dlib C++ Library - reduced.h

// Copyright (C) 2008 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_REDUCEd_TRAINERS_
#define DLIB_REDUCEd_TRAINERS_
#include "reduced_abstract.h"
#include "../matrix.h"
#include "../algs.h"
#include "function.h"
#include "kernel.h"
#include "kcentroid.h"
#include "linearly_independent_subset_finder.h"
#include "../optimization.h"
namespace dlib
{
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
 template <
 typename trainer_type 
 >
 class reduced_decision_function_trainer
 {
 public:
 typedef typename trainer_type::kernel_type kernel_type;
 typedef typename trainer_type::scalar_type scalar_type;
 typedef typename trainer_type::sample_type sample_type;
 typedef typename trainer_type::mem_manager_type mem_manager_type;
 typedef typename trainer_type::trained_function_type trained_function_type;
 reduced_decision_function_trainer (
 ) :num_bv(0) {}
 reduced_decision_function_trainer (
 const trainer_type& trainer_,
 const unsigned long num_sb_ 
 ) :
 trainer(trainer_),
 num_bv(num_sb_)
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(num_bv > 0,
 "\t reduced_decision_function_trainer()"
 << "\n\t you have given invalid arguments to this function"
 << "\n\t num_bv: " << num_bv 
 );
 }
 template <
 typename in_sample_vector_type,
 typename in_scalar_vector_type
 >
 const decision_function<kernel_type> train (
 const in_sample_vector_type& x,
 const in_scalar_vector_type& y
 ) const
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(num_bv > 0,
 "\t reduced_decision_function_trainer::train(x,y)"
 << "\n\t You have tried to use an uninitialized version of this object"
 << "\n\t num_bv: " << num_bv );
 return do_train(mat(x), mat(y));
 }
 private:
 // ------------------------------------------------------------------------------------
 template <
 typename in_sample_vector_type,
 typename in_scalar_vector_type
 >
 const decision_function<kernel_type> do_train (
 const in_sample_vector_type& x,
 const in_scalar_vector_type& y
 ) const
 {
 // get the decision function object we are going to try and approximate
 const decision_function<kernel_type>& dec_funct = trainer.train(x,y);
 
 // now find a linearly independent subset of the training points of num_bv points.
 linearly_independent_subset_finder<kernel_type> lisf(dec_funct.kernel_function, num_bv);
 fill_lisf(lisf, x);
 // The next few statements just find the best weights with which to approximate 
 // the dec_funct object with the smaller set of vectors in the lisf dictionary. This
 // is really just a simple application of some linear algebra. For the details 
 // see page 554 of Learning with kernels by Scholkopf and Smola where they talk 
 // about "Optimal Expansion Coefficients."
 const kernel_type kern(dec_funct.kernel_function);
 matrix<scalar_type,0,1,mem_manager_type> alpha;
 alpha = lisf.get_inv_kernel_marix()*(kernel_matrix(kern,lisf,dec_funct.basis_vectors)*dec_funct.alpha);
 decision_function<kernel_type> new_df(alpha, 
 0,
 kern, 
 lisf.get_dictionary());
 // now we have to figure out what the new bias should be. It might be a little
 // different since we just messed with all the weights and vectors.
 double bias = 0;
 for (long i = 0; i < x.nr(); ++i)
 {
 bias += new_df(x(i)) - dec_funct(x(i));
 }
 
 new_df.b = bias/x.nr();
 return new_df;
 }
 // ------------------------------------------------------------------------------------
 trainer_type trainer;
 unsigned long num_bv; 
 }; // end of class reduced_decision_function_trainer
 template <typename trainer_type>
 const reduced_decision_function_trainer<trainer_type> reduced (
 const trainer_type& trainer,
 const unsigned long num_bv
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(num_bv > 0,
 "\tconst reduced_decision_function_trainer reduced()"
 << "\n\t you have given invalid arguments to this function"
 << "\n\t num_bv: " << num_bv 
 );
 return reduced_decision_function_trainer<trainer_type>(trainer, num_bv);
 }
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
 namespace red_impl
 {
 // ------------------------------------------------------------------------------------
 template <typename kernel_type>
 class objective
 {
 /*
 This object represents the objective function we will try to
 minimize in approximate_distance_function(). 
 The objective is the distance, in kernel induced feature space, between
 the original distance function and the approximated version.
 */
 typedef typename kernel_type::scalar_type scalar_type;
 typedef typename kernel_type::sample_type sample_type;
 typedef typename kernel_type::mem_manager_type mem_manager_type;
 public:
 objective(
 const distance_function<kernel_type>& dist_funct_,
 matrix<scalar_type,0,1,mem_manager_type>& b_,
 matrix<sample_type,0,1,mem_manager_type>& out_vectors_
 ) :
 dist_funct(dist_funct_),
 b(b_),
 out_vectors(out_vectors_)
 {
 }
 const matrix<scalar_type, 0, 1, mem_manager_type> state_to_vector (
 ) const
 /*!
 ensures
 - returns a vector that contains all the information necessary to
 reproduce the current state of the approximated distance function
 !*/
 {
 matrix<scalar_type, 0, 1, mem_manager_type> z(b.nr() + out_vectors.size()*out_vectors(0).nr());
 long i = 0;
 for (long j = 0; j < b.nr(); ++j)
 {
 z(i) = b(j);
 ++i;
 }
 for (long j = 0; j < out_vectors.size(); ++j)
 {
 for (long k = 0; k < out_vectors(j).size(); ++k)
 {
 z(i) = out_vectors(j)(k);
 ++i;
 }
 }
 return z;
 }
 void vector_to_state (
 const matrix<scalar_type, 0, 1, mem_manager_type>& z
 ) const
 /*!
 requires
 - z came from the state_to_vector() function or has a compatible format
 ensures
 - loads the vector z into the state variables of the approximate
 distance function (i.e. b and out_vectors)
 !*/
 {
 long i = 0;
 for (long j = 0; j < b.nr(); ++j)
 {
 b(j) = z(i);
 ++i;
 }
 for (long j = 0; j < out_vectors.size(); ++j)
 {
 for (long k = 0; k < out_vectors(j).size(); ++k)
 {
 out_vectors(j)(k) = z(i);
 ++i;
 }
 }
 }
 double operator() (
 const matrix<scalar_type, 0, 1, mem_manager_type>& z
 ) const
 /*!
 ensures
 - loads the current approximate distance function with z
 - returns the distance between the original distance function
 and the approximate one.
 !*/
 {
 vector_to_state(z);
 const kernel_type k(dist_funct.get_kernel());
 double temp = 0;
 for (long i = 0; i < out_vectors.size(); ++i)
 {
 for (long j = 0; j < dist_funct.get_basis_vectors().nr(); ++j)
 {
 temp -= b(i)*dist_funct.get_alpha()(j)*k(out_vectors(i), dist_funct.get_basis_vectors()(j));
 }
 }
 temp *= 2;
 for (long i = 0; i < out_vectors.size(); ++i)
 {
 for (long j = 0; j < out_vectors.size(); ++j)
 {
 temp += b(i)*b(j)*k(out_vectors(i), out_vectors(j));
 }
 }
 return temp + dist_funct.get_squared_norm();
 }
 private:
 const distance_function<kernel_type>& dist_funct;
 matrix<scalar_type,0,1,mem_manager_type>& b;
 matrix<sample_type,0,1,mem_manager_type>& out_vectors;
 };
 // ------------------------------------------------------------------------------------
 template <typename kernel_type>
 class objective_derivative
 {
 /*!
 This object represents the derivative of the objective object
 !*/
 typedef typename kernel_type::scalar_type scalar_type;
 typedef typename kernel_type::sample_type sample_type;
 typedef typename kernel_type::mem_manager_type mem_manager_type;
 public:
 objective_derivative(
 const distance_function<kernel_type>& dist_funct_,
 matrix<scalar_type,0,1,mem_manager_type>& b_,
 matrix<sample_type,0,1,mem_manager_type>& out_vectors_
 ) :
 dist_funct(dist_funct_),
 b(b_),
 out_vectors(out_vectors_)
 {
 }
 void vector_to_state (
 const matrix<scalar_type, 0, 1, mem_manager_type>& z
 ) const
 /*!
 requires
 - z came from the state_to_vector() function or has a compatible format
 ensures
 - loads the vector z into the state variables of the approximate
 distance function (i.e. b and out_vectors)
 !*/
 {
 long i = 0;
 for (long j = 0; j < b.nr(); ++j)
 {
 b(j) = z(i);
 ++i;
 }
 for (long j = 0; j < out_vectors.size(); ++j)
 {
 for (long k = 0; k < out_vectors(j).size(); ++k)
 {
 out_vectors(j)(k) = z(i);
 ++i;
 }
 }
 }
 const matrix<scalar_type,0,1,mem_manager_type>& operator() (
 const matrix<scalar_type, 0, 1, mem_manager_type>& z
 ) const
 /*!
 ensures
 - loads the current approximate distance function with z
 - returns the derivative of the distance between the original 
 distance function and the approximate one.
 !*/
 {
 vector_to_state(z);
 res.set_size(z.nr());
 set_all_elements(res,0);
 const kernel_type k(dist_funct.get_kernel());
 const kernel_derivative<kernel_type> K_der(k);
 // first compute the gradient for the beta weights
 for (long i = 0; i < out_vectors.size(); ++i)
 {
 for (long j = 0; j < out_vectors.size(); ++j)
 {
 res(i) += b(j)*k(out_vectors(i), out_vectors(j)); 
 }
 }
 for (long i = 0; i < out_vectors.size(); ++i)
 {
 for (long j = 0; j < dist_funct.get_basis_vectors().size(); ++j)
 {
 res(i) -= dist_funct.get_alpha()(j)*k(out_vectors(i), dist_funct.get_basis_vectors()(j)); 
 }
 }
 // now compute the gradient of the actual vectors that go into the kernel functions
 long pos = out_vectors.size();
 const long num = out_vectors(0).nr();
 temp.set_size(num,1);
 for (long i = 0; i < out_vectors.size(); ++i)
 {
 set_all_elements(temp,0);
 for (long j = 0; j < out_vectors.size(); ++j)
 {
 temp += b(j)*K_der(out_vectors(j), out_vectors(i));
 }
 for (long j = 0; j < dist_funct.get_basis_vectors().nr(); ++j)
 {
 temp -= dist_funct.get_alpha()(j)*K_der(dist_funct.get_basis_vectors()(j), out_vectors(i) );
 }
 // store the gradient for out_vectors(i) into result in the proper spot
 set_subm(res,pos,0,num,1) = b(i)*temp;
 pos += num;
 }
 res *= 2;
 return res;
 }
 private:
 mutable matrix<scalar_type, 0, 1, mem_manager_type> res;
 mutable sample_type temp;
 const distance_function<kernel_type>& dist_funct;
 matrix<scalar_type,0,1,mem_manager_type>& b;
 matrix<sample_type,0,1,mem_manager_type>& out_vectors;
 };
 // ------------------------------------------------------------------------------------
 }
 template <
 typename K,
 typename stop_strategy_type,
 typename T
 >
 distance_function<K> approximate_distance_function (
 stop_strategy_type stop_strategy,
 const distance_function<K>& target,
 const T& starting_basis
 )
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(target.get_basis_vectors().size() > 0 &&
 starting_basis.size() > 0,
 "\t distance_function approximate_distance_function()"
 << "\n\t Invalid inputs were given to this function."
 << "\n\t target.get_basis_vectors().size(): " << target.get_basis_vectors().size() 
 << "\n\t starting_basis.size(): " << starting_basis.size() 
 );
 using namespace red_impl;
 // The next few statements just find the best weights with which to approximate 
 // the target object with the set of basis vectors in starting_basis. This
 // is really just a simple application of some linear algebra. For the details 
 // see page 554 of Learning with kernels by Scholkopf and Smola where they talk 
 // about "Optimal Expansion Coefficients."
 const K kern(target.get_kernel());
 typedef typename K::scalar_type scalar_type;
 typedef typename K::sample_type sample_type;
 typedef typename K::mem_manager_type mem_manager_type;
 matrix<scalar_type,0,1,mem_manager_type> beta;
 // Now we compute the fist approximate distance function. 
 beta = pinv(kernel_matrix(kern,starting_basis)) *
 (kernel_matrix(kern,starting_basis,target.get_basis_vectors())*target.get_alpha());
 matrix<sample_type,0,1,mem_manager_type> out_vectors(mat(starting_basis));
 // Now setup to do a global optimization of all the parameters in the approximate 
 // distance function. 
 const objective<K> obj(target, beta, out_vectors);
 const objective_derivative<K> obj_der(target, beta, out_vectors);
 matrix<scalar_type,0,1,mem_manager_type> opt_starting_point(obj.state_to_vector());
 // perform a full optimization of all the parameters (i.e. both beta and the basis vectors together)
 find_min(lbfgs_search_strategy(20),
 stop_strategy,
 obj, obj_der, opt_starting_point, 0); 
 // now make sure that the final optimized value is loaded into the beta and
 // out_vectors matrices
 obj.vector_to_state(opt_starting_point);
 // Do a final reoptimization of beta just to make sure it is optimal given the new
 // set of basis vectors.
 beta = pinv(kernel_matrix(kern,out_vectors))*(kernel_matrix(kern,out_vectors,target.get_basis_vectors())*target.get_alpha());
 // It is possible that some of the beta weights will be very close to zero. Lets remove
 // the basis vectors with these essentially zero weights.
 const scalar_type eps = max(abs(beta))*std::numeric_limits<scalar_type>::epsilon();
 for (long i = 0; i < beta.size(); ++i)
 {
 // if beta(i) is zero (but leave at least one beta no matter what)
 if (std::abs(beta(i)) < eps && beta.size() > 1)
 {
 beta = remove_row(beta, i);
 out_vectors = remove_row(out_vectors, i);
 --i;
 }
 }
 return distance_function<K>(beta, kern, out_vectors);
 }
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
 template <
 typename trainer_type 
 >
 class reduced_decision_function_trainer2
 {
 public:
 typedef typename trainer_type::kernel_type kernel_type;
 typedef typename trainer_type::scalar_type scalar_type;
 typedef typename trainer_type::sample_type sample_type;
 typedef typename trainer_type::mem_manager_type mem_manager_type;
 typedef typename trainer_type::trained_function_type trained_function_type;
 reduced_decision_function_trainer2 () : num_bv(0) {}
 reduced_decision_function_trainer2 (
 const trainer_type& trainer_,
 const long num_sb_,
 const double eps_ = 1e-3
 ) :
 trainer(trainer_),
 num_bv(num_sb_),
 eps(eps_)
 {
 COMPILE_TIME_ASSERT(is_matrix<sample_type>::value);
 // make sure requires clause is not broken
 DLIB_ASSERT(num_bv > 0 && eps > 0,
 "\t reduced_decision_function_trainer2()"
 << "\n\t you have given invalid arguments to this function"
 << "\n\t num_bv: " << num_bv 
 << "\n\t eps: " << eps 
 );
 }
 template <
 typename in_sample_vector_type,
 typename in_scalar_vector_type
 >
 const decision_function<kernel_type> train (
 const in_sample_vector_type& x,
 const in_scalar_vector_type& y
 ) const
 {
 // make sure requires clause is not broken
 DLIB_ASSERT(num_bv > 0,
 "\t reduced_decision_function_trainer2::train(x,y)"
 << "\n\t You have tried to use an uninitialized version of this object"
 << "\n\t num_bv: " << num_bv );
 return do_train(mat(x), mat(y));
 }
 private:
 template <
 typename in_sample_vector_type,
 typename in_scalar_vector_type
 >
 const decision_function<kernel_type> do_train (
 const in_sample_vector_type& x,
 const in_scalar_vector_type& y
 ) const
 {
 // get the decision function object we are going to try and approximate
 const decision_function<kernel_type>& dec_funct = trainer.train(x,y);
 const kernel_type kern(dec_funct.kernel_function);
 
 // now find a linearly independent subset of the training points of num_bv points.
 linearly_independent_subset_finder<kernel_type> lisf(kern, num_bv);
 fill_lisf(lisf,x);
 distance_function<kernel_type> approx, target;
 target = dec_funct;
 approx = approximate_distance_function(objective_delta_stop_strategy(eps), target, lisf);
 decision_function<kernel_type> new_df(approx.get_alpha(), 
 0,
 kern, 
 approx.get_basis_vectors());
 // now we have to figure out what the new bias should be. It might be a little
 // different since we just messed with all the weights and vectors.
 double bias = 0;
 for (long i = 0; i < x.nr(); ++i)
 {
 bias += new_df(x(i)) - dec_funct(x(i));
 }
 
 new_df.b = bias/x.nr();
 return new_df;
 }
 // ------------------------------------------------------------------------------------
 trainer_type trainer;
 long num_bv;
 double eps;
 }; // end of class reduced_decision_function_trainer2
 template <typename trainer_type>
 const reduced_decision_function_trainer2<trainer_type> reduced2 (
 const trainer_type& trainer,
 const long num_bv,
 double eps = 1e-3
 )
 {
 COMPILE_TIME_ASSERT(is_matrix<typename trainer_type::sample_type>::value);
 // make sure requires clause is not broken
 DLIB_ASSERT(num_bv > 0 && eps > 0,
 "\tconst reduced_decision_function_trainer2 reduced2()"
 << "\n\t you have given invalid arguments to this function"
 << "\n\t num_bv: " << num_bv 
 << "\n\t eps: " << eps 
 );
 return reduced_decision_function_trainer2<trainer_type>(trainer, num_bv, eps);
 }
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_REDUCEd_TRAINERS_