Bio Data Visualization 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

Decision Tree by Scenario

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.