High-dimensional embeddings (PCA, UMAP, etc.)

Summary

Dimension-reduction plots (PCA, t-SNE, UMAP) compress many variables into 2D. Axes have no direct unit: interpret them as abstract components. Do not infer scales or absolute distances literally. Emphasize clusters or gradients qualitatively. Use colour/shape to encode known metadata (cell types, batch). Avoid overinterpreting spacing between clusters: embedding algorithms can distort distances. Always specify the algorithm and parameters in caption.

Core rules

• Axis meaning: Do not label axes with original variable names; use generic terms (“Component 1”) and mention variance explained if PCA.
• No absolute scales: Do not mark axes in data units (e.g. gene counts); they are algorithmic axes.
• Cluster caution: Clusters seen are suggestive; don’t read quantitative gene expression values directly from these plots.
• Color encoding: If coloring points, add a legend or labels, and include redundant cues if many categories.
• Reproducibility: Record the random seed or parameters used, as different runs can produce different layouts.

Required context

• Dimensionality reduction method and parameters used.
• The proportion of variance explained by plotted dimensions (if PCA).
• Metadata categories (labels) to encode in the plot.

AI behaviour

• Explain axes: In captions or alt text, clarify axes (e.g. “PC1 and PC2 from PCA of log(expr)” or “UMAP1, UMAP2 from 30 PCs”).
• Avoid false precision: Do not assign numeric interpretation to point positions beyond the relative clustering.
• Check coloring: Ensure distinct categories use clearly separate colors/shapes.

Common failure modes

• Interpreting axes as variables: Saying “higher PC1 means more gene X” (unsupported without loading information).
• Neglecting batch: Plot looks clustered by batch but that context is hidden (should color by batch to reveal artifact).
• Comparing layouts: Using UMAP as if distances are linear (they are not guaranteed meaningful in absolute terms).

Authoritative standards

• Dimension reduction norms: Texts by Butcher & Fowlkes on PCA interpretability. Emphasize semantics: axes are mathematical constructs, not real measures.

Examples

Example: PCA scatter

• Data: Gene expression PCA colored by treatment.
• Check: Axes labeled “PC1 (40% var)”, “PC2 (15% var)”. Legend with treatment names (blue, orange) and possibly shapes.
• Good outcome: Caption “PCA of scaled expression (batch-corrected); shapes= timepoint, colors= treatment, two PCs explaining 55% total variance.”

Example: UMAP clustering

• Data: scRNA-seq of immune cells.
• Check: Color by cell type (distinct colors); caption notes “UMAP of first 30 PCs (Seurat default)”.
• Good outcome: Legend lists cell types, each with distinct color. X/Y axes labeled “UMAP1”, “UMAP2”.