diff options
26 files changed, 1664 insertions, 34 deletions
diff --git a/CMakeLists.txt b/CMakeLists.txt index 10373f75..b28dcbf2 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -50,6 +50,7 @@ add_gudhi_module(Subsampling) add_gudhi_module(Tangential_complex) add_gudhi_module(Witness_complex) add_gudhi_module(Nerve_GIC) +add_gudhi_module(Kernels) message("++ GUDHI_MODULES list is:\"${GUDHI_MODULES}\"") diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 16f43d6f..24c0f718 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -1079,27 +1079,25 @@ language={English} year = {2016} } -@inproceedings{cavanna15geometric, - author = {Nicholas J. Cavanna and Mahmoodreza Jahanseir and Donald R. Sheehy}, - booktitle = {Proceedings of the Canadian Conference on Computational Geometry}, - title = {A Geometric Perspective on Sparse Filtrations}, - year = {2015} -} - -@inproceedings{cavanna15visualizing, - author = {Nicholas J. Cavanna and Mahmoodreza Jahanseir and Donald R. Sheehy}, - booktitle = {Proceedings of the 31st International Symposium on Computational Geometry}, - title = {Visualizing Sparse Filtrations}, - year = {2015}, - doi = {10.4230/LIPIcs.SOCG.2015.23} -} - -@article{sheehy13linear, - title = {Linear-Size Approximations to the {V}ietoris-{R}ips Filtration}, - author = {Donald R. Sheehy}, - journal = {Discrete \& Computational Geometry}, - volume = {49}, - number = {4}, - pages = {778--796}, - year = {2013} + +@InProceedings{pmlr-v70-carriere17a, + title = {Sliced {W}asserstein Kernel for Persistence Diagrams}, + author = {Mathieu Carri{\`e}re and Marco Cuturi and Steve Oudot}, + booktitle = {Proceedings of the 34th International Conference on Machine Learning}, + pages = {664--673}, + year = {2017}, + editor = {Doina Precup and Yee Whye Teh}, + volume = {70}, + series = {Proceedings of Machine Learning Research}, + address = {International Convention Centre, Sydney, Australia}, + month = {06--11 Aug}, + publisher = {PMLR}, +} + +@INPROCEEDINGS{Rahimi07randomfeatures, + author = {Ali Rahimi and Ben Recht}, + title = {Random features for large-scale kernel machines}, + booktitle = {In Neural Information Processing Systems}, + year = {2007} } + diff --git a/data/persistence_diagram/PD1.pers b/data/persistence_diagram/PD1.pers new file mode 100644 index 00000000..404199b4 --- /dev/null +++ b/data/persistence_diagram/PD1.pers @@ -0,0 +1,3 @@ +2.7 3.7 +9.6 14 +34.2 34.974
\ No newline at end of file diff --git a/data/persistence_diagram/PD2.pers b/data/persistence_diagram/PD2.pers new file mode 100644 index 00000000..125d8e4b --- /dev/null +++ b/data/persistence_diagram/PD2.pers @@ -0,0 +1,2 @@ +2.8 4.45 +9.5 14.1
\ No newline at end of file diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt index 94587044..0ae26081 100644 --- a/src/CMakeLists.txt +++ b/src/CMakeLists.txt @@ -26,6 +26,7 @@ add_gudhi_module(Subsampling) add_gudhi_module(Tangential_complex) add_gudhi_module(Witness_complex) add_gudhi_module(Nerve_GIC) +add_gudhi_module(Kernels) message("++ GUDHI_MODULES list is:\"${GUDHI_MODULES}\"") diff --git a/src/Doxyfile b/src/Doxyfile index f1981e2e..2348b290 100644 --- a/src/Doxyfile +++ b/src/Doxyfile @@ -854,7 +854,8 @@ IMAGE_PATH = doc/Skeleton_blocker/ \ doc/Tangential_complex/ \ doc/Bottleneck_distance/ \ doc/Nerve_GIC/ \ - doc/Persistence_representations/ + doc/Persistence_representations/ \ + doc/Kernels/ # The INPUT_FILTER tag can be used to specify a program that doxygen should # invoke to filter for each input file. Doxygen will invoke the filter program diff --git a/src/Persistence_representations/doc/Persistence_representations_doc.h b/src/Persistence_representations/doc/Persistence_representations_doc.h index 38bd3a21..ca283017 100644 --- a/src/Persistence_representations/doc/Persistence_representations_doc.h +++ b/src/Persistence_representations/doc/Persistence_representations_doc.h @@ -24,7 +24,6 @@ #define DOC_GUDHI_STAT_H_ namespace Gudhi { - namespace Persistence_representations { /** \defgroup Persistence_representations Persistence representations @@ -250,6 +249,68 @@ namespace Persistence_representations { absolute value of differences between coordinates. A scalar product is a sum of products of values at the corresponding positions of two vectors. + + + + +\section sec_persistence_kernels Kernels on persistence diagrams + <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Sliced_Wasserstein <br> + <b>Reference manual:</b> \ref Gudhi::Persistence_representations::Persistence_weighted_gaussian <br> + + Kernels for persistence diagrams can be regarded as infinite-dimensional vectorizations. More specifically, + they are similarity functions whose evaluations on pairs of persistence diagrams equals the scalar products + between images of these pairs under a map \f$\Phi\f$ taking values in a specific (possibly non Euclidean) Hilbert space \f$k(D_i, D_j) = \langle \Phi(D_i),\Phi(D_j)\rangle\f$. + Reciprocally, classical results of learning theory ensure that such a \f$\Phi\f$ exists for a given similarity function \f$k\f$ if and only if \f$k\f$ is <i>positive semi-definite</i>. + Kernels are designed for algorithms that can be <i>kernelized</i>, i.e., algorithms that only require to know scalar products between instances in order to run. + Examples of such algorithms include Support Vector Machines, Principal Component Analysis and Ridge Regression. + + There have been several attempts at defining kernels, i.e., positive semi-definite functions, between persistence diagrams within the last few years. We provide implementation + for three of them: + + \li the <i>Persistence Scale Space Kernel</i>---see \cite Reininghaus_Huber_ALL_PSSK, which is the classical scalar product between \f$L^2\f$ functions, where persistence diagrams + are turned into functions by centering and summing Gaussian functions over the diagram points and their symmetric counterparts w.r.t. the diagonal: \f$k(D_1,D_2)=\int \Phi(D_1)\Phi(D_2)\f$, + where \f$\Phi(D)=\sum_{p\in D} {\rm exp}\left(-\frac{\|p-\cdot\|_2^2}{2\sigma^2}\right)\f$. + + \li the <i>Persistence Weighted Gaussian Kernel</i>---see \cite Kusano_Fukumizu_Hiraoka_PWGK, which is a slight generalization of the previous kernel, is the scalar product between + weighted Kernel Mean Embeddings of persistence diagrams w.r.t. the Gaussian Kernel \f$k_G\f$ (with corresponding map \f$\Phi_G\f$) in \f$\mathbb{R}^2\f$: + \f$k(D_1,D_2)=\langle\sum_{p\in D_1} w(p)\Phi_G(p), \sum_{q\in D_2} w(q)\Phi_G(q)\rangle\f$ + + \li the <i>Sliced Wasserstein Kernel</i>---see \cite pmlr-v70-carriere17a, which takes the form of a Gaussian kernel with a specific distance between persistence diagrams + called the <i>Sliced Wasserstein Distance</i>: \f$k(D_1,D_2)={\rm exp}\left(-\frac{SW(D_1,D_2)}{2\sigma^2}\right)\f$ + + When launching: + + \code $> ./Sliced_Wasserstein + \endcode + + the program output is: + + \code $> Approx SW distance: 5.33648 + $> Exact SW distance: 5.33798 + $> Approx SW kernel: 0.0693743 + $> Exact SW kernel: 0.0693224 + $> Distance induced by approx SW kernel: 1.36428 + $> Distance induced by exact SW kernel: 1.3643 + \endcode + + + and when launching: + + \code $> ./Persistence_weighted_gaussian + \endcode + + the program output is: + + \code $> Approx PWG kernel: 1.21509 + $> Exact PWG kernel: 1.13628 + $> Distance induced by approx PWG kernel: 3.23354 + $> Distance induced by exact PWG kernel: 3.25697 + $> Approx Gaussian PWG kernel: 0.0194222 + $> Exact Gaussian PWG kernel: 0.0192524 + $> Approx PSS kernel: 0.134413 + $> Exact PSS kernel: 0.133394 + \endcode + */ /** @} */ // end defgroup Persistence_representations diff --git a/src/Persistence_representations/example/CMakeLists.txt b/src/Persistence_representations/example/CMakeLists.txt index 54d719ac..89284e38 100644 --- a/src/Persistence_representations/example/CMakeLists.txt +++ b/src/Persistence_representations/example/CMakeLists.txt @@ -27,3 +27,22 @@ add_test(NAME Persistence_representations_example_heat_maps COMMAND $<TARGET_FILE:Persistence_representations_example_heat_maps>) install(TARGETS Persistence_representations_example_heat_maps DESTINATION bin) +add_executable ( Sliced_Wasserstein sliced_wasserstein.cpp ) +add_test(NAME Sliced_Wasserstein + COMMAND $<TARGET_FILE:Sliced_Wasserstein>) +install(TARGETS Sliced_Wasserstein DESTINATION bin) + +add_executable ( Persistence_weighted_gaussian persistence_weighted_gaussian.cpp ) +add_test(NAME Persistence_weighted_gaussian + COMMAND $<TARGET_FILE:Persistence_weighted_gaussian>) +install(TARGETS Persistence_weighted_gaussian DESTINATION bin) + +add_executable ( Persistence_image persistence_image.cpp ) +add_test(NAME Persistence_image + COMMAND $<TARGET_FILE:Persistence_image>) +install(TARGETS Persistence_image DESTINATION bin) + +add_executable ( Landscape landscape.cpp ) +add_test(NAME Landscape + COMMAND $<TARGET_FILE:Landscape>) +install(TARGETS Landscape DESTINATION bin) diff --git a/src/Persistence_representations/example/landscape.cpp b/src/Persistence_representations/example/landscape.cpp new file mode 100644 index 00000000..5fa84a7c --- /dev/null +++ b/src/Persistence_representations/example/landscape.cpp @@ -0,0 +1,51 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#include <gudhi/Landscape.h> + +#include <iostream> +#include <vector> +#include <utility> + +using LS = Gudhi::Persistence_representations::Landscape; + +int main(int argc, char** argv) { + + std::vector<std::pair<double, double> > persistence; + + persistence.push_back(std::make_pair(1, 2)); + persistence.push_back(std::make_pair(6, 8)); + persistence.push_back(std::make_pair(0, 4)); + persistence.push_back(std::make_pair(3, 8)); + + int nb_ls = 3; double min_x = 0.0; double max_x = 10.0; int res_x = 100; + + LS ls(persistence, nb_ls, min_x, max_x, res_x); + std::vector<std::vector<double> > L = ls.vectorize(); + + for(int i = 0; i < nb_ls; i++){ + for(int j = 0; j < res_x; j++) std::cout << L[i][j] << " "; + std::cout << std::endl; + } + + return 0; +} diff --git a/src/Persistence_representations/example/persistence_image.cpp b/src/Persistence_representations/example/persistence_image.cpp new file mode 100644 index 00000000..cdce3bbf --- /dev/null +++ b/src/Persistence_representations/example/persistence_image.cpp @@ -0,0 +1,54 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#include <gudhi/Persistence_image.h> +#include <gudhi/Persistence_weighted_gaussian.h> + +#include <iostream> +#include <vector> +#include <utility> +#include <string> + +using PI = Gudhi::Persistence_representations::Persistence_image; +using Weight = std::function<double (std::pair<double,double>) >; + +int main(int argc, char** argv) { + + std::vector<std::pair<double, double> > persistence; + + persistence.push_back(std::make_pair(1, 2)); + persistence.push_back(std::make_pair(6, 8)); + persistence.push_back(std::make_pair(0, 4)); + persistence.push_back(std::make_pair(3, 8)); + + double min_x = 0.0; double max_x = 10.0; int res_x = 100; double min_y = 0.0; double max_y = 10.0; int res_y = 100; double sigma = 1.0; Weight weight = Gudhi::Persistence_representations::linear_weight; + + PI pim(persistence, min_x, max_x, res_x, min_y, max_y, res_y, weight, sigma); + std::vector<std::vector<double> > P = pim.vectorize(); + + for(int i = 0; i < res_y; i++){ + for(int j = 0; j < res_x; j++) std::cout << P[i][j] << " "; + std::cout << std::endl; + } + + return 0; +} diff --git a/src/Persistence_representations/example/persistence_weighted_gaussian.cpp b/src/Persistence_representations/example/persistence_weighted_gaussian.cpp new file mode 100644 index 00000000..db60755f --- /dev/null +++ b/src/Persistence_representations/example/persistence_weighted_gaussian.cpp @@ -0,0 +1,98 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#include <gudhi/Persistence_weighted_gaussian.h> + +#include <iostream> +#include <vector> +#include <utility> + +using PWG = Gudhi::Persistence_representations::Persistence_weighted_gaussian; + +int main(int argc, char** argv) { + + Persistence_diagram persistence1, persistence2; + + persistence1.push_back(std::make_pair(1, 2)); + persistence1.push_back(std::make_pair(6, 8)); + persistence1.push_back(std::make_pair(0, 4)); + persistence1.push_back(std::make_pair(3, 8)); + + persistence2.push_back(std::make_pair(2, 9)); + persistence2.push_back(std::make_pair(1, 6)); + persistence2.push_back(std::make_pair(3, 5)); + persistence2.push_back(std::make_pair(6, 10)); + + double sigma = 1; + double tau = 1; + int m = 10000; + + PWG PWG1(persistence1, sigma, m, Gudhi::Persistence_representations::arctan_weight(1,1)); + PWG PWG2(persistence2, sigma, m, Gudhi::Persistence_representations::arctan_weight(1,1)); + + PWG PWGex1(persistence1, sigma, -1, Gudhi::Persistence_representations::arctan_weight(1,1)); + PWG PWGex2(persistence2, sigma, -1, Gudhi::Persistence_representations::arctan_weight(1,1)); + + + // Linear PWG + + std::cout << "Approx PWG kernel: " << PWG1.compute_scalar_product (PWG2) << std::endl; + std::cout << "Exact PWG kernel: " << PWGex1.compute_scalar_product (PWGex2) << std::endl; + + std::cout << "Distance induced by approx PWG kernel: " << PWG1.distance (PWG2) << std::endl; + std::cout << "Distance induced by exact PWG kernel: " << PWGex1.distance (PWGex2) << std::endl; + + + + + + + + // Gaussian PWG + + std::cout << "Approx Gaussian PWG kernel: " << std::exp( -PWG1.distance (PWG2) ) / (2*tau*tau) << std::endl; + std::cout << "Exact Gaussian PWG kernel: " << std::exp( -PWGex1.distance (PWGex2) ) / (2*tau*tau) << std::endl; + + + + + + + + // PSS + + Persistence_diagram pd1 = persistence1; int numpts = persistence1.size(); for(int i = 0; i < numpts; i++) pd1.emplace_back(persistence1[i].second,persistence1[i].first); + Persistence_diagram pd2 = persistence2; numpts = persistence2.size(); for(int i = 0; i < numpts; i++) pd2.emplace_back(persistence2[i].second,persistence2[i].first); + + PWG pwg1(pd1, 2*std::sqrt(sigma), m, Gudhi::Persistence_representations::pss_weight); + PWG pwg2(pd2, 2*std::sqrt(sigma), m, Gudhi::Persistence_representations::pss_weight); + + PWG pwgex1(pd1, 2*std::sqrt(sigma), -1, Gudhi::Persistence_representations::pss_weight); + PWG pwgex2(pd2, 2*std::sqrt(sigma), -1, Gudhi::Persistence_representations::pss_weight); + + std::cout << "Approx PSS kernel: " << pwg1.compute_scalar_product (pwg2) / (16*Gudhi::Persistence_representations::pi*sigma) << std::endl; + std::cout << "Exact PSS kernel: " << pwgex1.compute_scalar_product (pwgex2) / (16*Gudhi::Persistence_representations::pi*sigma) << std::endl; + + + + return 0; +} diff --git a/src/Persistence_representations/example/sliced_wasserstein.cpp b/src/Persistence_representations/example/sliced_wasserstein.cpp new file mode 100644 index 00000000..d37cb23c --- /dev/null +++ b/src/Persistence_representations/example/sliced_wasserstein.cpp @@ -0,0 +1,60 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#include <gudhi/Sliced_Wasserstein.h> + +#include <iostream> +#include <vector> +#include <utility> + +using SW = Gudhi::Persistence_representations::Sliced_Wasserstein; + +int main(int argc, char** argv) { + + Persistence_diagram persistence1, persistence2; + + persistence1.push_back(std::make_pair(1, 2)); + persistence1.push_back(std::make_pair(6, 8)); + persistence1.push_back(std::make_pair(0, 4)); + persistence1.push_back(std::make_pair(3, 8)); + + persistence2.push_back(std::make_pair(2, 9)); + persistence2.push_back(std::make_pair(1, 6)); + persistence2.push_back(std::make_pair(3, 5)); + persistence2.push_back(std::make_pair(6, 10)); + + + SW sw1(persistence1, 1, 100); + SW sw2(persistence2, 1, 100); + + SW swex1(persistence1, 1, -1); + SW swex2(persistence2, 1, -1); + + std::cout << "Approx SW distance: " << sw1.compute_sliced_wasserstein_distance(sw2) << std::endl; + std::cout << "Exact SW distance: " << swex1.compute_sliced_wasserstein_distance(swex2) << std::endl; + std::cout << "Approx SW kernel: " << sw1.compute_scalar_product(sw2) << std::endl; + std::cout << "Exact SW kernel: " << swex1.compute_scalar_product(swex2) << std::endl; + std::cout << "Distance induced by approx SW kernel: " << sw1.distance(sw2) << std::endl; + std::cout << "Distance induced by exact SW kernel: " << swex1.distance(swex2) << std::endl; + + return 0; +} diff --git a/src/Persistence_representations/include/gudhi/Landscape.h b/src/Persistence_representations/include/gudhi/Landscape.h new file mode 100644 index 00000000..bbbca36b --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Landscape.h @@ -0,0 +1,108 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef LANDSCAPE_H_ +#define LANDSCAPE_H_ + +// gudhi include +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> +#include <gudhi/Debug_utils.h> + +// standard include +#include <cmath> +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <string> +#include <utility> +#include <functional> + +namespace Gudhi { +namespace Persistence_representations { + +/** + * \class Landscape gudhi/Landscape.h + * \brief A class implementing landscapes. + * + * \ingroup Persistence_representations + * + * \details + * + * The landscape is a way to turn a persistence diagram into \f$L^2\f$ functions. Roughly, the idea is to see the boundaries of the rank functions as scalar functions taking values on the diagonal. + * See \cite bubenik_landscapes_2015 for more details. Here we provide a way to approximate such functions by computing their values on a set of samples. + * +**/ + +class Landscape { + + protected: + Persistence_diagram diagram; + int res_x, nb_ls; + double min_x, max_x; + + public: + + /** \brief Landscape constructor. + * \ingroup Landscape + * + * @param[in] _diagram persistence diagram. + * @param[in] _nb_ls number of landscape functions. + * @param[in] _min_x minimum value of samples. + * @param[in] _max_x maximum value of samples. + * @param[in] _res_x number of samples. + * + */ + Landscape(const Persistence_diagram & _diagram, int _nb_ls = 5, double _min_x = 0.0, double _max_x = 1.0, int _res_x = 10){diagram = _diagram; nb_ls = _nb_ls; min_x = _min_x; max_x = _max_x; res_x = _res_x;} + + /** \brief Computes the landscape of a diagram. + * \ingroup Landscape + * + */ + std::vector<std::vector<double> > vectorize() const { + std::vector<std::vector<double> > ls; for(int i = 0; i < nb_ls; i++) ls.emplace_back(); + int num_pts = diagram.size(); double step = (max_x - min_x)/res_x; + + for(int i = 0; i < res_x; i++){ + double x = min_x + i*step; double t = x / std::sqrt(2); std::vector<double> events; + for(int j = 0; j < num_pts; j++){ + double px = diagram[j].first; double py = diagram[j].second; + if(t >= px && t <= py){ if(t >= (px+py)/2) events.push_back(std::sqrt(2)*(py-t)); else events.push_back(std::sqrt(2)*(t-px)); } + } + + std::sort(events.begin(), events.end(), [](const double & a, const double & b){return a > b;}); int nb_events = events.size(); + for (int j = 0; j < nb_ls; j++){ if(j < nb_events) ls[j].push_back(events[j]); else ls[j].push_back(0); } + } + return ls; + } + + + + +}; // class Landscape +} // namespace Persistence_representations +} // namespace Gudhi + +#endif // LANDSCAPE_H_ diff --git a/src/Persistence_representations/include/gudhi/Persistence_image.h b/src/Persistence_representations/include/gudhi/Persistence_image.h new file mode 100644 index 00000000..76b34d8d --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Persistence_image.h @@ -0,0 +1,126 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef PERSISTENCE_IMAGE_H_ +#define PERSISTENCE_IMAGE_H_ + +// gudhi include +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> +#include <gudhi/Weight_functions.h> +#include <gudhi/Debug_utils.h> + +// standard include +#include <cmath> +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <string> +#include <utility> +#include <functional> + +namespace Gudhi { +namespace Persistence_representations { + +/** + * \class Persistence_image gudhi/Persistence_image.h + * \brief A class implementing the persistence images. + * + * \ingroup Persistence_representations + * + * \details + * + * Persistence images are a way to build images from persistence diagrams. Roughly, the idea is to center Gaussians on each diagram point, with a weight that usually depends on + * the distance to the diagonal, so that the diagram is turned into a function, and then to discretize the plane into pixels, and integrate this function on each pixel. + * See \cite Persistence_Images_2017 for more details. + * +**/ + +class Persistence_image { + + protected: + Persistence_diagram diagram; + int res_x, res_y; + double min_x, max_x, min_y, max_y; + Weight weight; + double sigma; + + public: + + /** \brief Persistence Image constructor. + * \ingroup Persistence_image + * + * @param[in] _diagram persistence diagram. + * @param[in] _min_x minimum value of pixel abscissa. + * @param[in] _max_x maximum value of pixel abscissa. + * @param[in] _res_x number of pixels for the x-direction. + * @param[in] _min_y minimum value of pixel ordinate. + * @param[in] _max_y maximum value of pixel ordinate. + * @param[in] _res_y number of pixels for the y-direction. + * @param[in] _weight weight function for the Gaussians. + * @param[in] _sigma bandwidth parameter for the Gaussians. + * + */ + Persistence_image(const Persistence_diagram & _diagram, double _min_x = 0.0, double _max_x = 1.0, int _res_x = 10, double _min_y = 0.0, double _max_y = 1.0, int _res_y = 10, const Weight & _weight = arctan_weight(1,1), double _sigma = 1.0){ + diagram = _diagram; min_x = _min_x; max_x = _max_x; res_x = _res_x; min_y = _min_y; max_y = _max_y; res_y = _res_y, weight = _weight; sigma = _sigma; + } + + /** \brief Computes the persistence image of a diagram. + * \ingroup Persistence_image + * + */ + std::vector<std::vector<double> > vectorize() const { + std::vector<std::vector<double> > im; for(int i = 0; i < res_y; i++) im.emplace_back(); + double step_x = (max_x - min_x)/res_x; double step_y = (max_y - min_y)/res_y; + + int num_pts = diagram.size(); + + for(int i = 0; i < res_y; i++){ + double y = min_y + i*step_y; + for(int j = 0; j < res_x; j++){ + double x = min_x + j*step_x; + + double pixel_value = 0; + for(int k = 0; k < num_pts; k++){ + double px = diagram[k].first; double py = diagram[k].second; + pixel_value += weight(std::pair<double,double>(px,py)) * std::exp( -((x-px)*(x-px) + (y-(py-px))*(y-(py-px))) / (2*sigma*sigma) ) / (sigma*std::sqrt(2*pi)); + } + im[i].push_back(pixel_value); + + } + } + + return im; + + } + + + + +}; // class Persistence_image +} // namespace Persistence_representations +} // namespace Gudhi + +#endif // PERSISTENCE_IMAGE_H_ diff --git a/src/Persistence_representations/include/gudhi/Persistence_weighted_gaussian.h b/src/Persistence_representations/include/gudhi/Persistence_weighted_gaussian.h new file mode 100644 index 00000000..76c43e65 --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Persistence_weighted_gaussian.h @@ -0,0 +1,181 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef PERSISTENCE_WEIGHTED_GAUSSIAN_H_ +#define PERSISTENCE_WEIGHTED_GAUSSIAN_H_ + +// gudhi include +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> +#include <gudhi/Weight_functions.h> + +// standard include +#include <cmath> +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <string> +#include <utility> +#include <functional> + +namespace Gudhi { +namespace Persistence_representations { +/** + * \class Persistence_weighted_gaussian gudhi/Persistence_weighted_gaussian.h + * \brief A class implementing the Persistence Weighted Gaussian kernel and a specific case thereof called the Persistence Scale Space kernel. + * + * \ingroup Persistence_representations + * + * \details + * The Persistence Weighted Gaussian kernel is built with Gaussian Kernel Mean Embedding, meaning that each persistence diagram is first + * sent to the Hilbert space of a Gaussian kernel with bandwidth parameter \f$\sigma >0\f$ using a weighted mean embedding \f$\Phi\f$: + * + * \f$ \Phi\,:\,D\,\rightarrow\,\sum_{p\in D}\,w(p)\,{\rm exp}\left(-\frac{\|p-\cdot\|_2^2}{2\sigma^2}\right) \f$, + * + * Usually, the weight function is chosen to be an arctan function of the distance of the point to the diagonal: + * \f$w(p) = {\rm arctan}(C\,|y-x|^\alpha)\f$, for some parameters \f$C,\alpha >0\f$. + * Then, their scalar product in this space is computed: + * + * \f$ k(D_1,D_2)=\langle\Phi(D_1),\Phi(D_2)\rangle + * \,=\,\sum_{p\in D_1}\,\sum_{q\in D_2}\,w(p)\,w(q)\,{\rm exp}\left(-\frac{\|p-q\|_2^2}{2\sigma^2}\right).\f$ + * + * Note that one may apply a second Gaussian kernel to their distance in this space and still get a kernel. + * + * It follows that the computation time is \f$O(n^2)\f$ where \f$n\f$ is the number of points + * in the diagrams. This time can be improved by computing approximations of the kernel + * with \f$m\f$ Fourier features \cite Rahimi07randomfeatures. In that case, the computation time becomes \f$O(mn)\f$. + * + * The Persistence Scale Space kernel is a Persistence Weighted Gaussian kernel between modified diagrams: + * the symmetric of each point with respect to the diagonal is first added in each diagram, and then the weight function + * is set to be +1 if the point is above the diagonal and -1 otherwise. + * + * For more details, please see \cite Kusano_Fukumizu_Hiraoka_PWGK + * and \cite Reininghaus_Huber_ALL_PSSK . + * +**/ +class Persistence_weighted_gaussian{ + + protected: + Persistence_diagram diagram; + Weight weight; + double sigma; + int approx; + + public: + + /** \brief Persistence Weighted Gaussian kernel constructor. + * \ingroup Persistence_weighted_gaussian + * + * @param[in] _diagram persistence diagram. + * @param[in] _sigma bandwidth parameter of the Gaussian kernel used for the Kernel Mean Embedding of the diagrams. + * @param[in] _approx number of random Fourier features in case of approximate computation, set to -1 for exact computation. + * @param[in] _weight weight function for the points in the diagrams. + * + */ + Persistence_weighted_gaussian(const Persistence_diagram & _diagram, double _sigma = 1.0, int _approx = 1000, const Weight & _weight = arctan_weight(1,1)){diagram = _diagram; sigma = _sigma; approx = _approx; weight = _weight;} + + + // ********************************** + // Utils. + // ********************************** + + std::vector<std::pair<double,double> > Fourier_feat(const Persistence_diagram & diag, const std::vector<std::pair<double,double> > & z, const Weight & weight = arctan_weight(1,1)) const { + int md = diag.size(); std::vector<std::pair<double,double> > b; int mz = z.size(); + for(int i = 0; i < mz; i++){ + double d1 = 0; double d2 = 0; double zx = z[i].first; double zy = z[i].second; + for(int j = 0; j < md; j++){ + double x = diag[j].first; double y = diag[j].second; + d1 += weight(diag[j])*cos(x*zx + y*zy); + d2 += weight(diag[j])*sin(x*zx + y*zy); + } + b.emplace_back(d1,d2); + } + return b; + } + + std::vector<std::pair<double,double> > random_Fourier(double sigma, int m = 1000) const { + std::normal_distribution<double> distrib(0,1); std::vector<std::pair<double,double> > z; std::random_device rd; + for(int i = 0; i < m; i++){ + std::mt19937 e1(rd()); std::mt19937 e2(rd()); + double zx = distrib(e1); double zy = distrib(e2); + z.emplace_back(zx/sigma,zy/sigma); + } + return z; + } + + + + // ********************************** + // Scalar product + distance. + // ********************************** + + /** \brief Evaluation of the kernel on a pair of diagrams. + * \ingroup Persistence_weighted_gaussian + * + * @pre sigma, approx and weight attributes need to be the same for both instances. + * @param[in] second other instance of class Persistence_weighted_gaussian. + * + */ + double compute_scalar_product(const Persistence_weighted_gaussian & second) const { + + GUDHI_CHECK(this->sigma != second.sigma || this->approx != second.approx || this->weight != second.weight, std::invalid_argument("Error: different values for representations")); + Persistence_diagram diagram1 = this->diagram; Persistence_diagram diagram2 = second.diagram; + + if(this->approx == -1){ + int num_pts1 = diagram1.size(); int num_pts2 = diagram2.size(); double k = 0; + for(int i = 0; i < num_pts1; i++) + for(int j = 0; j < num_pts2; j++) + k += this->weight(diagram1[i])*this->weight(diagram2[j])*exp(-((diagram1[i].first - diagram2[j].first) * (diagram1[i].first - diagram2[j].first) + + (diagram1[i].second - diagram2[j].second) * (diagram1[i].second - diagram2[j].second)) + /(2*this->sigma*this->sigma)); + return k; + } + else{ + std::vector<std::pair<double,double> > z = random_Fourier(this->sigma, this->approx); + std::vector<std::pair<double,double> > b1 = Fourier_feat(diagram1,z,this->weight); + std::vector<std::pair<double,double> > b2 = Fourier_feat(diagram2,z,this->weight); + double d = 0; for(int i = 0; i < this->approx; i++) d += b1[i].first*b2[i].first + b1[i].second*b2[i].second; + return d/this->approx; + } + } + + /** \brief Evaluation of the distance between images of diagrams in the Hilbert space of the kernel. + * \ingroup Persistence_weighted_gaussian + * + * @pre sigma, approx and weight attributes need to be the same for both instances. + * @param[in] second other instance of class Persistence_weighted_gaussian. + * + */ + double distance(const Persistence_weighted_gaussian & second) const { + GUDHI_CHECK(this->sigma != second.sigma || this->approx != second.approx || this->weight != second.weight, std::invalid_argument("Error: different values for representations")); + return std::pow(this->compute_scalar_product(*this) + second.compute_scalar_product(second)-2*this->compute_scalar_product(second), 0.5); + } + + +}; // class Persistence_weighted_gaussian +} // namespace Persistence_representations +} // namespace Gudhi + +#endif // PERSISTENCE_WEIGHTED_GAUSSIAN_H_ diff --git a/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h b/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h new file mode 100644 index 00000000..235918fe --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Sliced_Wasserstein.h @@ -0,0 +1,340 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef SLICED_WASSERSTEIN_H_ +#define SLICED_WASSERSTEIN_H_ + +// gudhi include +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> +#include <gudhi/Debug_utils.h> + +// standard include +#include <cmath> +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <string> +#include <utility> +#include <functional> + +namespace Gudhi { +namespace Persistence_representations { + +/** + * \class Sliced_Wasserstein gudhi/Sliced_Wasserstein.h + * \brief A class implementing the Sliced Wasserstein kernel. + * + * \ingroup Persistence_representations + * + * \details + * The Sliced Wasserstein kernel is defined as a Gaussian-like kernel between persistence diagrams, where the distance used for + * comparison is the Sliced Wasserstein distance \f$SW\f$ between persistence diagrams, defined as the integral of the 1-norm + * between the sorted projections of the diagrams onto all lines passing through the origin: + * + * \f$ SW(D_1,D_2)=\int_{\theta\in\mathbb{S}}\,\|\pi_\theta(D_1\cup\pi_\Delta(D_2))-\pi_\theta(D_2\cup\pi_\Delta(D_1))\|_1{\rm d}\theta\f$, + * + * where \f$\pi_\theta\f$ is the projection onto the line defined with angle \f$\theta\f$ in the unit circle \f$\mathbb{S}\f$, + * and \f$\pi_\Delta\f$ is the projection onto the diagonal. + * The integral can be either computed exactly in \f$O(n^2{\rm log}(n))\f$ time, where \f$n\f$ is the number of points + * in the diagrams, or approximated by sampling \f$N\f$ lines in the circle in \f$O(Nn{\rm log}(n))\f$ time. The Sliced Wasserstein Kernel is then computed as: + * + * \f$ k(D_1,D_2) = {\rm exp}\left(-\frac{SW(D_1,D_2)}{2\sigma^2}\right).\f$ + * + * For more details, please see \cite pmlr-v70-carriere17a . + * +**/ + +class Sliced_Wasserstein { + + protected: + Persistence_diagram diagram; + int approx; + double sigma; + std::vector<std::vector<double> > projections, projections_diagonal; + + public: + + void build_rep(){ + + if(approx > 0){ + + double step = pi/this->approx; + int n = diagram.size(); + + for (int i = 0; i < this->approx; i++){ + std::vector<double> l,l_diag; + for (int j = 0; j < n; j++){ + + double px = diagram[j].first; double py = diagram[j].second; + double proj_diag = (px+py)/2; + + l.push_back ( px * cos(-pi/2+i*step) + py * sin(-pi/2+i*step) ); + l_diag.push_back ( proj_diag * cos(-pi/2+i*step) + proj_diag * sin(-pi/2+i*step) ); + } + + std::sort(l.begin(), l.end()); std::sort(l_diag.begin(), l_diag.end()); + projections.push_back(l); projections_diagonal.push_back(l_diag); + + } + + } + + } + + /** \brief Sliced Wasserstein kernel constructor. + * \ingroup Sliced_Wasserstein + * + * @param[in] _diagram persistence diagram. + * @param[in] _sigma bandwidth parameter. + * @param[in] _approx number of directions used to approximate the integral in the Sliced Wasserstein distance, set to -1 for exact computation. + * + */ + Sliced_Wasserstein(const Persistence_diagram & _diagram, double _sigma = 1.0, int _approx = 100){diagram = _diagram; approx = _approx; sigma = _sigma; build_rep();} + + // ********************************** + // Utils. + // ********************************** + + // Compute the angle formed by two points of a PD + double compute_angle(const Persistence_diagram & diag, int i, int j) const { + std::pair<double,double> vect; double x1,y1, x2,y2; + x1 = diag[i].first; y1 = diag[i].second; + x2 = diag[j].first; y2 = diag[j].second; + if (y1 - y2 > 0){ + vect.first = y1 - y2; + vect.second = x2 - x1;} + else{ + if(y1 - y2 < 0){ + vect.first = y2 - y1; + vect.second = x1 - x2; + } + else{ + vect.first = 0; + vect.second = abs(x1 - x2);} + } + double norm = std::sqrt(vect.first*vect.first + vect.second*vect.second); + return asin(vect.second/norm); + } + + // Compute the integral of |cos()| between alpha and beta, valid only if alpha is in [-pi,pi] and beta-alpha is in [0,pi] + double compute_int_cos(double alpha, double beta) const { + double res = 0; + if (alpha >= 0 && alpha <= pi){ + if (cos(alpha) >= 0){ + if(pi/2 <= beta){res = 2-sin(alpha)-sin(beta);} + else{res = sin(beta)-sin(alpha);} + } + else{ + if(1.5*pi <= beta){res = 2+sin(alpha)+sin(beta);} + else{res = sin(alpha)-sin(beta);} + } + } + if (alpha >= -pi && alpha <= 0){ + if (cos(alpha) <= 0){ + if(-pi/2 <= beta){res = 2+sin(alpha)+sin(beta);} + else{res = sin(alpha)-sin(beta);} + } + else{ + if(pi/2 <= beta){res = 2-sin(alpha)-sin(beta);} + else{res = sin(beta)-sin(alpha);} + } + } + return res; + } + + double compute_int(double theta1, double theta2, int p, int q, const Persistence_diagram & diag1, const Persistence_diagram & diag2) const { + double norm = std::sqrt( (diag1[p].first-diag2[q].first)*(diag1[p].first-diag2[q].first) + (diag1[p].second-diag2[q].second)*(diag1[p].second-diag2[q].second) ); + double angle1; + if (diag1[p].first > diag2[q].first) + angle1 = theta1 - asin( (diag1[p].second-diag2[q].second)/norm ); + else + angle1 = theta1 - asin( (diag2[q].second-diag1[p].second)/norm ); + double angle2 = angle1 + theta2 - theta1; + double integral = compute_int_cos(angle1,angle2); + return norm*integral; + } + + + + + // ********************************** + // Scalar product + distance. + // ********************************** + + /** \brief Evaluation of the Sliced Wasserstein Distance between a pair of diagrams. + * \ingroup Sliced_Wasserstein + * + * @pre approx attribute needs to be the same for both instances. + * @param[in] second other instance of class Sliced_Wasserstein. + * + * + */ + double compute_sliced_wasserstein_distance(const Sliced_Wasserstein & second) const { + + GUDHI_CHECK(this->approx != second.approx, std::invalid_argument("Error: different approx values for representations")); + + Persistence_diagram diagram1 = this->diagram; Persistence_diagram diagram2 = second.diagram; double sw = 0; + + if(this->approx == -1){ + + // Add projections onto diagonal. + int n1, n2; n1 = diagram1.size(); n2 = diagram2.size(); double max_ordinate = std::numeric_limits<double>::lowest(); + for (int i = 0; i < n2; i++){ + max_ordinate = std::max(max_ordinate, diagram2[i].second); + diagram1.emplace_back( (diagram2[i].first+diagram2[i].second)/2, (diagram2[i].first+diagram2[i].second)/2 ); + } + for (int i = 0; i < n1; i++){ + max_ordinate = std::max(max_ordinate, diagram1[i].second); + diagram2.emplace_back( (diagram1[i].first+diagram1[i].second)/2, (diagram1[i].first+diagram1[i].second)/2 ); + } + int num_pts_dgm = diagram1.size(); + + // Slightly perturb the points so that the PDs are in generic positions. + int mag = 0; while(max_ordinate > 10){mag++; max_ordinate/=10;} + double thresh = pow(10,-5+mag); + srand(time(NULL)); + for (int i = 0; i < num_pts_dgm; i++){ + diagram1[i].first += thresh*(1.0-2.0*rand()/RAND_MAX); diagram1[i].second += thresh*(1.0-2.0*rand()/RAND_MAX); + diagram2[i].first += thresh*(1.0-2.0*rand()/RAND_MAX); diagram2[i].second += thresh*(1.0-2.0*rand()/RAND_MAX); + } + + // Compute all angles in both PDs. + std::vector<std::pair<double, std::pair<int,int> > > angles1, angles2; + for (int i = 0; i < num_pts_dgm; i++){ + for (int j = i+1; j < num_pts_dgm; j++){ + double theta1 = compute_angle(diagram1,i,j); double theta2 = compute_angle(diagram2,i,j); + angles1.emplace_back(theta1, std::pair<int,int>(i,j)); + angles2.emplace_back(theta2, std::pair<int,int>(i,j)); + } + } + + // Sort angles. + std::sort(angles1.begin(), angles1.end(), [=](std::pair<double, std::pair<int,int> >& p1, const std::pair<double, std::pair<int,int> >& p2){return (p1.first < p2.first);}); + std::sort(angles2.begin(), angles2.end(), [=](std::pair<double, std::pair<int,int> >& p1, const std::pair<double, std::pair<int,int> >& p2){return (p1.first < p2.first);}); + + // Initialize orders of the points of both PDs (given by ordinates when theta = -pi/2). + std::vector<int> orderp1, orderp2; + for (int i = 0; i < num_pts_dgm; i++){ orderp1.push_back(i); orderp2.push_back(i); } + std::sort( orderp1.begin(), orderp1.end(), [=](int i, int j){ if(diagram1[i].second != diagram1[j].second) return (diagram1[i].second < diagram1[j].second); else return (diagram1[i].first > diagram1[j].first); } ); + std::sort( orderp2.begin(), orderp2.end(), [=](int i, int j){ if(diagram2[i].second != diagram2[j].second) return (diagram2[i].second < diagram2[j].second); else return (diagram2[i].first > diagram2[j].first); } ); + + // Find the inverses of the orders. + std::vector<int> order1(num_pts_dgm); std::vector<int> order2(num_pts_dgm); + for(int i = 0; i < num_pts_dgm; i++) for (int j = 0; j < num_pts_dgm; j++) if(orderp1[j] == i){ order1[i] = j; break; } + for(int i = 0; i < num_pts_dgm; i++) for (int j = 0; j < num_pts_dgm; j++) if(orderp2[j] == i){ order2[i] = j; break; } + + // Record all inversions of points in the orders as theta varies along the positive half-disk. + std::vector<std::vector<std::pair<int,double> > > anglePerm1(num_pts_dgm); + std::vector<std::vector<std::pair<int,double> > > anglePerm2(num_pts_dgm); + + int m1 = angles1.size(); + for (int i = 0; i < m1; i++){ + double theta = angles1[i].first; int p = angles1[i].second.first; int q = angles1[i].second.second; + anglePerm1[order1[p]].emplace_back(p,theta); + anglePerm1[order1[q]].emplace_back(q,theta); + int a = order1[p]; int b = order1[q]; order1[p] = b; order1[q] = a; + } + + int m2 = angles2.size(); + for (int i = 0; i < m2; i++){ + double theta = angles2[i].first; int p = angles2[i].second.first; int q = angles2[i].second.second; + anglePerm2[order2[p]].emplace_back(p,theta); + anglePerm2[order2[q]].emplace_back(q,theta); + int a = order2[p]; int b = order2[q]; order2[p] = b; order2[q] = a; + } + + for (int i = 0; i < num_pts_dgm; i++){ + anglePerm1[order1[i]].emplace_back(i,pi/2); + anglePerm2[order2[i]].emplace_back(i,pi/2); + } + + // Compute the SW distance with the list of inversions. + for (int i = 0; i < num_pts_dgm; i++){ + std::vector<std::pair<int,double> > u,v; u = anglePerm1[i]; v = anglePerm2[i]; + double theta1, theta2; theta1 = -pi/2; + unsigned int ku, kv; ku = 0; kv = 0; theta2 = std::min(u[ku].second,v[kv].second); + while(theta1 != pi/2){ + if(diagram1[u[ku].first].first != diagram2[v[kv].first].first || diagram1[u[ku].first].second != diagram2[v[kv].first].second) + if(theta1 != theta2) + sw += compute_int(theta1, theta2, u[ku].first, v[kv].first, diagram1, diagram2); + theta1 = theta2; + if ( (theta2 == u[ku].second) && ku < u.size()-1 ) ku++; + if ( (theta2 == v[kv].second) && kv < v.size()-1 ) kv++; + theta2 = std::min(u[ku].second, v[kv].second); + } + } + } + + + else{ + + double step = pi/this->approx; + for (int i = 0; i < this->approx; i++){ + + std::vector<double> v1; std::vector<double> l1 = this->projections[i]; std::vector<double> l1bis = second.projections_diagonal[i]; std::merge(l1.begin(), l1.end(), l1bis.begin(), l1bis.end(), std::back_inserter(v1)); + std::vector<double> v2; std::vector<double> l2 = second.projections[i]; std::vector<double> l2bis = this->projections_diagonal[i]; std::merge(l2.begin(), l2.end(), l2bis.begin(), l2bis.end(), std::back_inserter(v2)); + int n = v1.size(); double f = 0; + for (int j = 0; j < n; j++) f += std::abs(v1[j] - v2[j]); + sw += f*step; + + } + } + + return sw/pi; + } + + /** \brief Evaluation of the kernel on a pair of diagrams. + * \ingroup Sliced_Wasserstein + * + * @pre approx and sigma attributes need to be the same for both instances. + * @param[in] second other instance of class Sliced_Wasserstein. + * + */ + double compute_scalar_product(const Sliced_Wasserstein & second) const { + GUDHI_CHECK(this->sigma != second.sigma, std::invalid_argument("Error: different sigma values for representations")); + return std::exp(-compute_sliced_wasserstein_distance(second)/(2*this->sigma*this->sigma)); + } + + /** \brief Evaluation of the distance between images of diagrams in the Hilbert space of the kernel. + * \ingroup Sliced_Wasserstein + * + * @pre approx and sigma attributes need to be the same for both instances. + * @param[in] second other instance of class Sliced_Wasserstein. + * + */ + double distance(const Sliced_Wasserstein & second) const { + GUDHI_CHECK(this->sigma != second.sigma, std::invalid_argument("Error: different sigma values for representations")); + return std::pow(this->compute_scalar_product(*this) + second.compute_scalar_product(second)-2*this->compute_scalar_product(second), 0.5); + } + + + + +}; // class Sliced_Wasserstein +} // namespace Persistence_representations +} // namespace Gudhi + +#endif // SLICED_WASSERSTEIN_H_ diff --git a/src/Persistence_representations/include/gudhi/Weight_functions.h b/src/Persistence_representations/include/gudhi/Weight_functions.h new file mode 100644 index 00000000..78de406d --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Weight_functions.h @@ -0,0 +1,81 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef WEIGHT_FUNCTIONS_H_ +#define WEIGHT_FUNCTIONS_H_ + +// gudhi include +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> + +// standard include +#include <cmath> +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <string> +#include <utility> +#include <functional> + +namespace Gudhi { +namespace Persistence_representations { + +/** \fn static double pss_weight(std::pair<double,double> p) + * \brief Persistence Scale Space kernel weight function. + * \ingroup Persistence_representations + * + * @param[in] p point in 2D. + */ +static double pss_weight(std::pair<double,double> p) {if(p.second > p.first) return 1; else return -1;} + +/** \fn static double linear_weight(std::pair<double,double> p) + * \brief Linear weight function. + * \ingroup Persistence_representations + * + * @param[in] p point in 2D. + */ +static double linear_weight(std::pair<double,double> p) {return std::abs(p.second - p.first);} + +/** \fn static double const_weight(std::pair<double,double> p) + * \brief Constant weight function. + * \ingroup Persistence_representations + * + * @param[in] p point in 2D. + */ +static double const_weight(std::pair<double,double> p) {return 1;} + +/** \fn static std::function<double (std::pair<double,double>) > arctan_weight(double C, double alpha) + * \brief Returns the arctan weight function with parameters C and alpha. + * \ingroup Persistence_representations + * + * @param[in] C positive constant. + * @param[in] alpha positive power. + */ +static std::function<double (std::pair<double,double>) > arctan_weight(double C, double alpha) {return [=](std::pair<double,double> p){return C * atan(std::pow(std::abs(p.second - p.first), alpha));};} + +} // namespace Persistence_representations +} // namespace Gudhi + +#endif // WEIGHT_FUNCTIONS_H_ diff --git a/src/Persistence_representations/include/gudhi/common_persistence_representations.h b/src/Persistence_representations/include/gudhi/common_persistence_representations.h index 44e125a7..884fce58 100644 --- a/src/Persistence_representations/include/gudhi/common_persistence_representations.h +++ b/src/Persistence_representations/include/gudhi/common_persistence_representations.h @@ -26,17 +26,30 @@ #include <utility> #include <string> #include <cmath> +#include <boost/math/constants/constants.hpp> + +/** + * In this module, we use the name Persistence_diagram for the representation of a diagram in a vector of pairs of two double. + */ +using Persistence_diagram = std::vector<std::pair<double,double> >; + +/** + * In this module, we use the name Weight for the representation of a function taking a pair of two double and returning a double. + */ +using Weight = std::function<double (std::pair<double,double>) >; namespace Gudhi { namespace Persistence_representations { // this file contain an implementation of some common procedures used in Persistence_representations. +static constexpr double pi = boost::math::constants::pi<double>(); + // double epsi = std::numeric_limits<double>::epsilon(); double epsi = 0.000005; /** * A procedure used to compare doubles. Typically given two doubles A and B, comparing A == B is not good idea. In this - *case, we use the procedure almostEqual with the epsi defined at + * case, we use the procedure almostEqual with the epsi defined at * the top of the file. Setting up the epsi gives the user a tolerance on what should be consider equal. **/ inline bool almost_equal(double a, double b) { @@ -53,8 +66,7 @@ double birth_plus_deaths(std::pair<double, double> a) { return a.first + a.secon // landscapes /** - * Given two points in R^2, the procedure compute the parameters A and B of the line y = Ax + B that crosses those two - *points. + * Given two points in R^2, the procedure compute the parameters A and B of the line y = Ax + B that crosses those two points. **/ std::pair<double, double> compute_parameters_of_a_line(std::pair<double, double> p1, std::pair<double, double> p2) { double a = (p2.second - p1.second) / (p2.first - p1.first); @@ -64,8 +76,7 @@ std::pair<double, double> compute_parameters_of_a_line(std::pair<double, double> // landscapes /** - * This procedure given two points which lies on the opposite sides of x axis, compute x for which the line connecting - *those two points crosses x axis. + * This procedure given two points which lies on the opposite sides of x axis, compute x for which the line connecting those two points crosses x axis. **/ double find_zero_of_a_line_segment_between_those_two_points(std::pair<double, double> p1, std::pair<double, double> p2) { @@ -89,8 +100,7 @@ double find_zero_of_a_line_segment_between_those_two_points(std::pair<double, do // landscapes /** * This method provides a comparison of points that is used in construction of persistence landscapes. The ordering is - *lexicographical for the first coordinate, and reverse-lexicographical for the - * second coordinate. + * lexicographical for the first coordinate, and reverse-lexicographical for the second coordinate. **/ bool compare_points_sorting(std::pair<double, double> f, std::pair<double, double> s) { if (f.first < s.first) { diff --git a/src/Persistence_representations/test/CMakeLists.txt b/src/Persistence_representations/test/CMakeLists.txt index 335a71ef..ca1713c3 100644 --- a/src/Persistence_representations/test/CMakeLists.txt +++ b/src/Persistence_representations/test/CMakeLists.txt @@ -35,6 +35,11 @@ target_link_libraries(Read_persistence_from_file_test_unit ${Boost_UNIT_TEST_FRA gudhi_add_coverage_test(Read_persistence_from_file_test_unit) +add_executable ( kernels_unit kernels.cpp ) +target_link_libraries(kernels_unit ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY}) + +gudhi_add_coverage_test(kernels_unit) + if (NOT CGAL_WITH_EIGEN3_VERSION VERSION_LESS 4.8.1) add_executable (Persistence_intervals_with_distances_test_unit persistence_intervals_with_distances_test.cpp ) target_link_libraries(Persistence_intervals_with_distances_test_unit ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY}) diff --git a/src/Persistence_representations/test/kernels.cpp b/src/Persistence_representations/test/kernels.cpp new file mode 100644 index 00000000..9db19123 --- /dev/null +++ b/src/Persistence_representations/test/kernels.cpp @@ -0,0 +1,54 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carrière + * + * Copyright (C) 2018 INRIA + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#define BOOST_TEST_DYN_LINK +#define BOOST_TEST_MODULE "kernel" + +#include <boost/test/unit_test.hpp> +#include <cmath> // float comparison +#include <limits> +#include <string> +#include <vector> +#include <algorithm> // std::max +#include <gudhi/common_persistence_representations.h> +#include <gudhi/Weight_functions.h> +#include <gudhi/Persistence_weighted_gaussian.h> +#include <gudhi/Sliced_Wasserstein.h> +#include <gudhi/distance_functions.h> +#include <gudhi/reader_utils.h> + +using SW = Gudhi::Persistence_representations::Sliced_Wasserstein; +using PWG = Gudhi::Persistence_representations::Persistence_weighted_gaussian; + +BOOST_AUTO_TEST_CASE(check_PWG) { + Persistence_diagram v1, v2; v1.emplace_back(0,1); v2.emplace_back(0,2); + PWG pwg1(v1, 1.0, 1000, Gudhi::Persistence_representations::arctan_weight(1,1)); PWG pwgex1(v1, 1.0, -1, Gudhi::Persistence_representations::arctan_weight(1,1)); + PWG pwg2(v2, 1.0, 1000, Gudhi::Persistence_representations::arctan_weight(1,1)); PWG pwgex2(v2, 1.0, -1, Gudhi::Persistence_representations::arctan_weight(1,1)); + BOOST_CHECK(std::abs(pwg1.compute_scalar_product(pwg2) - pwgex1.compute_scalar_product(pwgex2)) <= 1e-1); +} + +BOOST_AUTO_TEST_CASE(check_SW) { + Persistence_diagram v1, v2; v1.emplace_back(0,1); v2.emplace_back(0,2); + SW sw1(v1, 1.0, 100); SW swex1(v1, 1.0, -1); + SW sw2(v2, 1.0, 100); SW swex2(v2, 1.0, -1); + BOOST_CHECK(std::abs(sw1.compute_scalar_product(sw2) - swex1.compute_scalar_product(swex2)) <= 1e-1); +} diff --git a/src/cmake/modules/GUDHI_modules.cmake b/src/cmake/modules/GUDHI_modules.cmake index f95d0c34..205ee8a1 100644 --- a/src/cmake/modules/GUDHI_modules.cmake +++ b/src/cmake/modules/GUDHI_modules.cmake @@ -16,8 +16,8 @@ function(add_gudhi_module file_path) endfunction(add_gudhi_module) -option(WITH_GUDHI_BENCHMARK "Activate/desactivate benchmark compilation" OFF) -option(WITH_GUDHI_EXAMPLE "Activate/desactivate examples compilation and installation" OFF) +option(WITH_GUDHI_BENCHMARK "Activate/desactivate benchmark compilation" ON) +option(WITH_GUDHI_EXAMPLE "Activate/desactivate examples compilation and installation" ON) option(WITH_GUDHI_PYTHON "Activate/desactivate python module compilation and installation" ON) option(WITH_GUDHI_TEST "Activate/desactivate examples compilation and installation" ON) option(WITH_GUDHI_UTILITIES "Activate/desactivate utilities compilation and installation" ON) diff --git a/src/cython/cython/kernels.pyx b/src/cython/cython/kernels.pyx new file mode 100644 index 00000000..0cb296ec --- /dev/null +++ b/src/cython/cython/kernels.pyx @@ -0,0 +1,126 @@ +from cython cimport numeric +from libcpp.vector cimport vector +from libcpp.utility cimport pair +import os + +"""This file is part of the Gudhi Library. The Gudhi library + (Geometric Understanding in Higher Dimensions) is a generic C++ + library for computational topology. + + Author(s): Mathieu Carriere + + Copyright (C) 2018 INRIA + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <http://www.gnu.org/licenses/>. +""" + +__author__ = "Mathieu Carriere" +__copyright__ = "Copyright (C) 2018 INRIA" +__license__ = "GPL v3" + +cdef extern from "Kernels_interface.h" namespace "Gudhi::persistence_diagram": + double sw (vector[pair[double, double]], vector[pair[double, double]], double, int) + vector[vector[double]] sw_matrix (vector[vector[pair[double, double]]], vector[vector[pair[double, double]]], double, int) + double pss (vector[pair[double, double]], vector[pair[double, double]], double, int) + vector[vector[double]] pss_matrix (vector[vector[pair[double, double]]], vector[vector[pair[double, double]]], double, int) + double pwg (vector[pair[double, double]], vector[pair[double, double]], double, int, double, double) + vector[vector[double]] pwg_matrix (vector[vector[pair[double, double]]], vector[vector[pair[double, double]]], double, int, double, double) + +def sliced_wasserstein(diagram_1, diagram_2, sigma = 1, N = 100): + """ + + :param diagram_1: The first diagram. + :type diagram_1: vector[pair[double, double]] + :param diagram_2: The second diagram. + :type diagram_2: vector[pair[double, double]] + :param sigma: bandwidth of Gaussian + :param N: number of directions + + :returns: the sliced wasserstein kernel. + """ + return sw(diagram_1, diagram_2, sigma, N) + +def sliced_wasserstein_matrix(diagrams_1, diagrams_2, sigma = 1, N = 100): + """ + + :param diagram_1: The first set of diagrams. + :type diagram_1: vector[vector[pair[double, double]]] + :param diagram_2: The second set of diagrams. + :type diagram_2: vector[vector[pair[double, double]]] + :param sigma: bandwidth of Gaussian + :param N: number of directions + + :returns: the sliced wasserstein kernel matrix. + """ + return sw_matrix(diagrams_1, diagrams_2, sigma, N) + +def persistence_weighted_gaussian(diagram_1, diagram_2, sigma = 1, N = 100, C = 1, p = 1): + """ + + :param diagram_1: The first diagram. + :type diagram_1: vector[pair[double, double]] + :param diagram_2: The second diagram. + :type diagram_2: vector[pair[double, double]] + :param sigma: bandwidth of Gaussian + :param N: number of Fourier features + :param C: cost of persistence weight + :param p: power of persistence weight + + :returns: the persistence weighted gaussian kernel. + """ + return pwg(diagram_1, diagram_2, sigma, N, C, p) + +def persistence_weighted_gaussian_matrix(diagrams_1, diagrams_2, sigma = 1, N = 100, C = 1, p = 1): + """ + + :param diagram_1: The first set of diagrams. + :type diagram_1: vector[vector[pair[double, double]]] + :param diagram_2: The second set of diagrams. + :type diagram_2: vector[vector[pair[double, double]]] + :param sigma: bandwidth of Gaussian + :param N: number of Fourier features + :param C: cost of persistence weight + :param p: power of persistence weight + + :returns: the persistence weighted gaussian kernel matrix. + """ + return pwg_matrix(diagrams_1, diagrams_2, sigma, N, C, p) + +def persistence_scale_space(diagram_1, diagram_2, sigma = 1, N = 100): + """ + + :param diagram_1: The first diagram. + :type diagram_1: vector[pair[double, double]] + :param diagram_2: The second diagram. + :type diagram_2: vector[pair[double, double]] + :param sigma: bandwidth of Gaussian + :param N: number of Fourier features + + :returns: the persistence scale space kernel. + """ + return pss(diagram_1, diagram_2, sigma, N) + +def persistence_scale_space_matrix(diagrams_1, diagrams_2, sigma = 1, N = 100): + """ + + :param diagram_1: The first set of diagrams. + :type diagram_1: vector[vector[pair[double, double]]] + :param diagram_2: The second set of diagrams. + :type diagram_2: vector[vector[pair[double, double]]] + :param sigma: bandwidth of Gaussian + :param N: number of Fourier features + + :returns: the persistence scale space kernel matrix. + """ + return pss_matrix(diagrams_1, diagrams_2, sigma, N) diff --git a/src/cython/cython/vectors.pyx b/src/cython/cython/vectors.pyx new file mode 100644 index 00000000..42390ae6 --- /dev/null +++ b/src/cython/cython/vectors.pyx @@ -0,0 +1,65 @@ +from cython cimport numeric +from libcpp.vector cimport vector +from libcpp.utility cimport pair +import os + +"""This file is part of the Gudhi Library. The Gudhi library + (Geometric Understanding in Higher Dimensions) is a generic C++ + library for computational topology. + + Author(s): Mathieu Carriere + + Copyright (C) 2018 INRIA + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <http://www.gnu.org/licenses/>. +""" + +__author__ = "Mathieu Carriere" +__copyright__ = "Copyright (C) 2018 INRIA" +__license__ = "GPL v3" + +cdef extern from "Vectors_interface.h" namespace "Gudhi::persistence_diagram": + vector[vector[double]] compute_ls (vector[pair[double, double]], int, double, double, int) + vector[vector[double]] compute_pim (vector[pair[double, double]], double, double, int, double, double, int, string, double, double, double) + +def landscape(diagram, nb_ls = 10, min_x = 0.0, max_x = 1.0, res_x = 100): + """ + + :param diagram: The diagram + :type diagram: vector[pair[double, double]] + :param nb_ls: Number of landscapes + :param min_x: Minimum abscissa + :param max_x: Maximum abscissa + :param res_x: Number of samples + + :returns: the landscape + """ + return compute_ls(diagram, nb_ls, min_x, max_x, res_x) + +def persistence_image(diagram, min_x = 0.0, max_x = 1.0, res_x = 10, min_y = 0.0, max_y = 1.0, res_y = 10, weight = "linear", sigma = 1.0, C = 1.0, p = 1.0): + """ + + :param diagram: The diagram + :type diagram: vector[vector[pair[double, double]]] + :param min_x: Minimum abscissa + :param max_x: Maximum abscissa + :param res_x: Number of abscissa pixels + :param min_x: Minimum ordinate + :param max_x: Maximum ordinate + :param res_x: Number of ordinate pixels + :param sigma: bandwidth of Gaussian + + :returns: the persistence image + """ + return compute_pim(diagram, min_x, max_x, res_x, min_y, max_y, res_y, weight, sigma, C, p) diff --git a/src/cython/gudhi.pyx.in b/src/cython/gudhi.pyx.in index a8dd9f80..3ff68085 100644 --- a/src/cython/gudhi.pyx.in +++ b/src/cython/gudhi.pyx.in @@ -36,6 +36,8 @@ include '@CMAKE_CURRENT_SOURCE_DIR@/cython/persistence_graphical_tools.py' include '@CMAKE_CURRENT_SOURCE_DIR@/cython/reader_utils.pyx' include '@CMAKE_CURRENT_SOURCE_DIR@/cython/witness_complex.pyx' include '@CMAKE_CURRENT_SOURCE_DIR@/cython/strong_witness_complex.pyx' +include '@CMAKE_CURRENT_SOURCE_DIR@/cython/kernels.pyx' +include '@CMAKE_CURRENT_SOURCE_DIR@/cython/vectors.pyx' @GUDHI_CYTHON_ALPHA_COMPLEX@ @GUDHI_CYTHON_EUCLIDEAN_WITNESS_COMPLEX@ @GUDHI_CYTHON_SUBSAMPLING@ diff --git a/src/cython/include/Kernels_interface.h b/src/cython/include/Kernels_interface.h new file mode 100644 index 00000000..03050408 --- /dev/null +++ b/src/cython/include/Kernels_interface.h @@ -0,0 +1,124 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef INCLUDE_KERNELS_INTERFACE_H_ +#define INCLUDE_KERNELS_INTERFACE_H_ + +#include <gudhi/Sliced_Wasserstein.h> +#include <gudhi/Persistence_weighted_gaussian.h> + +#include <iostream> +#include <vector> +#include <utility> // for std::pair + +namespace Gudhi { + +namespace persistence_diagram { + + + // ******************* + // Kernel evaluations. + // ******************* + + double sw(const std::vector<std::pair<double, double>>& diag1, const std::vector<std::pair<double, double>>& diag2, double sigma, int N) { + Gudhi::Persistence_representations::Sliced_Wasserstein sw1(diag1, sigma, N); + Gudhi::Persistence_representations::Sliced_Wasserstein sw2(diag2, sigma, N); + return sw1.compute_scalar_product(sw2); + } + + double pwg(const std::vector<std::pair<double, double>>& diag1, const std::vector<std::pair<double, double>>& diag2, double sigma, int N, double C, double p) { + Gudhi::Persistence_representations::Persistence_weighted_gaussian pwg1(diag1, sigma, N, Gudhi::Persistence_representations::arctan_weight(C,p)); + Gudhi::Persistence_representations::Persistence_weighted_gaussian pwg2(diag2, sigma, N, Gudhi::Persistence_representations::arctan_weight(C,p)); + return pwg1.compute_scalar_product(pwg2); + } + + double pss(const std::vector<std::pair<double, double>>& diag1, const std::vector<std::pair<double, double>>& diag2, double sigma, int N) { + std::vector<std::pair<double, double>> pd1 = diag1; int numpts = diag1.size(); for(int i = 0; i < numpts; i++) pd1.emplace_back(diag1[i].second,diag1[i].first); + std::vector<std::pair<double, double>> pd2 = diag2; numpts = diag2.size(); for(int i = 0; i < numpts; i++) pd2.emplace_back(diag2[i].second,diag2[i].first); + + Gudhi::Persistence_representations::Persistence_weighted_gaussian pwg1(pd1, 2*std::sqrt(sigma), N, Gudhi::Persistence_representations::pss_weight); + Gudhi::Persistence_representations::Persistence_weighted_gaussian pwg2(pd2, 2*std::sqrt(sigma), N, Gudhi::Persistence_representations::pss_weight); + + return pwg1.compute_scalar_product (pwg2) / (16*Gudhi::Persistence_representations::pi*sigma); + } + + double pss_sym(const std::vector<std::pair<double, double>>& diag1, const std::vector<std::pair<double, double>>& diag2, double sigma, int N) { + Gudhi::Persistence_representations::Persistence_weighted_gaussian pwg1(diag1, 2*std::sqrt(sigma), N, Gudhi::Persistence_representations::pss_weight); + Gudhi::Persistence_representations::Persistence_weighted_gaussian pwg2(diag2, 2*std::sqrt(sigma), N, Gudhi::Persistence_representations::pss_weight); + + return pwg1.compute_scalar_product (pwg2) / (16*Gudhi::Persistence_representations::pi*sigma); + } + + + // **************** + // Kernel matrices. + // **************** + + std::vector<std::vector<double> > sw_matrix(const std::vector<std::vector<std::pair<double, double> > >& s1, const std::vector<std::vector<std::pair<double, double> > >& s2, double sigma, int N){ + std::vector<std::vector<double> > matrix; + std::vector<Gudhi::Persistence_representations::Sliced_Wasserstein> ss1; + int num_diag_1 = s1.size(); for(int i = 0; i < num_diag_1; i++){Gudhi::Persistence_representations::Sliced_Wasserstein sw1(s1[i], sigma, N); ss1.push_back(sw1);} + std::vector<Gudhi::Persistence_representations::Sliced_Wasserstein> ss2; + int num_diag_2 = s2.size(); for(int i = 0; i < num_diag_2; i++){Gudhi::Persistence_representations::Sliced_Wasserstein sw2(s2[i], sigma, N); ss2.push_back(sw2);} + for(int i = 0; i < num_diag_1; i++){ + std::cout << 100.0*i/num_diag_1 << " %" << std::endl; + std::vector<double> ps; for(int j = 0; j < num_diag_2; j++) ps.push_back(ss1[i].compute_scalar_product(ss2[j])); matrix.push_back(ps); + } + return matrix; + } + + std::vector<std::vector<double> > pwg_matrix(const std::vector<std::vector<std::pair<double, double> > >& s1, const std::vector<std::vector<std::pair<double, double> > >& s2, double sigma, int N, double C, double p){ + std::vector<std::vector<double> > matrix; int num_diag_1 = s1.size(); int num_diag_2 = s2.size(); + for(int i = 0; i < num_diag_1; i++){ + std::cout << 100.0*i/num_diag_1 << " %" << std::endl; + std::vector<double> ps; for(int j = 0; j < num_diag_2; j++) ps.push_back(pwg(s1[i], s2[j], sigma, N, C, p)); matrix.push_back(ps); + } + return matrix; + } + + std::vector<std::vector<double> > pss_matrix(const std::vector<std::vector<std::pair<double, double> > >& s1, const std::vector<std::vector<std::pair<double, double> > >& s2, double sigma, int N){ + std::vector<std::vector<std::pair<double, double> > > ss1, ss2; std::vector<std::vector<double> > matrix; int num_diag_1 = s1.size(); int num_diag_2 = s2.size(); + for(int i = 0; i < num_diag_1; i++){ + std::vector<std::pair<double, double>> pd1 = s1[i]; int numpts = s1[i].size(); + for(int j = 0; j < numpts; j++) pd1.emplace_back(s1[i][j].second,s1[i][j].first); + ss1.push_back(pd1); + } + + for(int i = 0; i < num_diag_2; i++){ + std::vector<std::pair<double, double>> pd2 = s2[i]; int numpts = s2[i].size(); + for(int j = 0; j < numpts; j++) pd2.emplace_back(s2[i][j].second,s2[i][j].first); + ss2.push_back(pd2); + } + + for(int i = 0; i < num_diag_1; i++){ + std::cout << 100.0*i/num_diag_1 << " %" << std::endl; + std::vector<double> ps; for(int j = 0; j < num_diag_2; j++) ps.push_back(pss_sym(ss1[i], ss2[j], sigma, N)); matrix.push_back(ps); + } + return matrix; + } + +} // namespace persistence_diagram + +} // namespace Gudhi + + +#endif // INCLUDE_KERNELS_INTERFACE_H_ diff --git a/src/cython/include/Vectors_interface.h b/src/cython/include/Vectors_interface.h new file mode 100644 index 00000000..7e191f2a --- /dev/null +++ b/src/cython/include/Vectors_interface.h @@ -0,0 +1,59 @@ +/* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Mathieu Carriere + * + * Copyright (C) 2018 INRIA + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef INCLUDE_VECTORS_INTERFACE_H_ +#define INCLUDE_VECTORS_INTERFACE_H_ + +#include <gudhi/Landscape.h> +#include <gudhi/Persistence_image.h> +#include <gudhi/Persistence_weighted_gaussian.h> + +#include <iostream> +#include <vector> +#include <utility> // for std::pair + +using Weight = std::function<double (std::pair<double,double>) >; + +namespace Gudhi { + +namespace persistence_diagram { + + std::vector<std::vector<double> > compute_ls(const std::vector<std::pair<double, double> >& diag, int nb_ls, double min_x, double max_x, int res_x) { + Gudhi::Persistence_representations::Landscape L(diag, nb_ls, min_x, max_x, res_x); + return L.vectorize(); + } + + std::vector<std::vector<double> > compute_pim(const std::vector<std::pair<double, double> >& diag, double min_x, double max_x, int res_x, double min_y, double max_y, int res_y, std::string weight, double sigma, double C, double p) { + Weight weight_fn; + if(weight.compare("linear") == 0) weight_fn = Gudhi::Persistence_representations::linear_weight; + if(weight.compare("arctan") == 0) weight_fn = Gudhi::Persistence_representations::arctan_weight(C,p); + if(weight.compare("const") == 0) weight_fn = Gudhi::Persistence_representations::const_weight; + Gudhi::Persistence_representations::Persistence_image P(diag, min_x, max_x, res_x, min_y, max_y, res_y, weight_fn, sigma); + return P.vectorize(); + } + +} // namespace persistence_diagram + +} // namespace Gudhi + + +#endif // INCLUDE_VECTORS_INTERFACE_H_ |