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. 2019 Feb 4;9:1139. doi: 10.1038/s41598-018-36798-y

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Persistent homology differentiates Gleason 4 poorly formed pattern from cribriform and fused pattern. (a) Representative Gleason 4 ROIs from green cluster iii, comprising cribriform and corded pattern ROIs with attenuated lumen, and blue cluster iv, comprising fused pattern ROIs with lumen preservation. (b) Zero-dimensional and one-dimensional persistence intensity diagrams, for cluster ii and iii respectively, with intensity values ranging 0 to 5 for zero-dimensional diagrams, and 0 to 10 for one-dimensional diagrams, as indicated by the included legend. (c) Hierarchical Ward clustering results of first six principle components, with t-SNE dimensionality reduction for visualization, with unique clusters indicated by color, and Gleason pattern indicated by shape (Gleason 3: circle; Gleason 4: triangle; Gleason 5: square). Relevant clusters ii (red) and iii (blue) are labeled accordingly. Light grey points correspond to Gleason 3 and Gleason 5 points present in all clusters, but not considered in this figure. Dark grey points correspond to Gleason 4 points present in clusters other than the two being considered in this figure.