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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_ |