// 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_