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Visualizing Transitions and Structure for High Dimensional Data Exploration

Kevin R. Moon, David van Dijk, Zheng Wang, Daniel Burkhardt, William S. Chen, Antonia van den Elzen, Matthew J. Hirn, Ronald R. Coifman, Natalia B. Ivanova, Guy Wolf, Smita Krishnaswamy
doi: https://doi.org/10.1101/120378
Kevin R. Moon
1Department of Genetics;
2Applied Mathematics Program;
3Department of Computer Science;
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David van Dijk
1Department of Genetics;
3Department of Computer Science;
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Zheng Wang
4 Yale Stem Cell Center, Department of Genetics, Yale University, New Haven, CT, USA
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Daniel Burkhardt
1Department of Genetics;
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William S. Chen
1Department of Genetics;
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Antonia van den Elzen
1Department of Genetics;
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Matthew J. Hirn
5 Department of Computational Mathematics, Science and Engineering;
6 Department of Mathematics, Michigan State University, East Lansing, MI, USA
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Ronald R. Coifman
2Applied Mathematics Program;
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Natalia B. Ivanova
4 Yale Stem Cell Center, Department of Genetics, Yale University, New Haven, CT, USA
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  • For correspondence: natalia.ivanova@yale.edu
Guy Wolf
2Applied Mathematics Program;
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Smita Krishnaswamy
1Department of Genetics;
3Department of Computer Science;
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  • For correspondence: smita.krishnaswamy@yale.edu
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Abstract

In the era of ‘Big Data’ there is a pressing need for tools that provide human interpretable visualizations of emergent patterns in high-throughput high-dimensional data. Further, to enable insightful data exploration, such visualizations should faithfully capture and emphasize emergent structures and patterns without enforcing prior assumptions on the shape or form of the data. In this paper, we present PHATE (Potential of Heat-diffusion for Affinity-based Transition Embedding) - an unsupervised low-dimensional embedding for visualization of data that is aimed at solving these issues. Unlike previous methods that are commonly used for visualization, such as PCA and tSNE, PHATE is able to capture and highlight both local and global structure in the data. In particular, in addition to clustering patterns, PHATE also uncovers and emphasizes progression and transitions (when they exist) in the data, which are often missed in other visualization-capable methods. Such patterns are especially important in biological data that contain, for example, single-cell phenotypes at different phases of differentiation, patients at different stages of disease progression, and gut microbial compositions that vary gradually between individuals, even of the same enterotype.

The embedding provided by PHATE is based on a novel informational distance that captures long-range nonlinear relations in the data by computing energy potentials of data-adaptive diffusion processes. We demonstrate the effectiveness of the produced visualization in revealing insights on a wide variety of biomedical data, including single-cell RNA-sequencing, mass cytometry, gut microbiome sequencing, human SNP data, Hi-C data, as well as non-biomedical data, such as facebook network and facial image data. In order to validate the capability of PHATE to enable exploratory analysis, we generate a new dataset of 31,000 single-cells from a human embryoid body differentiation system. Here, PHATE provides a comprehensive picture of the differentiation process, while visualizing major and minor branching trajectories in the data. We validate that all known cell types are recapitulated in the PHATE embedding in proper organization. Furthermore, the global picture of the system offered by PHATE allows us to connect parts of the developmental progression and characterize novel regulators associated with developmental lineages.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted December 01, 2017.
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Visualizing Transitions and Structure for High Dimensional Data Exploration
Kevin R. Moon, David van Dijk, Zheng Wang, Daniel Burkhardt, William S. Chen, Antonia van den Elzen, Matthew J. Hirn, Ronald R. Coifman, Natalia B. Ivanova, Guy Wolf, Smita Krishnaswamy
bioRxiv 120378; doi: https://doi.org/10.1101/120378
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Visualizing Transitions and Structure for High Dimensional Data Exploration
Kevin R. Moon, David van Dijk, Zheng Wang, Daniel Burkhardt, William S. Chen, Antonia van den Elzen, Matthew J. Hirn, Ronald R. Coifman, Natalia B. Ivanova, Guy Wolf, Smita Krishnaswamy
bioRxiv 120378; doi: https://doi.org/10.1101/120378

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