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Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes.
Basic Topology
M. A. Armstrong · 1983
Earlier work this paper cites.
A computational approach to edge detection
J. Canny · 1986
Earlier work this paper cites.
Support-vector networks
C. Cortes and V. Vapnik · 1995
Earlier work this paper cites.
Random decision forests
T. K. Ho · 1995
Earlier work this paper cites.
Representing size functions by complex polynomials
M. Ferri and C. Landi · 1999
Earlier work this paper cites.
Algebraic topology
A. Hatcher · 2002
Earlier work this paper cites.
Outex-new framework for empirical evaluation of texture analysis algorithms
T. Ojala, T. Maenpaa, M. Pietikainen, J. Viertola, J. Kyllonen, and S. Huovinen · 2002
Earlier work this paper cites.
Computational homology
T. Kaczynski, K. M. Mischaikow, M. Mrozek, and K. Mischaikow · 2004
Earlier work this paper cites.
Computing persistent homology
A. Zomorodian and G. Carlsson · 2005
Earlier work this paper cites.
Barcodes: the persistent topology of data
R. Ghrist · 2008
Earlier work this paper cites.
Topology and data
G. Carlsson · 2009
Earlier work this paper cites.
A concise and provably informative multi-scale signature based on heat diffusion
J. Sun, M. Ovsjanikov, and L. Guibas · 2009
Earlier work this paper cites.
Computational Topology - an Introduction
H. Edelsbrunner and J. Harer · 2010
Earlier work this paper cites.
Scikit-learn: Machine learning in Python
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay · 2011
Earlier work this paper cites.
Geometry in the space of persistence modules
V. de Silva and V. Nanda · 2013
Earlier work this paper cites.
Stochastic convergence of persistence landscapes and silhouettes
F. Chazal, B. T. Fasy, F. Lecci, A. Rinaldo, and L. Wasserman · 2014
Earlier work this paper cites.
Simplicial models and topological inference in biological systems
V. Nanda and R. Sazdanovic · 2014
Earlier work this paper cites.
SHREC’14 track: Shape retrieval of non-rigid 3d human models
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian, M. Aono, A. Ben Hamza, A. Bronstein, M. Bronstein, S. Bu, U. Castellani, S. Cheng, V. Garro, A. Giachetti, A. Godil, J. Han, H. Johan, L. Lai, B. Li, C. Li, H. Li, R. Litman, X. Liu, Z. Liu, Y. Lu, A. Tatsuma, and J. Ye · 2014
Earlier work this paper cites.
Fréchet means for distributions of persistence diagrams
K. Turner, Y. Mileyko, S. Mukherjee, and J. Harer · 2014
Earlier work this paper cites.
Statistical topological data analysis using persistence landscapes
P. Bubenik · 2015
Earlier work this paper cites.
An entropy-based persistence barcode
H. Chintakunta, T. Gentimis, R. Gonzalez-Diaz, M. Jimenez, and H. Krim · 2015
Earlier work this paper cites.
Comparing persistence diagrams through complex vectors
B. Di Fabio and M. Ferri · 2015
Cited alongside, same era.
A stable multi-scale kernel for topological machine learning
J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt · 2015
Cited alongside, same era.
The ring of algebraic functions on persistence bar codes
A. Adcock, E. Carlsson, and G. Carlsson · 2016
Cited alongside, same era.
The Structure and Stability of Persistence Modules
F. Chazal, V. de Silva, M. Glisse, and S. Oudot · 2016
Cited alongside, same era.
A primer on the signature method in machine learning
I. Chevyrev and A. Kormilitzin · 2016
Cited alongside, same era.
Characterisation of the idiotypic immune network through persistent entropy
M. Rucco, F. Castiglione, E. Merelli, and M. Pettini · 2016
On the stability of persistent entropy and new summary functions for topological data analysis
N. Atienza, R. Gonzalez-Diaz, and M. Soriano-Trigueros · 2020
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Functional summaries of persistence diagrams
E. Berry, Y.-C. Chen, J. Cisewski-Kehe, and B. T. Fasy · 2020
Later among the works it cites.
Topological approaches to deep learning
G. Carlsson and R. B. Gabrielsson · 2020
Later among the works it cites.
Perslay: A neural network layer for persistence diagrams and new graph topological signatures
M. Carrière, F. Chazal, Y. Ike, T. Lacombe, M. Royer, and Y. Umeda · 2020
Later among the works it cites.
Persistence paths and signature features in topological data analysis
I. Chevyrev, V. Nanda, and H. Oberhauser · 2020
Later among the works it cites.
Vectorization of persistence barcode with applications in pattern classification of porous structures
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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
Cited alongside, same era.
Higher interpolation and extension for persistence modules
P. Bubenik, V. de Silva, and V. Nanda · 2017
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A persistence landscapes toolbox for topological statistics
P. Bubenik and P. Dłotko · 2017
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Sliced wasserstein kernel for persistence diagrams
M. Carriere, M. Cuturi, and S. Oudot · 2017
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Persistence theory: from quiver representations to data analysis
S. Y. Oudot · 2017
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Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms
H. Xiao, K. Rasul, and R. Vollgraf · 2017
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Z. Dong, C. Hu, C. Zhou, and H. Lin · 2020
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Topological autoencoders
M. Moor, M. Horn, B. Rieck, and K. Borgwardt · 2020
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Geometric metrics for topological representations
A. Som, K. N. Ramamurthy, and P. Turaga · 2020
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A comparative study of machine learning methods for persistence diagrams
D. Barnes, L. Polanco, and J. A. Perea · 2021
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Signatures, lipschitz-free spaces, and paths of persistence diagrams
C. Giusti and D. Lee · 2021
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Atol: Measure vectorization for automatic topologically-oriented learning
M. Royer, F. Chazal, C. Levrard, Y. Umeda, and Y. Ike · 2021
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Persistence codebooks for topological data analysis
B. Zieliński, M. Lipiński, M. Juda, M. Zeppelzauer, and P. Dłotko · 2021
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Persistent homology for breast tumor classification using mammogram scans
A. Asaad, D. Ali, T. Majeed, and R. Rashid · 2022
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Persistence curves: A canonical framework for summarizing persistence diagrams
Y. Chung and A. Lawson · 2022
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A topological machine learning pipeline for classification
F. Conti, D. Moroni, and M. A. Pascali · 2022
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Cubical complex
P. Dlotko · 2022
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Dist2Cycle: a simplicial neural network for homology localization
A. Keros, V. Nanda, and K. Subr · 2022
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Approximating continuous functions on persistence diagrams using template functions
J. A. Perea, E. Munch, and F. A. Khasawneh · 2022
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GUDHI User and Reference Manual
The GUDHI Project · 2022
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Capturing dynamics of time-varying data via topology
L. Xian, H. Adams, C. M. Topaz, and L. Ziegelmeier · 2022
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