Abstract
In recent years, dimensionality reduction methods have become critical for visualization, exploration, and interpretation of high-throughput, high-dimensional biological data, as they enable the extraction of major trends in the data while discarding noise. However, biological data contains a type of predominant structure that is not preserved in commonly used methods such as PCA and tSNE, namely, branching progression structure. This structure, which is often non-linear, arises from underlying biological processes such as differentiation, graded responses to stimuli, and population drift, which generate cellular (or population) diversity. We propose a novel, affinity-preserving embedding called PHATE (Potential of Heat-diffusion for Affinity-based Trajectory Embedding), designed explicitly to preserve progression structure in data. PHATE provides a denoised, two or three-dimensional visualization of the complete branching trajectory structure in high-dimensional data. It uses heat-diffusion processes, which naturally denoise the data, to compute cell-cell affinities. Then, PHATE creates a diffusion-potential geometry by free-energy potentials of these processes. This geometry captures high-dimensional trajectory structures, while enabling a natural embedding of the intrinsic data geometry. This embedding accurately visualizes trajectories and data distances, without requiring strict assumptions typically used by path-finding and tree-fitting algorithms, which have recently been used for pseudotime orderings or tree-renderings of cellular data. Furthermore, PHATE supports a wide range of data exploration tasks by providing interpretable overlays on top of the visualization. We show that such overlays can emphasize and reveal trajectory end-points, branch points and associated split-decisions, progression-forming variables (e.g., specific genes), and paths between developmental events in cellular state-space. We demonstrate PHATE on single-cell RNA sequencing and mass cytometry data pertaining to embryoid body differentiation, IPSC reprogramming, and hematopoiesis in the bone marrow. We also demonstrate PHATE on non-single cell data including single-nucleotide polymorphism (SNP) measurements of European populations, and 16s sequencing of gut microbiota.
