From 8d06fbeae596a0372bf9a921de7d04cc734eaa3b Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 30 Mar 2020 08:14:46 +0200 Subject: Biblio --- biblio/bibliography.bib | 15 +++++++++++++++ 1 file changed, 15 insertions(+) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 3bbe7960..f9d43638 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -1192,3 +1192,18 @@ numpages = {11}, location = {Montr\'{e}al, Canada}, series = {NIPS’18} } +@Article{dtm, +author={Chazal, Fr{\'e}d{\'e}ric +and Cohen-Steiner, David +and M{\'e}rigot, Quentin}, +title={Geometric Inference for Probability Measures}, +journal={Foundations of Computational Mathematics}, +year={2011}, +volume={11}, +number={6}, +pages={733-751}, +abstract={Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (e.g., Betti numbers, normals) of this subset from the approximating point cloud data. It appears that the study of distance functions allows one to address many of these questions successfully. However, one of the main limitations of this framework is that it does not cope well with outliers or with background noise. In this paper, we show how to extend the framework of distance functions to overcome this problem. Replacing compact subsets by measures, we introduce a notion of distance function to a probability distribution in Rd. These functions share many properties with classical distance functions, which make them suitable for inference purposes. In particular, by considering appropriate level sets of these distance functions, we show that it is possible to reconstruct offsets of sampled shapes with topological guarantees even in the presence of outliers. Moreover, in settings where empirical measures are considered, these functions can be easily evaluated, making them of particular practical interest.}, +issn={1615-3383}, +doi={10.1007/s10208-011-9098-0}, +url={https://doi.org/10.1007/s10208-011-9098-0} +} -- cgit v1.2.3 From 0a404547afec2e43dd5edf9410ff079d156d691a Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 30 Mar 2020 08:18:38 +0200 Subject: One more ref, to be cited later --- biblio/bibliography.bib | 12 ++++++++++++ 1 file changed, 12 insertions(+) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index f9d43638..056ccd72 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -1207,3 +1207,15 @@ issn={1615-3383}, doi={10.1007/s10208-011-9098-0}, url={https://doi.org/10.1007/s10208-011-9098-0} } +@article{dtmdensity, +author = "Biau, Gérard and Chazal, Frédéric and Cohen-Steiner, David and Devroye, Luc and Rodríguez, Carlos", +doi = "10.1214/11-EJS606", +fjournal = "Electronic Journal of Statistics", +journal = "Electron. J. Statist.", +pages = "204--237", +publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", +title = "A weighted k-nearest neighbor density estimate for geometric inference", +url = "https://doi.org/10.1214/11-EJS606", +volume = "5", +year = "2011" +} -- cgit v1.2.3 From 65f6ca41a9cd6574a0ca8fa9b781c787064fe4ed Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Thu, 23 Apr 2020 14:40:44 +0200 Subject: Add missing DOI --- biblio/bibliography.bib | 2 ++ 1 file changed, 2 insertions(+) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index b017a07e..07623a31 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -30,6 +30,7 @@ journal = {Foundations of Computational Mathematics}, number = {6}, pages = {1333--1396}, publisher = {Springer-Verlag}, +doi = {10.1007/s10208-017-9370-z}, title = {{Structure and stability of the one-dimensional Mapper}}, volume = {18}, year = {2017} @@ -47,6 +48,7 @@ journal = {Foundations of Computational Mathematics}, number = {1}, pages = {79--103}, publisher = {Springer-Verlag}, +doi = {10.1007/s10208-008-9027-z}, title = {{Extending persistence using Poincar{\'{e}} and Lefschetz duality}}, volume = {9}, year = {2009} -- cgit v1.2.3 From f94c2e1b7ba982fda62239f5c6b378bda867cd40 Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 11 May 2020 19:56:06 +0200 Subject: More DOI in the biblio and update references from a preprint to the published version --- biblio/bibliography.bib | 8 +++++++- src/Persistent_cohomology/doc/Intro_persistent_cohomology.h | 2 +- src/common/doc/main_page.md | 2 +- src/python/doc/persistent_cohomology_sum.inc | 2 +- src/python/doc/persistent_cohomology_user.rst | 2 +- 5 files changed, 11 insertions(+), 5 deletions(-) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 99a15c5e..3ea2f59f 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -13,7 +13,9 @@ pages = {1--39}, publisher = {JMLR.org}, title = {{Statistical analysis and parameter selection for Mapper}}, volume = {19}, -year = {2018} +year = {2018}, +url = {http://jmlr.org/papers/v19/17-291.html}, +doi = {10.5555/3291125.3291137} } @inproceedings{Dey13, @@ -22,6 +24,7 @@ year = {2018} booktitle = {Proceedings of the Twenty-ninth Annual Symposium on Computational Geometry}, year = {2013}, pages = {107--116}, + doi = {10.1145/2462356.2462387} } @article{Carriere16, @@ -832,6 +835,7 @@ book{hatcher2002algebraic, number = {4}, year = {2010}, pages = {367-405}, + doi = {10.1007/s10208-010-9066-0}, ee = {http://dx.doi.org/10.1007/s10208-010-9066-0}, bibsource = {DBLP, http://dblp.uni-trier.de} } @@ -927,6 +931,7 @@ language={English} booktitle = {Symposium on Computational Geometry}, year = {2014}, pages = {345}, + doi = {10.1145/2582112.2582165}, ee = {http://doi.acm.org/10.1145/2582112.2582165}, bibsource = {DBLP, http://dblp.uni-trier.de} } @@ -1241,6 +1246,7 @@ year = "2011" title={Fr{\'e}chet means for distributions of persistence diagrams}, author={Turner, Katharine and Mileyko, Yuriy and Mukherjee, Sayan and Harer, John}, journal={Discrete \& Computational Geometry}, + doi={10.1007/s00454-014-9604-7}, volume={52}, number={1}, pages={44--70}, diff --git a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h index 46b784d8..b4f9fd2c 100644 --- a/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h +++ b/src/Persistent_cohomology/doc/Intro_persistent_cohomology.h @@ -21,7 +21,7 @@ namespace persistent_cohomology { \author Clément Maria Computation of persistent cohomology using the algorithm of - \cite DBLP:journals/dcg/SilvaMV11 and \cite DBLP:journals/corr/abs-1208-5018 + \cite DBLP:journals/dcg/SilvaMV11 and \cite DBLP:conf/compgeom/DeyFW14 and the Compressed Annotation Matrix implementation of \cite DBLP:conf/esa/BoissonnatDM13 diff --git a/src/common/doc/main_page.md b/src/common/doc/main_page.md index 6ea10b88..a33d98cd 100644 --- a/src/common/doc/main_page.md +++ b/src/common/doc/main_page.md @@ -312,7 +312,7 @@ theory is essentially composed of three elements: topological spaces, their homology groups and an evolution scheme. Computation of persistent cohomology using the algorithm of \cite DBLP:journals/dcg/SilvaMV11 and - \cite DBLP:journals/corr/abs-1208-5018 and the Compressed Annotation Matrix implementation of + \cite DBLP:conf/compgeom/DeyFW14 and the Compressed Annotation Matrix implementation of \cite DBLP:conf/esa/BoissonnatDM13 . diff --git a/src/python/doc/persistent_cohomology_sum.inc b/src/python/doc/persistent_cohomology_sum.inc index 0effb50f..a1ff2eee 100644 --- a/src/python/doc/persistent_cohomology_sum.inc +++ b/src/python/doc/persistent_cohomology_sum.inc @@ -12,7 +12,7 @@ | | | | | | Computation of persistent cohomology using the algorithm of | | | | :cite:`DBLP:journals/dcg/SilvaMV11` and | | - | | :cite:`DBLP:journals/corr/abs-1208-5018` and the Compressed | | + | | :cite:`DBLP:conf/compgeom/DeyFW14` and the Compressed | | | | Annotation Matrix implementation of | | | | :cite:`DBLP:conf/esa/BoissonnatDM13`. | | | | | | diff --git a/src/python/doc/persistent_cohomology_user.rst b/src/python/doc/persistent_cohomology_user.rst index 4d743aac..a3f294b2 100644 --- a/src/python/doc/persistent_cohomology_user.rst +++ b/src/python/doc/persistent_cohomology_user.rst @@ -21,7 +21,7 @@ Definition Computation of persistent cohomology using the algorithm of :cite:`DBLP:journals/dcg/SilvaMV11` and -:cite:`DBLP:journals/corr/abs-1208-5018` and the Compressed Annotation Matrix implementation of +:cite:`DBLP:conf/compgeom/DeyFW14` and the Compressed Annotation Matrix implementation of :cite:`DBLP:conf/esa/BoissonnatDM13`. The theory of homology consists in attaching to a topological space a sequence of (homology) groups, capturing global -- cgit v1.2.3 From 6c17494e02721ca826750155bac14c7f91a173fa Mon Sep 17 00:00:00 2001 From: yuichi-ike Date: Tue, 12 May 2020 09:37:32 +0900 Subject: reference and comments added --- biblio/bibliography.bib | 26 ++++++++++++++++++++++++++ src/python/CMakeLists.txt | 4 +++- src/python/doc/rips_complex_ref.rst | 4 +++- src/python/gudhi/weighted_rips_complex.py | 6 +++--- src/python/test/test_weighted_rips.py | 4 ++-- 5 files changed, 37 insertions(+), 7 deletions(-) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 99a15c5e..f405b9bb 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -1247,3 +1247,29 @@ year = "2011" year={2014}, publisher={Springer} } + +@inproceedings{dtmfiltrations, + author = {Hirokazu Anai and + Fr{\'{e}}d{\'{e}}ric Chazal and + Marc Glisse and + Yuichi Ike and + Hiroya Inakoshi and + Rapha{\"{e}}l Tinarrage and + Yuhei Umeda}, + editor = {Gill Barequet and + Yusu Wang}, + title = {DTM-Based Filtrations}, + booktitle = {35th International Symposium on Computational Geometry, SoCG 2019, + June 18-21, 2019, Portland, Oregon, {USA}}, + series = {LIPIcs}, + volume = {129}, + pages = {58:1--58:15}, + publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik}, + year = {2019}, + url = {https://doi.org/10.4230/LIPIcs.SoCG.2019.58}, + doi = {10.4230/LIPIcs.SoCG.2019.58}, + timestamp = {Tue, 11 Feb 2020 15:52:14 +0100}, + biburl = {https://dblp.org/rec/conf/compgeom/AnaiCGIITU19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt index adf4923b..0aa55467 100644 --- a/src/python/CMakeLists.txt +++ b/src/python/CMakeLists.txt @@ -487,7 +487,9 @@ if(PYTHONINTERP_FOUND) endif() # Weighted Rips - add_gudhi_py_test(test_weighted_rips) + if(SCIPY_FOUND) + add_gudhi_py_test(test_weighted_rips) + endif() # Set missing or not modules set(GUDHI_MODULES ${GUDHI_MODULES} "python" CACHE INTERNAL "GUDHI_MODULES") diff --git a/src/python/doc/rips_complex_ref.rst b/src/python/doc/rips_complex_ref.rst index 8fc7e1b0..3c25564a 100644 --- a/src/python/doc/rips_complex_ref.rst +++ b/src/python/doc/rips_complex_ref.rst @@ -25,7 +25,7 @@ Weighted Rips complex reference manual .. automethod:: gudhi.WeightedRipsComplex.__init__ Basic examples -------------- +-------------- The following example computes the weighted Rips filtration associated with a distance matrix and weights on vertices. @@ -60,6 +60,8 @@ Combining with DistanceToMeasure, one can compute the DTM-filtration of a point st = w_rips.create_simplex_tree(max_dimension=2) print(st.persistence()) +The output is: + .. testoutput:: [(0, (3.1622776601683795, inf)), (0, (3.1622776601683795, 5.39834563766817)), (0, (3.1622776601683795, 5.39834563766817))] diff --git a/src/python/gudhi/weighted_rips_complex.py b/src/python/gudhi/weighted_rips_complex.py index 7401c428..bccac1ff 100644 --- a/src/python/gudhi/weighted_rips_complex.py +++ b/src/python/gudhi/weighted_rips_complex.py @@ -12,9 +12,9 @@ from gudhi import SimplexTree class WeightedRipsComplex: """ Class to generate a weighted Rips complex from a distance matrix and weights on vertices, - in the way described in the paper 'DTM-based filtrations' https://arxiv.org/abs/1811.04757. - Remark that the filtration value of a vertex is twice of its weight for the consistency with - RipsComplex, which is different from the definition in the paper. + in the way described in :cite:`dtmfiltrations`. + Remark that all the filtration values of vertices are twice of the given weights for the consistency + with RipsComplex, which is different from the definition in the paper. """ def __init__(self, distance_matrix, diff --git a/src/python/test/test_weighted_rips.py b/src/python/test/test_weighted_rips.py index 59ec022a..7ef48333 100644 --- a/src/python/test/test_weighted_rips.py +++ b/src/python/test/test_weighted_rips.py @@ -35,8 +35,8 @@ def test_compatibility_with_rips(): ([0, 2], 1.0), ([1, 3], 1.0), ([2, 3], 1.0), - ([1, 2], 1.4142135623730951), - ([0, 3], 1.4142135623730951), + ([1, 2], sqrt(2)), + ([0, 3], sqrt(2)), ] def test_compatibility_with_filtered_rips(): -- cgit v1.2.3