spatial autocorrelation and cross-correlation analyses. It uses Voronoi tessellation to define cellular neighborhoods. Moran's I is calculated to identify spatially heterogeneous genes, and the scale of significantly spatially heterogeneous genes is characterized based on a local indicator of spatial association (LISA). Further, MERINGUE computes a spatial cross-correlation index (SCI) to group genes into primary spatial patterns.

SOMDE is a machine learning-based method to identify spatially variable genes (SVGs) in large-scale spatial expression data. It builds upon Self-Organizing Map (SOM), an unsupervised neural network for dimensionality reduction while preserving the topological structure of the data, to merge spatially neighboring data into different nodes. SVGs are then identified based on the node-level spatial location and converted gene meta-expression profiles using a modified Gaussian process with Gaussian, linear or periodic kernels.
Available in Python package “somde” 
Version: 0.1.8

SPARK-X (SPARK-eXpedited) is a scalable non-parametric model for spatial expression analysis. It builds on a robust covariance test framework and incorporates various spatial kernels to model sparse count data from large studies, and thus enables rapid and effective spatially variable gene (SVG) detection with statistical robustness and enhanced power. Compared with SPARK, SPARK-X reduces computational complexity and space usage, leading to significant improvements in speed and memory efficiency.

Seurat is a R package for analyzing and visualizing single-cell RNA sequencing (scRNA-seq) and sequencing and imaging-based spatially resolved data. It provides statistical methods to integrate data from multiple sources and perform flexible data analysis and visualization. For spatial transcriptomics data analysis, it equips with a tool for spatially variable gene (SVG) detection by calculating Moran’s I, a statistical measure used to assess spatial autocorrelation in geographical data. Associated p-value is provided to measure the significance of the observed spatial pattern.

SpaGCN is a spatial domain and spatially variable gene (SVG) identification approach based on the graph convolutional network for spatially resolved transcriptomics data. Unlike other SVGs detection methods, it takes spatial domains into consideration and aims at distinguishing regional SVGs. First, SpaGCN integrates the information from gene expression profile, location and pathology image to identify spatial domains via graph convolution. Then, domain guided differential expression analysis for each gene is conducted. SVGs are defined by having a large expression fold change between the target and neighboring domains.

SpatialDE uses a geostatistical modeling framework with a Gaussian process to identify spatially variable genes (SVGs). It can only apply to normalized expression levels (e.g. converted from gene expression counts via variance stabilizing transformation). The Gaussian process covariance in the linear mixed model is composed of spatial effect and random noise. The spatial kernels include squared exponential, periodic, and linear. The fraction of variance attribute to spatial effects is determined by gradient-based optimization. Based on the asymptotic chi-square test, SpatialDE outputs p-values to indicate if the test gene is an SVG.

Trendsceek is a nonparametric method without distribution specification which models data as marked point process. Points represents spatial locations of cells or spots, marks of each point represent expression levels. SVGs are identified by mark-segregation hypothesis testing since for the distribution of all pairs at a particular radius, a mark segregation is said to be present if the distribution is dependent on r such that it deviates from what would be expected if the marks were randomly distributed over the spatial locations of the points. The testing is carried out with permutation tests to randomize expression level and keeping cells location fixed. Four summary statistics are reported: conditional mean (E-mark), conditional variance (V-mark), Stoyan’s mark correlation and the mark-variogram.

nnSVG is a scalable approach to identify spatially variable genes (SVGs) based on nearest-neighbor Gaussian processes (NNGP) model. It uses squared exponential covariance function to model the spatial patterns and estimates a gene-specific length scale parameter within the spatial covariance function in Gaussian Processes (GPs). The recent statistical advancements in computationally scalable parameter estimation enables low computational complexity for GPs model fitting.