Visualizing structure and transitions in high-dimensional biological data
Authors: Kevin R Moon
Kristina Yim
David van Dijk
Ronald R Coifman
William S Chen
Guy Wolf
Scott Gigante
Matthew J Hirn
Zheng Wang
Antonia van den Elzen
Smita Krishnaswamy
Daniel B Burkhardt
Natalia B Ivanova
Journal: Nature Biotechnology (2019)
Discipline: BIOLOGY & BIOCHEMISTRY
Keywords: High-dimensional data; Visualization tools; PHATE; Information-geometric distance; Nonlinear structure
Affiliations: Department of Mathematics and Statistics, Utah State University, Logan, UT, USA., Cardiovascular Research Center, section Cardiology, Department of Internal Medicine, Yale University, New Haven, CT, USA., Department of Computer Science, Yale University, New Haven, CT, USA., School of Basic Medicine, Qingdao University, Qingdao, China., Yale Stem Cell Center, Department of Genetics, Yale University, New Haven, CT, USA., Computational Biology and Bioinformatics Program, Yale University, New Haven, CT, USA., Department of Genetics, Yale University, New Haven, CT, USA., Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, USA., Department of Mathematics, Michigan State University, East Lansing, MI, USA., Applied Mathematics Program, Yale University, New Haven, CT, USA., Department of Genetics, Center for Molecular Medicine, University of Georgia, Athens, GA, USA. ., Department of Mathematics and Statistics, Université de Montréal, Montréal, Quebec, Canada. ., Mila-Quebec Artificial Intelligence Institute, Montréal, Quebec, Canada. ., Department of Computer Science, Yale University, New Haven, CT, USA. ., Department of Genetics, Yale University, New Haven, CT, USA. .

Abstract:  The high-dimensional data created by high-throughput technologies require visualization tools that reveal data structure and patterns in an intuitive form. We present PHATE, a visualization method that captures both local and global nonlinear structure using an information-geometric distance between data points. We compare PHATE to other tools on a variety of artificial and biological datasets, and find that it consistently preserves a range of patterns in data, including continual progressions, branches and clusters, better than other tools. We define a manifold preservation metric, which we call denoised embedding manifold preservation (DEMaP), and show that PHATE produces lower-dimensional embeddings that are quantitatively better denoised as compared to existing visualization methods. An analysis of a newly generated single-cell RNA sequencing dataset on human germ-layer differentiation demonstrates how PHATE reveals unique biological insight into the main developmental branches, including identification of three previously undescribed subpopulations. We also show that PHATE is applicable to a wide variety of data types, including mass cytometry, single-cell RNA sequencing, Hi-C and gut microbiome data. 

Retracted: No

PubPeer comments:
 Authors did not disclose the fact that their benchmarking tool, **DEMaP** , is derived from their own method, and that the reference ( geodesic distance ) is implemented on a separate library named **graphtools** . In fact, the geodesic distance they define is a direct result of this algorithm, and not applied in an unbiased fashion. **Graphtools** performs virtually **all** PHATE computations (defines the kernel, estimate affinities, diffusion operator), with the exception of the MDS embedding and is called from within the main PHATE script . A direct result is that any method based on such a library that is used both for computations AND benchmarking will invariably score better than others, as the DEMaP metric is defined as the spearman correlation between such geodesic distance and the embedded distance - in PHATE, both are defined by almost identical computations. A similar result would be possible for t-SNE if the reference measure ( geodesic distance ) were also defined on the same algorithm. This explains why Fig. 4b shows PHATE outperforming existing methods despite its poorer visual representation when compared to UMAP and t-SNE in Fig.5, for instance. ,