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-// 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_
-
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