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ComputeMMD.h
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ComputeMMD.h
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/*
* Copyright (c) The Shogun Machine Learning Toolbox
* Written (w) 2014 - 2016 Soumyajit De
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* The views and conclusions contained in the software and documentation are those
* of the authors and should not be interpreted as representing official policies,
* either expressed or implied, of the Shogun Development Team.
*/
#ifndef COMPUTE_MMD_H_
#define COMPUTE_MMD_H_
#include <array>
#include <vector>
#include <shogun/lib/config.h>
#include <shogun/lib/SGVector.h>
#include <shogun/lib/SGMatrix.h>
#include <shogun/kernel/Kernel.h>
#include <shogun/statistical_testing/MMD.h>
#include <shogun/statistical_testing/internals/KernelManager.h>
#include <shogun/mathematics/eigen3.h>
#include <shogun/io/SGIO.h>
namespace shogun
{
namespace internal
{
namespace mmd
{
struct terms_t
{
std::array<float64_t, 3> term{};
std::array<float64_t, 3> diag{};
};
/**
* @brief Class Compute blah blah.
*/
struct ComputeMMD
{
ComputeMMD() : m_n_x(0), m_n_y(0), m_stype(EStatisticType::ST_UNBIASED_FULL)
{
}
template <class Kernel>
float32_t operator()(const Kernel& kernel) const
{
ASSERT(m_n_x>0 && m_n_y>0);
const index_t size=m_n_x+m_n_y;
terms_t terms;
for (auto i=0; i<size; ++i)
{
for (auto j=i; j<size; ++j)
add_term(terms, kernel(i, j), i, j);
}
return compute(terms);
}
template <typename T>
float32_t operator()(const SGMatrix<T>& kernel_matrix) const
{
ASSERT(m_n_x>0 && m_n_y>0);
const index_t size=m_n_x+m_n_y;
ASSERT(kernel_matrix.num_rows==size && kernel_matrix.num_cols==size);
typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> MatrixXt;
typedef Eigen::Block<Eigen::Map<const MatrixXt> > BlockXt;
Eigen::Map<const MatrixXt> map(kernel_matrix.matrix, kernel_matrix.num_rows, kernel_matrix.num_cols);
const BlockXt& b_x=map.block(0, 0, m_n_x, m_n_x);
const BlockXt& b_y=map.block(m_n_x, m_n_x, m_n_y, m_n_y);
const BlockXt& b_xy=map.block(m_n_x, 0, m_n_y, m_n_x);
terms_t terms;
terms.diag[0]=b_x.diagonal().sum();
terms.diag[1]=b_y.diagonal().sum();
terms.diag[2]=b_xy.diagonal().sum();
terms.term[0]=(b_x.sum()-terms.diag[0])/2+terms.diag[0];
terms.term[1]=(b_y.sum()-terms.diag[1])/2+terms.diag[1];
terms.term[2]=b_xy.sum();
return compute(terms);
}
SGVector<float64_t> operator()(const KernelManager& kernel_mgr) const
{
ASSERT(m_n_x>0 && m_n_y>0);
std::vector<terms_t> terms(kernel_mgr.num_kernels());
const index_t size=m_n_x+m_n_y;
for (auto j=0; j<size; ++j)
{
for (auto i=j; i<size; ++i)
{
for (size_t k=0; k<kernel_mgr.num_kernels(); ++k)
{
auto kernel=kernel_mgr.kernel_at(k)->kernel(i, j);
add_term(terms[k], kernel, i, j);
}
}
}
SGVector<float64_t> result(kernel_mgr.num_kernels());
for (size_t k=0; k<kernel_mgr.num_kernels(); ++k)
{
result[k]=compute(terms[k]);
SG_SDEBUG("result[%d] = %f!\n", k, result[k]);
}
terms.resize(0);
return result;
}
/**
* Adds the kernel value to to the term that corresponding to K(i, j). It only
* uses the lower triangular half of the matrix to exploit symmetry.
*
* @param terms the terms for computing MMD
* @param kernel_value the kernel value between i-th and j-th features.
* @param i the row index for the Gram matrix
* @param j the col index for the Gram matrix
*/
template <typename T>
inline void add_term(terms_t& terms, T kernel_value, index_t i, index_t j) const
{
ASSERT(m_n_x>0 && m_n_y>0);
if (i<m_n_x && j<m_n_x && i>=j)
{
SG_SDEBUG("Adding Kernel(%d, %d)=%f to term_0!\n", i, j, kernel_value);
terms.term[0]+=kernel_value;
if (i==j)
terms.diag[0]+=kernel_value;
}
else if (i>=m_n_x && j>=m_n_x && i>=j)
{
SG_SDEBUG("Adding Kernel(%d, %d)=%f to term_1!\n", i, j, kernel_value);
terms.term[1]+=kernel_value;
if (i==j)
terms.diag[1]+=kernel_value;
}
else if (i>=m_n_x && j<m_n_x)
{
SG_SDEBUG("Adding Kernel(%d, %d)=%f to term_2!\n", i, j, kernel_value);
terms.term[2]+=kernel_value;
if (i-m_n_x==j)
terms.diag[2]+=kernel_value;
}
}
inline float64_t compute(terms_t& terms) const
{
ASSERT(m_n_x>0 && m_n_y>0);
terms.term[0]=2*(terms.term[0]-terms.diag[0]);
terms.term[1]=2*(terms.term[1]-terms.diag[1]);
SG_SDEBUG("term_0 sum (without diagonal) = %f!\n", terms.term[0]);
SG_SDEBUG("term_1 sum (without diagonal) = %f!\n", terms.term[1]);
if (m_stype!=EStatisticType::ST_BIASED_FULL)
{
terms.term[0]/=m_n_x*(m_n_x-1);
terms.term[1]/=m_n_y*(m_n_y-1);
}
else
{
terms.term[0]+=terms.diag[0];
terms.term[1]+=terms.diag[1];
SG_SDEBUG("term_0 sum (with diagonal) = %f!\n", terms.term[0]);
SG_SDEBUG("term_1 sum (with diagonal) = %f!\n", terms.term[1]);
terms.term[0]/=m_n_x*m_n_x;
terms.term[1]/=m_n_y*m_n_y;
}
SG_SDEBUG("term_0 (normalized) = %f!\n", terms.term[0]);
SG_SDEBUG("term_1 (normalized) = %f!\n", terms.term[1]);
SG_SDEBUG("term_2 sum (with diagonal) = %f!\n", terms.term[2]);
if (m_stype==EStatisticType::ST_UNBIASED_INCOMPLETE)
{
terms.term[2]-=terms.diag[2];
SG_SDEBUG("term_2 sum (without diagonal) = %f!\n", terms.term[2]);
terms.term[2]/=m_n_x*(m_n_x-1);
}
else
terms.term[2]/=m_n_x*m_n_y;
SG_SDEBUG("term_2 (normalized) = %f!\n", terms.term[2]);
auto result=terms.term[0]+terms.term[1]-2*terms.term[2];
SG_SDEBUG("result = %f!\n", result);
return result;
}
index_t m_n_x;
index_t m_n_y;
EStatisticType m_stype;
};
}
}
}
#endif // COMPUTE_MMD_H_