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KRRNystrom.cpp
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KRRNystrom.cpp
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/*
* Copyright (c) The Shogun Machine Learning Toolbox
* Written (W) 2016 Fredrik Hallgren
* 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.
*/
#include <limits>
#include <shogun/regression/KRRNystrom.h>
#include <shogun/labels/RegressionLabels.h>
#include <shogun/mathematics/eigen3.h>
#include <shogun/mathematics/Math.h>
using namespace shogun;
using namespace Eigen;
CKRRNystrom::CKRRNystrom() : CKernelRidgeRegression()
{
init();
}
CKRRNystrom::CKRRNystrom(float64_t tau, int32_t m, CKernel* k, CLabels* lab)
: CKernelRidgeRegression(tau, k, lab)
{
init();
m_num_rkhs_basis=m;
int32_t n=kernel->get_num_vec_lhs();
REQUIRE(m_num_rkhs_basis <= n, "Number of sampled rows (%d) must be \
less than number of data points (%d)\n", m_num_rkhs_basis, n);
}
void CKRRNystrom::init()
{
m_num_rkhs_basis=100;
}
SGVector<int32_t> CKRRNystrom::subsample_indices()
{
int32_t n=kernel->get_num_vec_lhs();
SGVector<int32_t> temp(n);
temp.range_fill();
CMath::permute(temp);
SGVector<int32_t> col(m_num_rkhs_basis);
for (auto i=0; i<m_num_rkhs_basis; ++i)
col[i]=temp[i];
CMath::qsort(col.vector, m_num_rkhs_basis);
return col;
}
bool CKRRNystrom::solve_krr_system()
{
int32_t n=kernel->get_num_vec_lhs();
SGVector<float64_t> y=((CRegressionLabels*)m_labels)->get_labels();
if (y==NULL)
SG_ERROR("Labels not set.\n");
SGVector<int32_t> col=subsample_indices();
SGMatrix<float64_t> K_mm(m_num_rkhs_basis, m_num_rkhs_basis);
SGMatrix<float64_t> K_nm(n, m_num_rkhs_basis);
#pragma omp parallel for
for (index_t j=0; j<m_num_rkhs_basis; ++j)
{
for (index_t i=0; i<n; ++i)
K_nm(i,j)=kernel->kernel(i,col[j]);
}
#pragma omp parallel for
for (index_t i=0; i<m_num_rkhs_basis; ++i)
memcpy(K_mm.matrix+i*m_num_rkhs_basis, K_nm.get_row_vector(col[i]), m_num_rkhs_basis*sizeof(float64_t));
Map<MatrixXd> K_mm_eig(K_mm.matrix, m_num_rkhs_basis, m_num_rkhs_basis);
Map<MatrixXd> K_nm_eig(K_nm.matrix, n, m_num_rkhs_basis);
MatrixXd K_mn_eig = K_nm_eig.transpose();
Map<VectorXd> y_eig(y.vector, n);
VectorXd alphas_eig(m_num_rkhs_basis);
/* Calculate the Moore-Penrose pseudoinverse */
MatrixXd Kplus=K_mn_eig*K_nm_eig+m_tau*K_mm_eig;
SelfAdjointEigenSolver<MatrixXd> solver(Kplus);
if (solver.info()!=Success)
{
SG_WARNING("Eigendecomposition failed.\n")
return false;
}
/* Solve the system for alphas */
MatrixXd D=solver.eigenvalues().asDiagonal();
MatrixXd eigvec=solver.eigenvectors();
float64_t dbl_epsilon=std::numeric_limits<float64_t>::epsilon();
const float64_t tolerance=m_num_rkhs_basis*dbl_epsilon*D.maxCoeff();
for (index_t i=0; i<m_num_rkhs_basis; ++i)
{
if (D(i,i)<tolerance)
D(i,i)=0;
else
D(i,i)=1/D(i,i);
}
MatrixXd pseudoinv=eigvec*D*eigvec.transpose();
alphas_eig=pseudoinv*K_mn_eig*y_eig;
/* Expand alpha with zeros to size n */
SGVector<float64_t> alpha_n(n);
alpha_n.zero();
for (index_t i=0; i<m_num_rkhs_basis; ++i)
alpha_n[col[i]]=alphas_eig[i];
m_alpha=alpha_n;
return true;
}