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added uwedge approximate joint diagonalizer and unit test
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#ifdef HAVE_EIGEN3 | ||
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#include <shogun/mathematics/ajd/UWedge.h> | ||
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#include <shogun/base/init.h> | ||
#include <shogun/lib/common.h> | ||
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#include <shogun/mathematics/Math.h> | ||
#include <shogun/mathematics/eigen3.h> | ||
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using namespace Eigen; | ||
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typedef Matrix< float64_t, Dynamic, 1, ColMajor > EVector; | ||
typedef Matrix< float64_t, Dynamic, Dynamic, ColMajor > EMatrix; | ||
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using namespace shogun; | ||
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SGMatrix<float64_t> CUWedge::diagonalize(SGNDArray<float64_t> &C, SGMatrix<float64_t> V0, | ||
double eps, int itermax) | ||
{ | ||
int d = C.dims[0]; | ||
int L = C.dims[2]; | ||
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SGMatrix<float64_t> V; | ||
if (V0.num_rows != 0) | ||
{ | ||
V = V0.clone(); | ||
} | ||
else | ||
{ | ||
Eigen::Map<EMatrix> C0(C.get_matrix(0),d,d); | ||
EigenSolver<EMatrix> eig; | ||
eig.compute(C0); | ||
V = SGMatrix<float64_t>::create_identity_matrix(d,1); | ||
Eigen::Map<EMatrix> EV(V.matrix, d,d); | ||
EV = eig.pseudoEigenvalueMatrix().cwiseAbs().cwiseSqrt().inverse() * eig.pseudoEigenvectors().transpose(); | ||
} | ||
Eigen::Map<EMatrix> EV(V.matrix, d,d); | ||
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index_t * Cs_dims = SG_MALLOC(index_t, 3); | ||
Cs_dims[0] = d; | ||
Cs_dims[1] = d; | ||
Cs_dims[2] = L; | ||
SGNDArray<float64_t> Cs(Cs_dims,3); | ||
memcpy(Cs.array, C.array, Cs.dims[0]*Cs.dims[1]*Cs.dims[2]*sizeof(float64_t)); | ||
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EMatrix Rs(d,L); | ||
std::vector<double> crit; | ||
crit.push_back(0.0); | ||
for(int l = 0; l < L; l++) | ||
{ | ||
Eigen::Map<EMatrix> Ci(C.get_matrix(l),d,d); | ||
Eigen::Map<EMatrix> Csi(Cs.get_matrix(l),d,d); | ||
Ci = 0.5 * (Ci + Ci.transpose()); | ||
Csi = EV * Ci * EV.transpose(); | ||
Rs.col(l) = Csi.diagonal(); | ||
crit.back() += Csi.cwiseAbs2().sum() - Rs.col(l).cwiseAbs2().sum(); | ||
} | ||
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double iter = 0; | ||
double improve = 10; | ||
while (improve > eps && iter < itermax) | ||
{ | ||
EMatrix B = Rs * Rs.transpose(); | ||
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EMatrix C1 = EMatrix::Zero(d,d); | ||
for(int id = 0; id < d; id++) | ||
{ | ||
// rowSums | ||
for(int l = 0; l < L; l++) | ||
{ | ||
Eigen::Map<EMatrix> Csi(Cs.get_matrix(l),d,d); | ||
C1.row(id) += Csi.row(id) * Rs(id,l); | ||
} | ||
} | ||
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EMatrix D0 = B.cwiseProduct(B.transpose()) - B.diagonal() * B.diagonal().transpose(); | ||
EMatrix A0 = EMatrix::Identity(d,d) + (C1.cwiseProduct(B) - B.diagonal().asDiagonal() * C1.transpose()).cwiseQuotient(D0+EMatrix::Identity(d,d)); | ||
EV = A0.inverse() * EV; | ||
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Eigen::Map<EMatrix> C0(C.get_matrix(0),d,d); | ||
EMatrix Raux = EV * C0 * EV.transpose(); | ||
EMatrix aux = Raux.diagonal().cwiseAbs().cwiseSqrt().asDiagonal().inverse(); | ||
EV = aux * EV; | ||
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crit.push_back(0.0); | ||
for(int l = 0; l < L; l++) | ||
{ | ||
Eigen::Map<EMatrix> Ci(C.get_matrix(l),d,d); | ||
Eigen::Map<EMatrix> Csi(Cs.get_matrix(l),d,d); | ||
Csi = EV * Ci * EV.transpose(); | ||
Rs.col(l) = Csi.diagonal(); | ||
crit.back() += Csi.cwiseAbs2().sum() - Rs.col(l).cwiseAbs2().sum(); | ||
} | ||
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improve = CMath::abs(crit.back() - crit[iter]); | ||
iter++; | ||
} | ||
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if(iter == itermax) | ||
{ | ||
SG_SERROR("Convergence not reached\n") | ||
} | ||
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return V; | ||
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} | ||
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#endif //HAVE_EIGEN3 |
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/* | ||
* This program is free software; you can redistribute it and/or modify | ||
* it under the terms of the GNU General Public License as published by | ||
* the Free Software Foundation; either version 3 of the License, or | ||
* (at your option) any later version. | ||
* | ||
* Written (W) 2013 Kevin Hughes | ||
* | ||
* Thanks to Andreas Ziehe and Cedric Gouy-Pailler | ||
*/ | ||
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#ifndef UWEDGE_H_ | ||
#define UWEDGE_H_ | ||
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#ifdef HAVE_EIGEN3 | ||
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#include <shogun/mathematics/ajd/ApproxJointDiagonalizer.h> | ||
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#include <shogun/lib/common.h> | ||
#include <shogun/base/SGObject.h> | ||
#include <shogun/lib/SGMatrix.h> | ||
#include <shogun/lib/SGNDArray.h> | ||
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#include <shogun/mathematics/Math.h> | ||
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namespace shogun | ||
{ | ||
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/** @brief Class FFDiag | ||
* | ||
* An Approximate Joint Diagonalizer (AJD) Implementation | ||
*/ | ||
class CUWedge : public CApproxJointDiagonalizer | ||
{ | ||
public: | ||
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/** constructor */ | ||
CUWedge() | ||
{ | ||
}; | ||
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/** destructor */ | ||
virtual ~CUWedge() | ||
{ | ||
} | ||
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/** Computes the matrix V that best diagonalizes C | ||
* @param C the set of matrices to be diagonalized | ||
* @param V0 an estimate of the matrix V | ||
* @param eps machine epsilon or desired epsilon | ||
* @param itermax maximum number of iterations | ||
* @return V the matrix the best diagonalizes C | ||
*/ | ||
static SGMatrix<float64_t> diagonalize(SGNDArray<float64_t> &C, | ||
SGMatrix<float64_t> V0= SGMatrix<float64_t>(NULL,0,0), | ||
double eps=CMath::MACHINE_EPSILON, | ||
int itermax=200); | ||
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/** Computes the matrix V that best diagonalizes C | ||
* @param C the set of matrices to be diagonalized | ||
* @param V0 an estimate of the matrix V | ||
* @param eps machine epsilon or desired epsilon | ||
* @param itermax maximum number of iterations | ||
* @return V the matrix the best diagonalizes C | ||
*/ | ||
virtual SGMatrix<float64_t> compute(SGNDArray<float64_t> &C, | ||
SGMatrix<float64_t> V0= SGMatrix<float64_t>(NULL,0,0), | ||
double eps=CMath::MACHINE_EPSILON, | ||
int itermax=200) | ||
{ | ||
m_V = diagonalize(C,V0,eps,itermax); | ||
return m_V; | ||
} | ||
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/** @return object name */ | ||
virtual const char* get_name() const { return "UWedge"; } | ||
}; | ||
} | ||
#endif //HAVE_EIGEN3 | ||
#endif //UWEDGE_H_ |
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#include <shogun/base/init.h> | ||
#include <shogun/lib/common.h> | ||
#include <gtest/gtest.h> | ||
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#ifdef HAVE_EIGEN3 | ||
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#include <shogun/lib/SGVector.h> | ||
#include <shogun/lib/SGMatrix.h> | ||
#include <shogun/lib/SGNDArray.h> | ||
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#include <shogun/mathematics/Math.h> | ||
#include <shogun/mathematics/eigen3.h> | ||
#include <shogun/mathematics/ajd/UWedge.h> | ||
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#include <shogun/evaluation/ica/PermutationMatrix.h> | ||
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using namespace Eigen; | ||
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typedef Matrix< float64_t, Dynamic, Dynamic, ColMajor > EMatrix; | ||
typedef Matrix< float64_t, Dynamic, 1, ColMajor > EVector; | ||
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using namespace shogun; | ||
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TEST(CUWedge, diagonalize) | ||
{ | ||
// Generating diagonal matrices | ||
index_t * C_dims = SG_MALLOC(index_t, 3); | ||
C_dims[0] = 10; | ||
C_dims[1] = 10; | ||
C_dims[2] = 30; | ||
SGNDArray< float64_t > C(C_dims, 3); | ||
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CMath::init_random(17); | ||
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for (int i = 0; i < C_dims[2]; i++) | ||
{ | ||
Eigen::Map<EMatrix> tmp(C.get_matrix(i),C_dims[0], C_dims[1]); | ||
tmp.setIdentity(); | ||
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for (int j = 0; j < C_dims[0]; j++) | ||
{ | ||
tmp(j,j) *= CMath::abs(CMath::random(1,5)); | ||
} | ||
} | ||
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// Mixing and demixing matrices | ||
EMatrix B(C_dims[0], C_dims[1]); | ||
B.setRandom(); | ||
EMatrix A = B.inverse(); | ||
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for (int i = 0; i < C_dims[2]; i++) | ||
{ | ||
Eigen::Map<EMatrix> Ci(C.get_matrix(i),C_dims[0], C_dims[1]); | ||
Ci = A * Ci * A.transpose(); | ||
} | ||
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/** Diagonalize **/ | ||
SGMatrix<float64_t> V = CUWedge::diagonalize(C); | ||
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// Test output size | ||
EXPECT_EQ(V.num_rows, C_dims[0]); | ||
EXPECT_EQ(V.num_cols, C_dims[1]); | ||
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// Close to a permutation matrix (with random scales) | ||
Eigen::Map<EMatrix> EV(V.matrix,C_dims[0], C_dims[1]); | ||
SGMatrix<float64_t> P(C_dims[0],C_dims[1]); | ||
Eigen::Map<EMatrix> EP(P.matrix,C_dims[0], C_dims[1]); | ||
EP = EV * A; | ||
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// Test if output is correct | ||
bool isperm = is_permutation_matrix(P); | ||
EXPECT_EQ(isperm,true); | ||
} | ||
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#endif //HAVE_EIGEN3 |