title: Diffusion maps for high-dimensional single-cell analysis of differentiation data.
abstract: BACKGROUND
  Single-cell technologies have recently gained popularity in cellular differentiation studies regarding their ability to resolve potential heterogeneities in cell populations. Analyzing such high-dimensional single-cell data has its own statistical and computational challenges. Popular multivariate approaches are based on data normalization, followed by dimension reduction and clustering to identify subgroups. However, in the case of cellular differentiation, we would not expect clear clusters to be present but instead expect the cells to follow continuous branching lineages.
  
  
  RESULTS
  Here, we propose the use of diffusion maps to deal with the problem of defining differentiation trajectories. We adapt this method to single-cell data by adequate choice of kernel width and inclusion of uncertainties or missing measurement values, which enables the establishment of a pseudotemporal ordering of single cells in a high-dimensional gene expression space. We expect this output to reflect cell differentiation trajectories, where the data originates from intrinsic diffusion-like dynamics. Starting from a pluripotent stage, cells move smoothly within the transcriptional landscape towards more differentiated states with some stochasticity along their path. We demonstrate the robustness of our method with respect to extrinsic noise (e.g. measurement noise) and sampling density heterogeneities on simulated toy data as well as two single-cell quantitative polymerase chain reaction datasets (i.e. mouse haematopoietic stem cells and mouse embryonic stem cells) and an RNA-Seq data of human pre-implantation embryos. We show that diffusion maps perform considerably better than Principal Component Analysis and are advantageous over other techniques for non-linear dimension reduction such as t-distributed Stochastic Neighbour Embedding for preserving the global structures and pseudotemporal ordering of cells.
  
  
  METHODS
  The Matlab implementation of diffusion maps for single-cell data is available at https://www.helmholtz-muenchen.de/icb/single-cell-diffusion-map.
  
  
  BACKGROUND
  fbuettner.phys@gmail.com, fabian.theis@helmholtz-muenchen.de
  
  
  BACKGROUND
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Institute of Computational Biology, Helmholtz Zentrum München 85764 Neuherberg, Germany and Department of Mathematics, Technische Universität München 85748 Garching, Germany Institute of Computational Biology, Helmholtz Zentrum München 85764 Neuherberg, Germany and Department of Mathematics, Technische Universität München 85748 Garching, Germany.
authors.forename: Laleh
authors.initials: L
authors.lastname: Haghverdi
authors.affiliation: Institute of Computational Biology, Helmholtz Zentrum München 85764 Neuherberg, Germany and Department of Mathematics, Technische Universität München 85748 Garching, Germany.
authors.forename: Florian
authors.initials: F
authors.lastname: Buettner
authors.affiliation: Institute of Computational Biology, Helmholtz Zentrum München 85764 Neuherberg, Germany and Department of Mathematics, Technische Universität München 85748 Garching, Germany Institute of Computational Biology, Helmholtz Zentrum München 85764 Neuherberg, Germany and Department of Mathematics, Technische Universität München 85748 Garching, Germany.
authors.forename: Fabian J
authors.initials: FJ
authors.lastname: Theis
mesh_terms: D000465:Algorithms; D000818:Animals; D001755:Blastocyst / Q000166:cytology* / Q000378:metabolism; D002454:Cell Differentiation / Q000235:genetics*; D016000:Cluster Analysis; D004058:Diffusion; D053595:Embryonic Stem Cells / Q000166:cytology* / Q000378:metabolism; D005786:Gene Expression Regulation; D006412:Hematopoietic Stem Cells / Q000166:cytology* / Q000378:metabolism; D059014:High-Throughput Nucleotide Sequencing; D006801:Humans; D051379:Mice; D025341:Principal Component Analysis; D011336:Probability; D060888:Real-Time Polymerase Chain Reaction / Q000379:methods; D059010:Single-Cell Analysis / Q000379:methods*