概念
一、SVG 的數學直覺
給定基因 g 在每個 spot 的表達 ei 與座標 (xi, yi)，「SVG」測試的是：e 跟 (x, y) 之間是否存在比隨機更顯著的空間自相關 (spatial autocorrelation)。
最常見的指標：
- Moran's I：經典空間統計，把每個 spot 跟鄰居比較加權平均；快、可解釋。
- Geary's C：類似 Moran's I 但對「相鄰差異」更敏感。
- Gaussian Process 系列（SpatialDE、nnSVG）：把 expression 視為 GP，估計 lengthscale 與 variance。
- SPARK / SPARK-X：用 multiple kernels 做 mixed-effects 檢定，scalable。
Given gene g with expression ei at coordinate (xi, yi) per spot, the SVG test asks: is there significant spatial autocorrelation between e and (x, y) beyond chance?
Most common scores:
- Moran's I: classic spatial statistic; weighted average of differences with neighbors. Fast, interpretable.
- Geary's C: similar to Moran's I but more sensitive to local differences.
- Gaussian Process family (SpatialDE, nnSVG): expression as GP — estimate lengthscale and variance.
- SPARK / SPARK-X: mixed-effects tests with multiple kernels; scalable.
方法比較
二、五大主流方法
| 方法 | 原理 | 2025 benchmark | 速度 | ||
|---|---|---|---|---|---|
| SPARK-X | multi-kernel non-parametric | 平均相關 0.88，整體第一 | ★★★★★ | Multi-kernel non-parametric | Avg correlation 0.88, top method |
| SpatialDE2 | Gaussian Process | 平均相關 0.81 | ★★ | Gaussian Process | Avg correlation 0.81 |
| nnSVG | Nearest-neighbor GP，可 scale 到大資料 | 平均相關 0.80；spatial-aware | ★★★ | Nearest-neighbor GP, scalable | Avg correlation 0.80; spatially-aware |
| Moran's I | 傳統空間自相關 | 平均相關 0.76，強大基線 | ★★★★★ | Classical spatial autocorrelation | Avg correlation 0.76, strong baseline |
| SpatialDE | 原版 GP | 記憶體吃緊；早期工作的代表 | ★ | Original GP | Memory hungry; historical reference |
實務建議：大資料 → SPARK-X；想要解釋直觀 → Moran's I（Squidpy 內建）；要看 lengthscale 結構 → nnSVG。
Practical tip: for large datasets → SPARK-X; for intuitive interpretation → Moran's I (built into Squidpy); to inspect lengthscale → nnSVG.
互動模擬
互動：什麼樣的 pattern 會被判定為 SVG？
切換 4 種模擬模式，左側顯示空間表達，右上顯示 Moran's I（越大越「空間」）。觀察：均勻雜訊 → I≈0；連續梯度 → I 大；隨機高斑點 → I 中等。
Try four simulated patterns. Left: spatial expression. Top-right: Moran's I (larger = more spatial). Uniform noise → I≈0; smooth gradient → high I; random hotspots → moderate I.
Moran's I = —
程式碼
實作
# nnSVG (Bioconductor) library(nnSVG) spe <- nnSVG(spe, assay_name = "logcounts") top <- rowData(spe)$gene_name[order(rowData(spe)$padj)][1:20] # Seurat Moran vis <- FindSpatiallyVariableFeatures(vis, assay = "SCT", features = VariableFeatures(vis), selection.method = "moransi") top <- SpatiallyVariableFeatures(vis)[1:20] SpatialFeaturePlot(vis, features = top[1:6])
# Squidpy Moran's I sq.gr.spatial_neighbors(adata, coord_type="generic", delaunay=True) sq.gr.spatial_autocorr(adata, mode="moran", n_perms=100, n_jobs=4) top = adata.uns["moranI"].head(20).index.tolist() sq.pl.spatial_scatter(adata, color=top[:6]) # SPARK-X (R via rpy2 or直接用 R)；Python 替代：SpatialDE2 import SpatialDE res = SpatialDE.test(adata, layer="logcounts") sig = res[res.padj < 0.05].sort_values("FSV", ascending=False)
📝 自我檢測
1. 「Highly Variable Gene」一定是 SVG 嗎？
1. Are HVGs always SVGs?
2. 2025 benchmark 中速度與準確度都領先的是？
2. Best speed–accuracy trade-off in the 2025 benchmark?
3. Moran's I 的核心概念是？
3. Core idea of Moran's I?