dlib C++ Library - empirical_kernel_map.cpp

// Copyright (C) 2009 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#include "tester.h"
#include <dlib/svm.h>
#include <dlib/rand.h>
#include <dlib/string.h>
#include <vector>
#include <sstream>
#include <ctime>
namespace 
{
 using namespace test;
 using namespace dlib;
 using namespace std;
 dlib::logger dlog("test.empirical_kernel_map");
 class empirical_kernel_map_tester : public tester
 {
 /*!
 WHAT THIS OBJECT REPRESENTS
 This object represents a unit test. When it is constructed
 it adds itself into the testing framework.
 !*/
 public:
 empirical_kernel_map_tester (
 ) :
 tester (
 "test_empirical_kernel_map", // the command line argument name for this test
 "Run tests on the empirical_kernel_map object.", // the command line argument description
 0 // the number of command line arguments for this test
 )
 {
 // always use the same time so that tests are repeatable
 thetime = 0;//time(0);
 }
 time_t thetime;
 dlib::rand rnd;
 void test_projection_error()
 {
 for (int runs = 0; runs < 10; ++runs)
 {
 print_spinner();
 typedef matrix<double,0,1> sample_type;
 typedef radial_basis_kernel<sample_type> kernel_type;
 const kernel_type kern(0.2);
 empirical_kernel_map<kernel_type> ekm;
 // generate samples
 const int num = rnd.get_random_8bit_number()%50 + 1;
 std::vector<sample_type> samples;
 for (int i = 0; i < num; ++i)
 {
 samples.push_back(randm(5,1,rnd));
 }
 ekm.load(kern, samples);
 DLIB_TEST(ekm.basis_size() == samples.size());
 double err;
 // the samples in the basis should have zero projection error
 for (unsigned long i = 0; i < samples.size(); ++i)
 {
 ekm.project(samples[i], err);
 DLIB_TEST_MSG(abs(err) < 1e-13, abs(err));
 }
 
 // Do some sanity tests on the conversion to distance functions while we are at it.
 for (int i = 0; i < 30; ++i)
 {
 // pick two random samples
 const sample_type samp1 = samples[rnd.get_random_32bit_number()%samples.size()];
 const sample_type samp2 = samples[rnd.get_random_32bit_number()%samples.size()];
 const matrix<double,0,1> proj1 = ekm.project(samp1);
 const matrix<double,0,1> proj2 = ekm.project(samp2);
 distance_function<kernel_type> df1 = ekm.convert_to_distance_function(proj1);
 distance_function<kernel_type> df2 = ekm.convert_to_distance_function(proj2);
 DLIB_TEST(df1.get_kernel() == kern);
 DLIB_TEST(df2.get_kernel() == kern);
 // make sure the norms are correct
 DLIB_TEST(std::abs(df1.get_squared_norm() - 
 trans(df1.get_alpha())*kernel_matrix(df1.get_kernel(),df1.get_basis_vectors())*df1.get_alpha()) < 1e-10);
 DLIB_TEST(std::abs(df2.get_squared_norm() - 
 trans(df2.get_alpha())*kernel_matrix(df2.get_kernel(),df2.get_basis_vectors())*df2.get_alpha()) < 1e-10);
 const double true_dist = std::sqrt(kern(samp1,samp1) + kern(samp2,samp2) - 2*kern(samp1,samp2));
 DLIB_TEST_MSG(abs(df1(df2) - true_dist) < 1e-7, abs(df1(df2) - true_dist));
 DLIB_TEST_MSG(abs(length(proj1-proj2) - true_dist) < 1e-7, abs(length(proj1-proj2) - true_dist));
 
 // test distance function operators
 const decision_function<kernel_type> dec1 = ekm.convert_to_decision_function(proj1);
 const decision_function<kernel_type> dec2 = ekm.convert_to_decision_function(proj2);
 DLIB_TEST(dec1.kernel_function == kern);
 DLIB_TEST(dec2.kernel_function == kern);
 distance_function<kernel_type> temp;
 temp = dec1;
 DLIB_TEST(std::abs(temp.get_squared_norm() - df1.get_squared_norm()) < 1e-10);
 temp = dec2;
 DLIB_TEST(std::abs(temp.get_squared_norm() - df2.get_squared_norm()) < 1e-10);
 temp = distance_function<kernel_type>(dec1.alpha, dec1.kernel_function, dec1.basis_vectors);
 DLIB_TEST(std::abs(temp.get_squared_norm() - df1.get_squared_norm()) < 1e-10);
 df1 = dec1;
 temp = df1 + df2;
 decision_function<kernel_type> dec3(temp.get_alpha(), 0, temp.get_kernel(), temp.get_basis_vectors()); 
 DLIB_TEST(std::abs(temp.get_squared_norm() - 
 trans(temp.get_alpha())*kernel_matrix(temp.get_kernel(),temp.get_basis_vectors())*temp.get_alpha()) < 1e-10);
 for (unsigned long j = 0; j < samples.size(); ++j)
 {
 DLIB_TEST(std::abs(dec3(samples[j]) - (dec1(samples[j]) + dec2(samples[j]))) < 1e-10);
 }
 temp = df1 - df2;
 dec3 = decision_function<kernel_type>(temp.get_alpha(), 0, temp.get_kernel(), temp.get_basis_vectors()); 
 DLIB_TEST(std::abs(temp.get_squared_norm() - 
 trans(temp.get_alpha())*kernel_matrix(temp.get_kernel(),temp.get_basis_vectors())*temp.get_alpha()) < 1e-10);
 for (unsigned long j = 0; j < samples.size(); ++j)
 {
 DLIB_TEST(std::abs(dec3(samples[j]) - (dec1(samples[j]) - dec2(samples[j]))) < 1e-10);
 }
 temp = 3*(df1 - df2)*2;
 dec3 = decision_function<kernel_type>(temp.get_alpha(), 0, temp.get_kernel(), temp.get_basis_vectors()); 
 DLIB_TEST(std::abs(temp.get_squared_norm() - 
 trans(temp.get_alpha())*kernel_matrix(temp.get_kernel(),temp.get_basis_vectors())*temp.get_alpha()) < 1e-10);
 for (unsigned long j = 0; j < samples.size(); ++j)
 {
 DLIB_TEST(std::abs(dec3(samples[j]) - 6*(dec1(samples[j]) - dec2(samples[j]))) < 1e-10);
 }
 distance_function<kernel_type> df_empty(kern);
 temp = df_empty + (df1 + df2)/2 + df_empty - df_empty + (df_empty + df_empty) - (df_empty - df_empty);
 dec3 = decision_function<kernel_type>(temp.get_alpha(), 0, temp.get_kernel(), temp.get_basis_vectors()); 
 DLIB_TEST(std::abs(temp.get_squared_norm() - 
 trans(temp.get_alpha())*kernel_matrix(temp.get_kernel(),temp.get_basis_vectors())*temp.get_alpha()) < 1e-10);
 for (unsigned long j = 0; j < samples.size(); ++j)
 {
 DLIB_TEST(std::abs(dec3(samples[j]) - 0.5*(dec1(samples[j]) + dec2(samples[j]))) < 1e-10);
 }
 }
 // Do some sanity tests on the conversion to distance functions while we are at it. This
 // time multiply one of the projections by 30 and see that it still all works out right.
 for (int i = 0; i < 30; ++i)
 {
 // pick two random samples
 const sample_type samp1 = samples[rnd.get_random_32bit_number()%samples.size()];
 const sample_type samp2 = samples[rnd.get_random_32bit_number()%samples.size()];
 matrix<double,0,1> proj1 = ekm.project(samp1);
 matrix<double,0,1> proj2 = 30*ekm.project(samp2);
 distance_function<kernel_type> df1 = ekm.convert_to_distance_function(proj1);
 distance_function<kernel_type> df2 = ekm.convert_to_distance_function(proj2);
 DLIB_TEST_MSG(abs(length(proj1-proj2) - df1(df2)) < 1e-7, abs(length(proj1-proj2) - df1(df2)));
 }
 // now generate points with projection error
 for (double i = 1; i < 10; ++i)
 {
 sample_type test_point = i*randm(5,1,rnd);
 ekm.project(test_point, err);
 // turn into normal distance rather than squared distance
 err = sqrt(err);
 dlog << LTRACE << "projection error: " << err;
 distance_function<kernel_type> df = ekm.convert_to_distance_function(ekm.project(test_point));
 // the projection error should be the distance between the test_point and the point it gets
 // projected onto
 DLIB_TEST_MSG(abs(df(test_point) - err) < 1e-10, abs(df(test_point) - err));
 // while we are at it make sure the squared norm in the distance function is right
 double df_error = abs(df.get_squared_norm() - trans(df.get_alpha())*kernel_matrix(kern, samples)*df.get_alpha());
 DLIB_TEST_MSG( df_error < 1e-10, df_error);
 }
 }
 }
 template <typename kernel_type>
 void test_with_kernel(const kernel_type& kern)
 {
 typedef typename kernel_type::sample_type sample_type;
 empirical_kernel_map<kernel_type> ekm, ekm2, ekm3;
 for (int j = 0; j < 10; ++j)
 {
 sample_type samp;
 std::vector<sample_type> samples;
 std::vector<sample_type> proj_samples;
 print_spinner();
 const int num = rnd.get_random_8bit_number()%200 + 1;
 // make some random samples
 for (int i = 0; i < num; ++i)
 {
 samples.push_back(randm(4,1,rnd));
 }
 // add on a little bit to make sure there is at least one non-zero sample. If all the 
 // samples are zero then empirical_kernel_map_error will be thrown and we don't want that.
 samples.front()(0) += 0.001;
 ekm2.load(kern, samples);
 DLIB_TEST(ekm2.basis_size() == samples.size());
 for (unsigned long i = 0; i < samples.size(); ++i)
 DLIB_TEST(dlib::equal(ekm2[i] , samples[i]));
 // test serialization
 ostringstream sout;
 serialize(ekm2, sout);
 ekm2.clear();
 istringstream sin(sout.str());
 deserialize(ekm3, sin);
 // also test swap
 ekm3.swap(ekm);
 DLIB_TEST(ekm.get_kernel() == kern);
 DLIB_TEST(ekm.out_vector_size() != 0);
 DLIB_TEST(ekm2.out_vector_size() == 0);
 DLIB_TEST(ekm3.out_vector_size() == 0);
 // project all the samples into kernel space
 for (unsigned long i = 0; i < samples.size(); ++i)
 {
 proj_samples.push_back(ekm.project(samples[i]));
 }
 DLIB_TEST(max(abs(kernel_matrix(kern, samples) - kernel_matrix(linear_kernel<sample_type>(), proj_samples))) < 1e-12);
 DLIB_TEST(ekm.out_vector_size() == proj_samples[0].size());
 for (int i = 0; i < 30; ++i)
 {
 const unsigned long idx1 = rnd.get_random_32bit_number()%samples.size();
 const unsigned long idx2 = rnd.get_random_32bit_number()%samples.size();
 decision_function<kernel_type> dec_funct = ekm.convert_to_decision_function(proj_samples[idx1]);
 distance_function<kernel_type> dist_funct = ekm.convert_to_distance_function(proj_samples[idx1]);
 // make sure the distances match 
 const double dist_error = abs(length(proj_samples[idx1] - proj_samples[idx2]) - dist_funct(samples[idx2]));
 DLIB_TEST_MSG( dist_error < 1e-6, dist_error);
 // make sure the dot products match 
 DLIB_TEST(abs(dot(proj_samples[idx1],proj_samples[idx2]) - dec_funct(samples[idx2])) < 1e-10);
 // also try the dec_funct with samples that weren't in the original set
 samp = 100*randm(4,1,rnd);
 // make sure the dot products match 
 DLIB_TEST(abs(dot(proj_samples[idx1],ekm.project(samp)) - dec_funct(samp)) < 1e-10);
 samp = randm(4,1,rnd);
 // make sure the dot products match 
 DLIB_TEST(abs(dot(proj_samples[idx1],ekm.project(samp)) - dec_funct(samp)) < 1e-10);
 }
 proj_samples.clear();
 // now do the projection but use the projection_function returned by get_projection_function()
 projection_function<kernel_type> proj2 = ekm.get_projection_function();
 projection_function<kernel_type> proj;
 sout.clear();
 sout.str("");
 sin.clear();
 sin.str("");
 // test serialization
 serialize(proj2, sout);
 sin.str(sout.str());
 deserialize(proj, sin);
 for (unsigned long i = 0; i < samples.size(); ++i)
 {
 proj_samples.push_back(proj(samples[i]));
 }
 DLIB_TEST(max(abs(kernel_matrix(kern, samples) - kernel_matrix(linear_kernel<sample_type>(), proj_samples))) < 1e-12);
 DLIB_TEST(ekm.out_vector_size() == proj_samples[0].size());
 DLIB_TEST(proj.out_vector_size() == proj_samples[0].size());
 ekm.clear();
 DLIB_TEST(ekm.out_vector_size() == 0);
 DLIB_TEST(ekm2.out_vector_size() == 0);
 DLIB_TEST(ekm3.out_vector_size() == 0);
 for (int i = 0; i < 30; ++i)
 {
 const unsigned long idx1 = rnd.get_random_32bit_number()%samples.size();
 const unsigned long idx2 = rnd.get_random_32bit_number()%samples.size();
 decision_function<kernel_type> dec_funct = convert_to_decision_function(proj,proj_samples[idx1]);
 // make sure the dot products match 
 DLIB_TEST(abs(dot(proj_samples[idx1],proj_samples[idx2]) - dec_funct(samples[idx2])) < 1e-10);
 // also try the dec_funct with samples that weren't in the original set
 samp = 100*randm(4,1,rnd);
 // make sure the dot products match 
 DLIB_TEST(abs(dot(proj_samples[idx1],proj(samp)) - dec_funct(samp)) < 1e-10);
 samp = randm(4,1,rnd);
 // make sure the dot products match 
 DLIB_TEST(abs(dot(proj_samples[idx1],proj(samp)) - dec_funct(samp)) < 1e-10);
 }
 }
 for (int j = 1; j <= 20; ++j)
 {
 dlog << LTRACE << "j: " << j;
 sample_type samp, samp2;
 std::vector<sample_type> samples1;
 std::vector<sample_type> samples2;
 print_spinner();
 // make some random samples. At the end samples1 will be a subset of samples2
 for (int i = 0; i < 5*j; ++i)
 {
 samples1.push_back(randm(10,1,rnd));
 samples2.push_back(samples1.back());
 }
 for (int i = 0; i < 5*j; ++i)
 {
 samples2.push_back(randm(10,1,rnd));
 }
 // add on a little bit to make sure there is at least one non-zero sample. If all the 
 // samples are zero then empirical_kernel_map_error will be thrown and we don't want that.
 samples1.front()(0) += 0.001;
 samples2.front()(0) += 0.001;
 ekm.load(kern, samples1);
 for (unsigned long i = 0; i < samples1.size(); ++i)
 DLIB_TEST(dlib::equal(ekm[i] , samples1[i]));
 DLIB_TEST(ekm.basis_size() == samples1.size());
 ekm2.load(kern, samples2);
 DLIB_TEST(ekm2.basis_size() == samples2.size());
 
 dlog << LTRACE << "ekm.out_vector_size(): " << ekm.out_vector_size();
 dlog << LTRACE << "ekm2.out_vector_size(): " << ekm2.out_vector_size();
 const double eps = 1e-6;
 matrix<double> transform;
 // Make sure transformations back to yourself work right. Note that we can't just
 // check that transform is the identity matrix since it might be an identity transform
 // for only a subspace of vectors (this happens if the ekm maps points into a subspace of
 // all possible ekm.out_vector_size() vectors).
 transform = ekm.get_transformation_to(ekm);
 DLIB_TEST(transform.nr() == ekm.out_vector_size());
 DLIB_TEST(transform.nc() == ekm.out_vector_size());
 for (unsigned long i = 0; i < samples1.size(); ++i)
 {
 samp = ekm.project(samples1[i]);
 DLIB_TEST_MSG(length(samp - transform*samp) < eps, length(samp - transform*samp));
 samp = ekm.project((samples1[0] + samples1[i])/2);
 DLIB_TEST_MSG(length(samp - transform*samp) < eps, length(samp - transform*samp));
 }
 transform = ekm2.get_transformation_to(ekm2);
 DLIB_TEST(transform.nr() == ekm2.out_vector_size());
 DLIB_TEST(transform.nc() == ekm2.out_vector_size());
 for (unsigned long i = 0; i < samples2.size(); ++i)
 {
 samp = ekm2.project(samples2[i]);
 DLIB_TEST_MSG(length(samp - transform*samp) < eps, length(samp - transform*samp));
 samp = ekm2.project((samples2[0] + samples2[i])/2);
 DLIB_TEST_MSG(length(samp - transform*samp) < eps, length(samp - transform*samp));
 //dlog << LTRACE << "mapping error: " << length(samp - transform*samp);
 }
 // now test the transform from ekm to ekm2
 transform = ekm.get_transformation_to(ekm2);
 DLIB_TEST(transform.nr() == ekm2.out_vector_size());
 DLIB_TEST(transform.nc() == ekm.out_vector_size());
 for (unsigned long i = 0; i < samples1.size(); ++i)
 {
 samp = ekm.project(samples1[i]);
 distance_function<kernel_type> df1 = ekm.convert_to_distance_function(samp);
 distance_function<kernel_type> df2 = ekm2.convert_to_distance_function(transform*samp);
 DLIB_TEST_MSG(df1(df2) < eps, df1(df2));
 //dlog << LTRACE << "mapping error: " << df1(df2);
 samp = ekm.project((samples1[0] + samples1[i])/2);
 df1 = ekm.convert_to_distance_function(samp);
 df2 = ekm2.convert_to_distance_function(transform*samp);
 DLIB_TEST_MSG(df1(df2) < eps, df1(df2));
 }
 }
 }
 void perform_test (
 )
 {
 ++thetime;
 typedef matrix<double,0,1> sample_type;
 dlog << LINFO << "time seed: " << thetime;
 rnd.set_seed(cast_to_string(thetime));
 print_spinner();
 test_projection_error();
 print_spinner();
 dlog << LINFO << "test with linear kernel";
 test_with_kernel(linear_kernel<sample_type>());
 print_spinner();
 dlog << LINFO << "test with rbf kernel";
 test_with_kernel(radial_basis_kernel<sample_type>(0.2));
 print_spinner();
 }
 };
 // Create an instance of this object. Doing this causes this test
 // to be automatically inserted into the testing framework whenever this cpp file
 // is linked into the project. Note that since we are inside an unnamed-namespace 
 // we won't get any linker errors about the symbol a being defined multiple times. 
 empirical_kernel_map_tester a;
}