Dimensionality reduction plots

Version Compatibility

Reference examples tested with: scanpy 1.10+, anndata 0.10+, scikit-learn 1.4+, umap-learn 0.5+, openTSNE 1.0+, phate 1.0+, ggplot2 3.5+, PCAtools 2.16+, matplotlib 3.8+.

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then help(module.function) to check signatures
• R: packageVersion('<pkg>') then ?function_name to verify parameters

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Dimensionality-Reduction Plots

"Make a PCA / UMAP / t-SNE plot" -> Choose a projection method aligned with what the plot must reveal — variance explained (PCA), local neighborhood structure (t-SNE), manifold approximation with some global structure (UMAP), or continuous transitions (PHATE). Set hyperparameters deliberately. Communicate the projection's limits and refuse to over-interpret 2D distances.

• Python: sklearn.decomposition.PCA, openTSNE, umap-learn, phate, scanpy.tl.umap / scanpy.tl.tsne / scanpy.tl.pca
• R: prcomp, PCAtools::pca, Seurat::RunPCA / RunUMAP / RunTSNE, phateR

The Single Most Important Modern Insight -- 2D Embeddings Distort

Chari & Pachter 2023 PLOS Comp Biol 19:e1011288 demonstrated that 2D embeddings of single-cell data lose >95% of the high-dimensional geometry — local neighborhoods are preserved by construction, but distances between distant cells, density estimates, and global topology are NOT preserved. The "specious art" of single-cell genomics is the practice of reading 2D layout as biology.

Practical consequence: a UMAP plot communicates "these cells are similar locally" and nothing more. Distance between clusters is meaningless. Density of points within a cluster is dominated by the embedding's repulsion parameter, not the underlying biology. A trajectory inferred from "the gap" between two clusters in UMAP space is an artifact unless validated against the high-dimensional data (RNA velocity, diffusion pseudotime, PHATE).

A second foundational paper is Kobak & Berens 2019 Nat Commun 10:5416 on t-SNE for single-cell: PCA initialization + early-exaggeration + multi-scale similarity kernels recover more global structure than default t-SNE settings. The same logic applies to UMAP via init='spectral' (default) and min_dist.

Algorithmic Taxonomy

Method	Preserves	Hyperparameters	Strength	Fails when
PCA	Linear variance (orthogonal, ordered)	n_components, scaling	Interpretable via loadings; deterministic; variance % per axis	Non-linear manifolds; high-dim data with few effective dims
t-SNE (van der Maaten 2008)	Local neighborhoods (Student-t similarity)	perplexity (typ. 30-50), learning_rate, n_iter, init	Crisp cluster separation	Global distances meaningless; cluster sizes deceptive; non-deterministic
UMAP (McInnes 2018, Becht 2018)	Manifold local + partial global	n_neighbors (typ. 15-50), min_dist (typ. 0.1-0.5), spread	Faster than t-SNE; better global preservation than default t-SNE; deterministic given seed	Still distorts; n_neighbors small -> shattered; large -> homogenized
PHATE (Moon 2019)	Continuous transitions, branching trajectories	k (knn), t (diffusion power)	Best for developmental trajectories; preserves transition geometry	Slower; less canonical for clustering display
Diffusion map	Diffusion distance	epsilon, n_components	Theoretically motivated; supports pseudotime	Less visually striking; less commonly used
MDS / classical MDS	Global Euclidean distances	n_components, dissimilarity matrix	Honest about distance preservation	Computationally expensive >5000 points
Isomap	Geodesic distance on knn graph	n_neighbors, n_components	Captures non-linear manifold	Sensitive to k; less popular than UMAP
Force-directed (PAGA, ForceAtlas2)	Graph topology	Layout-specific	Best for connectivity (PAGA cluster graph)	Not for dense cells; aesthetic

Decision Tree by Scenario

Scenario	Recommended	Why
Bulk RNA-seq sample QC	PCA on log-vst counts; show PC1 vs PC2 with metadata color	Variance explained is meaningful for batch detection
Single-cell broad cluster overview	UMAP n_neighbors=30, min_dist=0.3 after PCA(50)	Standard; preserves clusters; faster than t-SNE
Single-cell with delicate trajectories	PHATE OR diffusion map	Preserves continuous transitions
Cluster cardinality / boundary visualization	t-SNE with PCA init, perplexity=50 (Kobak-Berens)	Crisper cluster separation than UMAP
Multi-omics integration projection	MOFA factors + PCA, or UMAP of joint embedding	Per-omics projection often misleading
Spatial transcriptomics with histology	UMAP for transcriptional axis; SEPARATE spatial scatter	UMAP collapses physical space
Identify which genes drive variation	PCA biplot with loadings as arrows	Loadings are interpretable; UMAP/t-SNE has no loadings
Demonstrating batch confound	PCA color by batch -- if PC1/PC2 separates batches, batch is the dominant variance	UMAP can hide batch effect via local neighborhood preservation
Visualizing 50 conditions	UMAP/t-SNE for nuance; faceted PCA for interpretability	Method choice depends on question

PCA -- The Underused Workhorse

PCA is interpretable, deterministic, and the loadings explain WHY samples cluster — UMAP/t-SNE cannot do this. For bulk RNA-seq sample QC, PCA is the right answer 90% of the time.

Goal: Project samples into a low-dim space whose axes are linear combinations of features ordered by variance explained, then visualize PC1 vs PC2 colored by metadata.

Approach: Variance-stabilize counts (DESeq2 vst() / rlog()); run PCA on transposed expression matrix; annotate axes with variance-explained percentages; layer screeplot and loadings plot to support interpretation.

library(DESeq2)
library(PCAtools)
library(ggplot2)
vsd <- vst(dds, blind = FALSE)
p <- pca(assay(vsd), metadata = as.data.frame(colData(dds)))
biplot(p, colby = 'condition', shape = 'batch', lab = NULL,
       hline = 0, vline = 0,
       legendPosition = 'right',
       title = paste0('PCA: PC1 (', round(p$variance[1], 1), '%) vs PC2 (', round(p$variance[2], 1), '%)'))
screeplot(p, components = 1:10)
loadings_plot <- plotloadings(p, components = 1, rangeRetain = 0.05)

from sklearn.decomposition import PCA
import matplotlib.pyplot as plt

pca = PCA(n_components=10)
X_pca = pca.fit_transform(X)
var = pca.explained_variance_ratio_

fig, axes = plt.subplots(1, 2, figsize=(10, 4))
axes[0].scatter(X_pca[:, 0], X_pca[:, 1], c=labels, alpha=0.7)
axes[0].set_xlabel(f'PC1 ({var[0]*100:.1f}%)')
axes[0].set_ylabel(f'PC2 ({var[1]*100:.1f}%)')
axes[1].plot(range(1, 11), var, 'o-')
axes[1].set_xlabel('PC')
axes[1].set_ylabel('Variance explained')

Always label axes with variance explained. A PCA plot without PC1 (45%) annotation is unreadable. If PC1 = 5% and PC2 = 4%, apparent "clusters" may be noise.

t-SNE -- Kobak-Berens Modern Defaults

Default t-SNE (Maaten 2008) loses global structure. Kobak-Berens 2019 demonstrated that three changes recover it:

1. Initialize with PCA, not random — init='pca' (openTSNE) or pre-compute PCA scores as init
2. High learning rate — learning_rate = n/12 (n = number of points), not the default 200
3. Early exaggeration — exaggeration=12, early_exaggeration_iter=250 for large data

import openTSNE
import numpy as np

# Kobak-Berens defaults
embedding = openTSNE.TSNE(
    perplexity=30,                          # 30-50 typical
    n_iter=750,
    initialization='pca',                   # NOT random
    learning_rate=X.shape[0] / 12,          # scales with n
    n_jobs=-1,
    random_state=42).fit(X)

library(Rtsne)
set.seed(42)
ts <- Rtsne(X, perplexity = 30, theta = 0.5, pca_scale = TRUE,
            initial_dims = 50, max_iter = 750)
# Rtsne does not natively support PCA initialization; use external init via Y_init=

Perplexity is the local-vs-global trade-off. Low (5) -> local; high (100) -> global. 30-50 is standard for >1000 points.

UMAP -- Modern Defaults and the Random-Seed Trap

import umap
reducer = umap.UMAP(
    n_neighbors=30,        # local-global balance; 15-50 typical
    min_dist=0.3,          # tightness of clusters; 0.1-0.5 typical
    n_components=2,
    metric='euclidean',
    random_state=42)       # reproducibility
embedding = reducer.fit_transform(X)

library(uwot)
set.seed(42)
um <- umap(X, n_neighbors = 30, min_dist = 0.3, metric = 'euclidean')

# scanpy convention -- after sc.tl.pca, sc.pp.neighbors
sc.pp.neighbors(adata, n_neighbors=30, n_pcs=50)
sc.tl.umap(adata, min_dist=0.3, random_state=42)
sc.pl.umap(adata, color='leiden', palette='tab20', frameon=False,
           legend_loc='on data', legend_fontsize=7,
           save='_clusters.pdf')

min_dist controls tightness, NOT separation. Smaller min_dist = tighter clusters. Does not change which cells cluster together — only how dense the rendering is.

n_neighbors controls local-vs-global. Small n_neighbors = local fragmentation; large n_neighbors = clusters merge.

Random seed matters. UMAP is deterministic given seed; without setting seed, results vary across runs. Always set random_state (umap-learn) or seed= (uwot).

scanpy.pl.umap save trap: save='_x.pdf' writes to sc.settings.figdir (default ./figures/) with prefix umap, producing figures/umap_x.pdf — not the path specified. Default dpi_save = 150 is below journal requirements.

PHATE -- For Continuous Trajectories

import phate
phate_op = phate.PHATE(knn=10, decay=40, t='auto', n_jobs=-1, random_state=42)
emb = phate_op.fit_transform(X)
plt.scatter(emb[:, 0], emb[:, 1], c=pseudotime, cmap='viridis', s=5)

PHATE preserves transition geometry — for embryonic development, differentiation trajectories, or any continuous-state biology, PHATE is more faithful than UMAP. For discrete cell types, UMAP is fine.

Per-Method Failure Modes

Over-interpreting UMAP distances

Trigger: Reading "cluster A is closer to cluster B than to C" as biological similarity.

Mechanism: UMAP preserves local neighborhoods; global distances are NOT preserved (Chari-Pachter 2023).

Symptom: Conclusion contradicts hierarchical clustering / RNA velocity / known biology.

Fix: Validate inter-cluster relationships against high-dimensional metrics (correlation, distance in PCA space, RNA velocity).

t-SNE / UMAP without random seed

Trigger: Reproducibility request; figure differs between runs.

Mechanism: Both methods use stochastic optimization; default seed varies.

Symptom: Re-running the script produces visibly different layouts.

Fix: Set random_state=42 (umap-learn, sklearn) or seed=42 (R uwot/Rtsne).

Perplexity too low for the data

Trigger: Default t-SNE perplexity (30) on small dataset (<500 points).

Mechanism: Perplexity > n/3 fails; cells artificially fragment.

Symptom: Plot shows "shattered" small clusters that don't correspond to biology.

Fix: For small n: perplexity = max(5, n/30). For very large n: perplexity 50-100.

PCA without scaling

Trigger: prcomp(X) or PCA().fit(X) without scaling rows/columns first.

Mechanism: Genes with high absolute expression dominate variance; PCA captures library-size effect rather than biological variation.

Symptom: PC1 perfectly correlates with library size or with total expression.

Fix: Use vst() / rlog() (DESeq2) or log + scale (prcomp(X, scale.=TRUE)). For single-cell, normalize then sc.pp.scale_data.

UMAP cluster shapes "interpreted" as biological signal

Trigger: Reporting that a cluster is "elongated" or "round" as biological observation.

Mechanism: UMAP cluster shape is an artifact of min_dist and n_neighbors, not biology.

Symptom: Reviewer asks "why is the immune cluster elongated?"; no answer except the embedding.

Fix: Do not interpret cluster shape. Report cluster membership and validate biology via marker genes.

scanpy.pl.umap save writes to figures/ subdirectory

Trigger: sc.pl.umap(adata, save='myplot.pdf') with the expectation that myplot.pdf will land in the current directory.

Mechanism: save= is concatenated with sc.settings.figdir (default ./figures/) and prefixed with umap.

Symptom: File not at the requested path; actually at figures/umapmyplot.pdf.

Fix: Set sc.settings.figdir='/abs/path/' AND save='_descriptive.pdf' so result is figures/umap_descriptive.pdf. For full path control use matplotlib.savefig after sc.pl.umap(show=False).

Default DPI 150 below journal requirements

Trigger: scanpy sc.settings.set_figure_params() default dpi_save=150.

Mechanism: Nature/Cell require 300+ DPI for raster.

Symptom: Figure looks fine on screen, rejected at submission.

Fix: sc.set_figure_params(dpi_save=300, figsize=(4, 4)).

PCA loadings interpreted on UMAP/t-SNE coordinates

Trigger: "PC1 axis on UMAP" — projecting loadings onto UMAP.

Mechanism: UMAP/t-SNE coordinates have no linear interpretation; loadings are PCA-specific.

Symptom: Conclusion about "what UMAP-x means" that has no foundation.

Fix: Use PCA when loadings are needed. Show UMAP for visualization and PCA for axis-driving gene identification, separately.

Reconciliation: When Methods Disagree

Pattern	Likely cause	Action
t-SNE shows distinct clusters; UMAP merges them	t-SNE over-emphasizes local structure; UMAP n_neighbors too large	Both views valid; check Leiden cluster assignments rather than embedding
PCA shows batch on PC1; UMAP hides it	UMAP preserves local neighborhood within each batch	Run UMAP only after batch correction; PCA is the canonical batch-effect diagnostic
PHATE shows continuous trajectory; UMAP shows discrete clusters	PHATE preserves transitions; UMAP "blobifies" continuous data	Use PHATE for trajectory display; UMAP for discrete cell-type display
Reproducibility breaks across re-runs	Random seed not set	Set seed; document version of umap-learn/openTSNE
Cluster boundaries differ between Seurat/scanpy UMAP	Different defaults for n_neighbors, min_dist, init	Standardize hyperparameters; report explicitly

Operational rule: report ALL hyperparameters used (perplexity, n_neighbors, min_dist, random_state). State the embedding's interpretation limit ("local neighborhood; distances between clusters not meaningful"). For trajectory claims, validate with RNA velocity, pseudotime, or PHATE.

Quantitative Thresholds

Threshold	Value	Source
t-SNE perplexity	30-50 for n>1000; max(5, n/30) for n<500	Maaten 2008; Kobak-Berens 2019
UMAP n_neighbors	15-50 default range	umap-learn docs; Becht 2018
UMAP min_dist	0.1-0.5	Tighter for crisp clusters, looser for continua
t-SNE learning rate	n / 12 (Kobak-Berens)	Default 200 over-shrinks large data
PCA n_components for downstream UMAP	30-50	Standard scanpy workflow
Single-cell n_neighbors for sc.pp.neighbors	15-30	Wolf 2018 Scanpy paper
Save DPI for publication	300+	Nature/Cell figure guidelines
Random seed	42 (or any fixed integer)	Reproducibility

Common Errors

Error / symptom	Cause	Solution
Plot differs between runs	Random seed not set	random_state=42 always
PC1 = library size	No scaling/normalization	vst() or log + scale before PCA
Cluster shapes "interpreted" biologically	UMAP artifact	Do not interpret shape; report membership
scanpy save writes to wrong path	figdir + prefix concatenation	Set figdir explicitly OR use matplotlib.savefig
t-SNE fragments small dataset	Perplexity too high for n	Use perplexity = max(5, n/30)
Inter-cluster "distance" used in trajectory claim	UMAP distances not meaningful	Validate with RNA velocity / PHATE
Loadings interpreted on UMAP axes	UMAP has no loadings	Use PCA for loading-driven interpretation

Anticipated Reviewer Pushback

Pushback	Standard response
"Why UMAP and not t-SNE?"	UMAP for cluster overview (faster, better global preservation given Becht 2018); t-SNE in supplementary if cluster boundaries are the focus
"What hyperparameters?"	Explicit n_neighbors, min_dist, n_pcs, random_state in caption AND methods
"Why is cluster X shaped this way?"	UMAP/t-SNE cluster shape is an embedding artifact; cluster membership is the biological observation
"Are these trajectories real?"	Validated via RNA velocity / PHATE / diffusion pseudotime (NOT inferred from UMAP layout alone)
"Why PCA?"	Variance explained per axis is interpretable for sample QC; loadings identify driving genes (uniquely PCA, NOT UMAP)

References

• Becht E, McInnes L, Healy J, et al. 2019. Dimensionality reduction for visualizing single-cell data using UMAP. Nat Biotechnol 37(1):38-44.
• Chari T, Pachter L. 2023. The specious art of single-cell genomics. PLOS Comp Biol 19(8):e1011288.
• Kobak D, Berens P. 2019. The art of using t-SNE for single-cell transcriptomics. Nat Commun 10:5416.
• McInnes L, Healy J, Melville J. 2018. UMAP: Uniform Manifold Approximation and Projection for dimension reduction. arXiv:1802.03426.
• Moon KR, van Dijk D, Wang Z, et al. 2019. Visualizing structure and transitions in high-dimensional biological data. Nat Biotechnol 37(12):1482-1492.
• van der Maaten L, Hinton G. 2008. Visualizing data using t-SNE. J Mach Learn Res 9:2579-2605.
• Wolf FA, Angerer P, Theis FJ. 2018. SCANPY: large-scale single-cell gene expression data analysis. Genome Biol 19:15.

Related Skills

• single-cell/preprocessing - PCA / neighbor-graph computation before embedding
• single-cell/clustering - Leiden / Louvain cluster assignments visualized in UMAP
• single-cell/trajectory-inference - PHATE, diffusion pseudotime, RNA velocity for trajectory claims
• data-visualization/color-palettes - Categorical palette for cluster labels
• data-visualization/distribution-plots - Per-cluster gene-expression follow-up
• data-visualization/heatmaps-clustering - Alternative view of the same high-dim matrix