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We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes.
A course in metric geometry
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Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements
Xavier Pennec · 2006
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On the use of Gromov-Hausdorff Distances for Shape Comparison
Facundo Memoli · 2007
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Gradient flows: in metric spaces and in the space of probability measures
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IAM graph database repository for graph based pattern recognition and machine learning
Kaspar Riesen and Horst Bunke · 2008
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An introduction to Riemann-Finsler geometry
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Learning in Riemannian orbifolds
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The space of spaces: curvature bounds and gradient flows on the space of metric measure spaces
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Gromov-Wasserstein alignment of word embedding spaces
David Alvarez-Melis and Tommi Jaakkola · 2018
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Gromov-Monge quasi-metrics and distance distributions
Facundo Mémoli and Tom Needham · 2018
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Learning generative models across incomparable spaces
Charlotte Bunne, David Alvarez-Melis, Andreas Krause, and Stefanie Jegelka · 2019
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The gromov–wasserstein distance between networks and stable network invariants
Samir Chowdhury and Facundo Mémoli · 2019
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A quotient space formulation for statistical analysis of graphical data
Xiaoyang Guo, Anuj Srivastava, and Sudeep Sarkar · 2019
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Reigo Hendrikson · 2016
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Gromov-Wasserstein averaging of kernel and distance matrices
Gabriel Peyré, Marco Cuturi, and Justin Solomon · 2016
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Entropic metric alignment for correspondence problems
Justin Solomon, Gabriel Peyré, Vladimir G Kim, and Suvrit Sra · 2016
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GWCNN: A metric alignment layer for deep shape analysis
Danielle Ezuz, Justin Solomon, Vladimir G Kim, and Mirela Ben-Chen · 2017
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POT: Python Optimal Transport library, 2017
Rémi Flamary and Nicolas Courty · 2017
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Gromov-Wasserstein statistics Github repository
Samir Chowdhury and Tom Needham
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Vayer Titouan, Nicolas Courty, Romain Tavenard, and Rémi Flamary · 2019
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