Dimensionality Reduction

A linear transformation that identifies orthogonal axes of maximum variance in the data. PCA computes the principal components—linear combinations of genes—that capture the dominant transcriptional programs while filtering out technical noise.

• Computed via singular value decomposition (SVD) on the centered, scaled count matrix
• Typically retains 30–50 PCs for downstream clustering
• Assumes linear relationships between features
• Fast, deterministic, and highly interpretable

Example: In a PBMC dataset, PC1 often separates lymphoid from myeloid lineages based on variance in immune marker genes.

A non-linear dimensionality reduction technique optimized for preserving local neighborhood structure. t-SNE converts high-dimensional Euclidean distances into conditional probabilities representing similarities, then minimizes the Kullback-Leibler divergence between high- and low-dimensional distributions.

• Excels at revealing discrete cell clusters
• Perplexity hyperparameter controls the balance between local and global structure (typical range: 30–50)
• Non-deterministic; different runs produce different layouts
• Computationally intensive for large datasets (>100k cells)

Limitation: Global distances between clusters are not interpretable; cluster size and separation in the t-SNE plot do not reflect true relationships.

A manifold learning technique that constructs a fuzzy topological representation of the high-dimensional data and optimizes a low-dimensional embedding to preserve both local and global structure. UMAP assumes the data lies on a Riemannian manifold and uses category theory to approximate it.

• Better preservation of global structure than t-SNE
• Faster runtime via stochastic gradient descent optimization
• Key parameters: n_neighbors (local vs. global balance) and min_dist (point packing tightness)
• Deterministic when a random seed is set

Example: UMAP often reveals continuous trajectories (e.g., differentiation hierarchies) that t-SNE fragments into isolated islands.

A spectral method that embeds cells based on diffusion distances—the probability of transitioning between cells through a random walk on the data manifold. Diffusion maps excel at capturing continuous developmental trajectories because diffusion distance integrates over all paths, making it robust to noise and sampling density variations.

• Constructs a Markov transition matrix from the k-nearest neighbor graph
• Eigenvectors of this matrix define the embedding coordinates (diffusion components)
• Naturally recovers pseudotemporal ordering without explicit trajectory inference
• Parameter t (diffusion time) controls the scale of structure revealed

Use case: Hematopoietic stem cell differentiation hierarchies where continuous branching structure is critical.

Neural network architectures that learn a compressed latent representation of single-cell data through an encoder-decoder framework. The encoder compresses the gene expression vector into a low-dimensional bottleneck, and the decoder reconstructs the original input, forcing the bottleneck to capture essential biological variation.

• Variational autoencoders (VAEs) impose a probabilistic prior on the latent space, enabling generative sampling
• Can model non-linear gene-gene interactions missed by linear methods
• Denoising autoencoders explicitly correct for dropout events
• Tools like scVI integrate batch correction directly into the latent space

Advantage: Simultaneously performs dimensionality reduction, imputation, and batch correction in a unified probabilistic framework.

A linear decomposition method that separates a multivariate signal into additive, statistically independent components. Unlike PCA, which maximizes variance and enforces orthogonality, ICA maximizes non-Gaussianity to identify biologically meaningful gene modules that operate independently.

• Recovers gene expression programs representing distinct biological processes
• Assumes source signals are non-Gaussian and mutually independent
• Useful for deconvolving overlapping transcriptional signatures
• Applied in cell-type deconvolution of bulk RNA-seq using single-cell reference signatures

Example: ICA can separate cell-cycle gene programs from stress-response programs that PCA would conflate into a single component.