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Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems.
Shape descriptors for non-rigid shapes with a single closed contour
L. Latecki, R. Lakamper, and T. Eckhardt · 2000
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Topological persistence and simplification
H. Edelsbrunner, D. Letcher, and A. Zomorodian · 2002
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Algebraic Topology
A. Hatcher · 2002
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Stability of persistence diagrams
D. Cohen-Steiner, H. Edelsbrunner, and J. Harer · 2007
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On the local behavior of spaces of natural images
G. Carlsson, T. Ishkhanov, V. de Silva, and A. Zomorodian · 2008
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Topological analysis of population activity in visual cortex
G. Singh, F. Memoli, T. Ishkhanov, G. Sapiro, G. Carlsson, and D.L. Ringach · 2008
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Integrating contour and skeleton for shape classification
X. Bai, W. Liu, and Z. Tu · 2009
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Topology and data
G. Carlsson · 2009
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Gromov-Hausdorff stable signatures for shapes using persistence
F. Chazal, D. Cohen-Steiner, L. J. Guibas, F. Mémoli, and S. Y. Oudot · 2009
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Lipschitz functions have L p L_{p} -stable persistence
D. Cohen-Steiner, H. Edelsbrunner, J. Harer, and Y. Mileyko · 2010
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Computational Topology : An Introduction
H. Edelsbrunner and J. L. Harer · 2010
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Imagenet classification with deep convolutional neural networks
A. Krizhevsky, I. Sutskever, and G. E. Hinton · 2012
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The ring of algebraic functions on persistence bar codes
A. Adcock, E. Carlsson, and G. Carlsson · 2013
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Persistence-based clustering in Riemannian manifolds
F. Chazal, L.J. Guibas, S.Y. Oudot, and P. Skraba · 2013
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Morse theory for filtrations and efficient computation of persistent homology
K. Mischaikow and V. Nanda · 2013
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Stochastic convergence of persistence landscapes and silhouettes
F. Chazal, B.T. Fasy, F. Lecci, A. Rinaldo, and L. Wassermann · 2014
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Persistence-based structural recognition
C. Li, M. Ovsjanikov, and F. Chazal · 2014
A stable multi-scale kernel for topological machine learning
R. Reininghaus, U. Bauer, S. Huber, and R. Kwitt · 2015
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Deep graph kernels
P. Yanardag and S.V.N. Vishwanathan · 2015
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Feature-based classification of networks
I. Barnett, N. Malik, M.L. Kuijjer, P.J. Mucha, and J.-P. Onnela · 2016
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Persistent homology analysis of brain artery trees
P. Bendich, J.S. Marron, E. Miller, A. Pieloch, and S. Skwerer · 2016
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Deep residual learning for image recognition
K. He, X. Zhang, S. Ren, and J. Sun · 2016
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Persistence weighted Gaussian kernel for topological data analysis
G. Kusano, K. Fukumizu, and Y. Hiraoka · 2016
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Persistent homology transform for modeling shapes and surfaces
K. Turner, S. Mukherjee, and D. M. Boyer · 2014
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Bag of contour fragments for robust shape classification
X. Wang, B. Feng, X. Bai, W. Liu, and L.J. Latecki · 2014
Cited alongside, same era.
Statistical topological data analysis using persistence landscapes
P. Bubenik · 2015
Cited alongside, same era.
Statistical topological data analysis - a kernel perspective
R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer · 2015
Cited alongside, same era.
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Learning convolutional neural networks for graphs
M. Niepert, M. Ahmed, and K. Kutzkov · 2016
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Persistence images: A stable vector representation of persistent homology
H. Adams, T. Emerson, M. Kirby, R. Neville, C. Peterson, P. Shipman, S. Chepushtanova, E. Hanson, F. Motta, and L. Ziegelmeier · 2017
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PointNet: Deep learning on point sets for 3D classification and segmentation
C.R. Qi, H. Su, K. Mo, and L.J. Guibas · 2017
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Deep learning with sets and point clouds
S. Ravanbakhsh, S. Schneider, and B. Póczos · 2017
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