Continuation of point clouds via persistence diagrams
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- 作者：Marcio Gameiroa ; gameiro@icmc.usp.br" class="auth_mail" title="E-mail the corresponding author ; Yasuaki Hiraokab ; hiraoka@wpi-aimr.tohoku.ac.jp" class="auth_mail" title="E-mail the corresponding author ; Ippei Obayashib ; ippei.obayashi.d8@tohoku.ac.jp" class="auth_mail" title="E-mail the corresponding author
- 关键词：Point cloud ; Persistent homology ; Persistence diagram ; Continuation
- 刊名：Physica D: Nonlinear Phenomena
- 出版年：2016
- 出版时间：1 November 2016
- 年：2016
- 卷：334
- 期：Complete
- 页码：118-132
- 全文大小：1133 K
文摘
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We present a method for continuation of point clouds via persistence diagrams.
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The key property is the differentiability of the persistence map.
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The differentiability allows us to apply the Newton–Raphson method to our setting.
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Our method can solve the inverse problem: from persistence diagrams to point clouds.
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