Fetching the paper…
Reading the bibliography…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data.
On the asymptotic normality of persistent betti numbers
Krebs, J. T. and Polonik, W. (2019) · 1903
Earlier work this paper cites.
A topology layer for machine learning
Brüel-Gabrielsson, R., Nelson, B. J., Dwaraknath, A., Skraba, P., Guibas, L. J., and Carlsson, G. (2019) · 1905
Earlier work this paper cites.
A framework for differential calculus on persistence barcodes
Leygonie, J., Oudot, S., and Tillmann, U. (2019) · 1910
Earlier work this paper cites.
Approximation of reeb spaces with mappers and applications to stochastic filters
Carrière, M. and Michel, B. (2019) · 1912
Earlier work this paper cites.
Curvature measures
Federer, H. (1959) · 1959
Earlier work this paper cites.
Detection of abnormal behavior via nonparametric estimation of the support
Devroye, L. and Wise, G. L. (1980) · 1980
Earlier work this paper cites.
Measuring shapes by size functions
Frosini, P. (1992) · 1992
Earlier work this paper cites.
Critical point theory for distance functions
Grove, K. (1993) · 1993
Earlier work this paper cites.
The framed morse complex and its invariants
Barannikov, S. (1994) · 1994
Earlier work this paper cites.
Measuring mass concentrations and estimating density contour clusters-an excess mass approach
Polonik, W. (1995) · 1995
Earlier work this paper cites.
On nonparametric estimation of density level sets
Tsybakov, A. B. et al. (1997) · 1997
Earlier work this paper cites.
Towards computing homology from finite approximations
Robins, V. (1999) · 1999
Earlier work this paper cites.
Random forests
Breiman, L. (2001) · 2001
Earlier work this paper cites.
Algebraic Topology
Hatcher, A. (2001) · 2001
Earlier work this paper cites.
Central limit theorems for some graphs in computational geometry
Penrose, M. D. and Yukich, J. E. (2001) · 2001
Earlier work this paper cites.
Optimal quantization of the mean measure and application to clustering of measures
Chazal, F., Levrard, C., and Royer, M. (2020) · 2002
Earlier work this paper cites.
Topological persistence and simplification
Edelsbrunner, H., Letscher, D., and Zomorodian, A. (2002) · 2002
Earlier work this paper cites.
Topics in Optimal Transportation
Villani, C. (2003) · 2003
Earlier work this paper cites.
On boundary estimation
Cuevas, A. and Rodríguez-Casal, A. (2004) · 2004
Earlier work this paper cites.
On boundary estimation
Cuevas, A. and Rodríguez-Casal, A. (2004) · 2004
Earlier work this paper cites.
Topological estimation using witness complexes
De Silva, V. and Carlsson, G. (2004) · 2004
Earlier work this paper cites.
Stability of persistence diagrams
Cohen-Steiner, D., Edelsbrunner, H., and Harer, J. (2005) · 2005
Earlier work this paper cites.
Bootstrapping persistent betti numbers and other stabilizing statistics
Roycraft, B., Krebs, J., and Polonik, W. (2020) · 2005
Earlier work this paper cites.
Zomorodian, A. and Carlsson, G. (2005) · 2005
Earlier work this paper cites.
Kernel estimation of density level sets
Cadre, B. (2006) · 2006
Earlier work this paper cites.
Hypothesis testing for shapes using vectorized persistence diagrams
Moon, C. and Lazar, N. A. (2020) · 2006
Earlier work this paper cites.
Homological sensor networks
De Silva, V. and Ghrist, R. (2007) · 2007
Earlier work this paper cites.
Semiconcave functions in Alexandrov’s geometry
Petrunin, A. (2007) · 2007
Earlier work this paper cites.
Topological methods for the analysis of high dimensional data sets and 3d object recognition
Singh, G., Mémoli, F., and Carlsson, G. E. (2007) · 2007
Earlier work this paper cites.
Towards persistence-based reconstruction in euclidean spaces
Chazal, F. and Oudot, S. Y. (2008) · 2008
Earlier work this paper cites.
Finding the homology of submanifolds with high confidence from random samples
Niyogi, P., Smale, S., and Weinberger, S. (2008) · 2008
Earlier work this paper cites.
Topology and data
Carlsson, G. (2009) · 2009
Earlier work this paper cites.
Gromov-hausdorff stable signatures for shapes using persistence
Chazal, F., Cohen-Steiner, D., Guibas, L. J., M’emoli, F., and Oudot, S. Y. (2009b) · 2009
Earlier work this paper cites.
Stability of Curvature Measures
Chazal, F., Cohen-Steiner, D., Lieutier, A., and Thibert, B. (2008) · 2009
Earlier work this paper cites.
Adaptive Hausdorff estimation of density level sets
Singh, A., Scott, C., and Nowak, R. (2009) · 2009
Earlier work this paper cites.
Topological methods for exploring low-density states in biomolecular folding pathways
Yao, Y., Sun, J., Huang, X., Bowman, G. R., Singh, G., Lesnick, M., Guibas, L. J., Pande, V. S., and Carlsson, G. (2009) · 2009
Earlier work this paper cites.
Statistical topology via morse theory persistence and nonparametric estimation
Bubenik, P., Carlsson, G., Kim, P. T., and Luo, Z.-M. (2010) · 2010
Earlier work this paper cites.
Carriere, M., Chazal, F., Glisse, M., Ike, Y., and Kannan, H. (2020) · 2010
Cited alongside, same era.
Boundary measures for geometric inference
Chazal, F., Cohen-Steiner, D., and Mérigot, Q. (2010) · 2010
Cited alongside, same era.
Lipschitz functions have l p-stable persistence
Cohen-Steiner, D., Edelsbrunner, H., Harer, J., and Mileyko, Y. (2010) · 2010
Cited alongside, same era.
Persistence-based structural recognition
Li, C., Ovsjanikov, M., and Chazal, F. (2014) · 2010
Cited alongside, same era.
Data structures for statistical computing in python
McKinney, W. et al. (2010) · 2010
Cited alongside, same era.
Persistence-based segmentation of deformable shapes
Skraba, P., Ovsjanikov, M., Chazal, F., and Guibas, L. (2010) · 2010
Topological analysis of nerves, reeb spaces, mappers, and multiscale mappers
Dey, T. K., Mémoli, F., and Wang, Y. (2017) · 2017
Closest in time.
Homological algebra and data
Ghrist, R. (2017) · 2017
Closest in time.
Deep learning with topological signatures
Hofer, C., Kwitt, R., Niethammer, M., and Uhl, A. (2017) · 2017
Closest in time.
Kernel method for persistence diagrams via kernel embedding and weight factor
Kusano, G., Fukumizu, K., and Hiraoka, Y. (2017) · 2017
Closest in time.
Quantifying similarity of pore-geometry in nanoporous materials
Lee, Y., Barthel, S. D., Dłotko, P., Moosavi, S. M., Hess, K., and Smit, B. (2017) · 2017
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Persistence bag-of-words for topological data analysis
Zieliński, B., Lipiński, M., Juda, M., Zeppelzauer, M., and Dłotko, P. (2010) · 2010
Cited alongside, same era.
A weighted k-nearest neighbor density estimate for geometric inference
Biau, G., Chazal, F., Cohen-Steiner, D., Devroye, L., and Rodriguez, C. (2011) · 2011
Cited alongside, same era.
Probability measures on the space of persistence diagrams
Mileyko, Y., Mukherjee, S., and Harer, J. (2011) · 2011
Cited alongside, same era.
A topological view of unsupervised learning from noisy data
Niyogi, P., Smale, S., and Weinberger, S. (2011) · 2011
Cited alongside, same era.
Scikit-learn: Machine learning in python
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., et al. (2011) · 2011
Cited alongside, same era.
The numpy array: a structure for efficient numerical computation
Walt, S. v. d., Colbert, S. C., and Varoquaux, G. (2011) · 2011
Cited alongside, same era.
Obayashi, I. and Hiraoka, Y. (2017) · 2017
Closest in time.
Hypothesis testing for topological data analysis
Robinson, A. and Turner, K. (2017) · 2017
Closest in time.
Time series classification via topological data analysis
Umeda, Y. (2017) · 2017
Closest in time.
Statistical analysis and parameter selection for mapper
Carriere, M., Michel, B., and Oudot, S. (2018) · 2018
Closest in time.
How many directions determine a shape and other sufficiency results for two topological transforms
Curry, J., Mukherjee, S., and Turner, K. (2018) · 2018
Closest in time.
Large scale computation of means and clusters for persistence diagrams using optimal transport
Lacombe, T., Cuturi, M., and Oudot, S. (2018) · 2018
Closest in time.
Topological function optimization for continuous shape matching
Poulenard, A., Skraba, P., and Ovsjanikov, M. (2018) · 2018
Closest in time.
Estimating the reach of a manifold
Aamari, E., Kim, J., Chazal, F., Michel, B., Rinaldo, A., Wasserman, L., et al. (2019) · 2019
Closest in time.
The accumulated persistence function, a new useful functional summary statistic for topological data analysis, with a view to brain artery trees and spatial point process applications
Biscio, C. A. and Møller, J. (2019) · 2019
Closest in time.
A statistical test of isomorphism between metric-measure spaces using the distance-to-a-measure signature
Brécheteau, C. et al. (2019) · 2019
Closest in time.
A topological regularizer for classifiers via persistent homology
Chen, C., Ni, X., Bai, Q., and Wang, Y. (2019) · 2019
Closest in time.
Exposition and interpretation of the topology of neural networks
Gabrielsson, R. B. and Carlsson, G. (2019) · 2019
Closest in time.
On the expectation of a persistence diagram by the persistence weighted kernel
Kusano, G. (2019) · 2019
Closest in time.
Fast and accurate tumor segmentation of histology images using persistent homology and deep convolutional features
Qaiser, T., Tsang, Y.-W., Taniyama, D., Sakamoto, N., Nakane, K., Epstein, D., and Rajpoot, N. (2019) · 2019
Closest in time.
Topological data analysis of decision boundaries with application to model selection
Ramamurthy, K. N., Varshney, K., and Mody, K. (2019) · 2019
Closest in time.
Neural persistence: A complexity measure for deep neural networks using algebraic topology
Rieck, B. A., Togninalli, M., Bock, C., Moor, M., Horn, M., Gumbsch, T., and Borgwardt, K. (2019) · 2019
Closest in time.
Dtm-based filtrations
Anai, H., Chazal, F., Glisse, M., Ike, Y., Inakoshi, H., Tinarrage, R., and Umeda, Y. (2020) · 2020
Closest in time.
Functional summaries of persistence diagrams
Berry, E., Chen, Y.-C., Cisewski-Kehe, J., and Fasy, B. T. (2020) · 2020
Closest in time.
A k k -points-based distance for robust geometric inference
Brécheteau, C., Levrard, C., et al. (2020) · 2020
Closest in time.
Probabilistic convergence and stability of random mapper graphs
Brown, A., Bobrowski, O., Munch, E., and Wang, B. (2020) · 2020
Closest in time.
Topological approaches to deep learning
Carlsson, G. and Gabrielsson, R. B. (2020) · 2020
Closest in time.
Perslay: a neural network layer for persistence diagrams and new graph topological signatures
Carrière, M., Chazal, F., Ike, Y., Lacombe, T., Royer, M., and Umeda, Y. (2020) · 2020
Closest in time.
Topological data analysis of single-cell hi-c contact maps
Carrière, M. and Rabadán, R. (2020) · 2020
Closest in time.
Topological data analysis for arrhythmia detection through modular neural networks
Dindin, M., Umeda, Y., and Chazal, F. (2020) · 2020
Closest in time.
The density of expected persistence diagrams and its kernel based estimation
Divol, V. and Chazal, F. (2020) · 2020
Closest in time.
Understanding the topology and the geometry of the persistence diagram space via optimal partial transport
Divol, V. and Lacombe, T. (2020) · 2020
Closest in time.
Pllay: Efficient topological layer based on persistence landscapes
Kim, K., Kim, J., Zaheer, M., Kim, J., Chazal, F., and Wasserman, L. (2020) · 2020
Closest in time.
A bayesian framework for persistent homology
Maroulas, V., Nasrin, F., and Oballe, C. (2020) · 2020
Closest in time.
Topological autoencoders
Moor, M., Horn, M., Rieck, B., and Borgwardt, K. (2020) · 2020
Closest in time.
Uncovering the topology of time-varying fmri data using cubical persistence
Rieck, B., Yates, T., Bock, C., Borgwardt, K., Wolf, G., Turk-Browne, N., and Krishnaswamy, S. (2020) · 2020
Closest in time.
Atol: Measure vectorisation for automatic topologically-oriented learning
Royer, M., Chazal, F., Levrard, C., Ike, Y., and Umeda, Y. (2021) · 2021
Closest in time.