EmbeddingResult embed(const LMatrixType& lhs, const RMatrixType& rhs, IndexType target_dimension, unsigned int skip)
{
timed_context context("ARPACK DSXUPD generalized eigendecomposition");
#ifndef TAPKEE_NO_ARPACK
ArpackGeneralizedSelfAdjointEigenSolver<LMatrixType, RMatrixType, MatrixTypeOperation>
arpack(lhs,rhs,target_dimension+skip,"SM");
if (arpack.info() == Eigen::Success)
{
stringstream ss;
ss << "Took " << arpack.getNbrIterations() << " iterations.";
LoggingSingleton::instance().message_info(ss.str());
DenseMatrix embedding_feature_matrix = (arpack.eigenvectors()).block(0,skip,lhs.cols(),target_dimension);
return EmbeddingResult(embedding_feature_matrix,arpack.eigenvalues().tail(target_dimension));
}
else
{
throw eigendecomposition_error("eigendecomposition failed");
}
return EmbeddingResult();
#else
return EmbeddingResult();
#endif
}
EmbeddingResult embed(const LMatrixType& lhs, const RMatrixType& rhs, IndexType target_dimension, unsigned int skip)
{
timed_context context("Eigen dense generalized eigendecomposition");
DenseMatrix dense_lhs = lhs;
DenseMatrix dense_rhs = rhs;
Eigen::GeneralizedSelfAdjointEigenSolver<DenseMatrix> solver(dense_lhs, dense_rhs);
if (solver.info() == Eigen::Success)
{
if (MatrixOperationType::largest)
{
assert(skip==0);
DenseMatrix embedding_feature_matrix = solver.eigenvectors().rightCols(target_dimension);
return EmbeddingResult(embedding_feature_matrix,solver.eigenvalues().tail(target_dimension));
}
else
{
DenseMatrix embedding_feature_matrix = solver.eigenvectors().leftCols(target_dimension+skip).rightCols(target_dimension);
return EmbeddingResult(embedding_feature_matrix,solver.eigenvalues().segment(skip,skip+target_dimension));
}
}
else
{
throw eigendecomposition_error("eigendecomposition failed");
}
return EmbeddingResult();
}
EmbeddingResult embed(const MatrixType& wm, IndexType target_dimension, unsigned int skip)
{
timed_context context("Randomized eigendecomposition");
DenseMatrix O(wm.rows(), target_dimension+skip);
for (IndexType i=0; i<O.rows(); ++i)
{
IndexType j=0;
for ( ; j+1 < O.cols(); j+= 2)
{
ScalarType v1 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType v2 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType len = sqrt(-2.f*log(v1));
O(i,j) = len*cos(2.f*M_PI*v2);
O(i,j+1) = len*sin(2.f*M_PI*v2);
}
for ( ; j < O.cols(); j++)
{
ScalarType v1 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType v2 = (ScalarType)(rand()+1.f)/((float)RAND_MAX+2.f);
ScalarType len = sqrt(-2.f*log(v1));
O(i,j) = len*cos(2.f*M_PI*v2);
}
}
MatrixTypeOperation operation(wm);
DenseMatrix Y = operation(O);
for (IndexType i=0; i<Y.cols(); i++)
{
for (IndexType j=0; j<i; j++)
{
ScalarType r = Y.col(i).dot(Y.col(j));
Y.col(i) -= r*Y.col(j);
}
ScalarType norm = Y.col(i).norm();
if (norm < 1e-4)
{
for (int k = i; k<Y.cols(); k++)
Y.col(k).setZero();
}
Y.col(i) *= (1.f / norm);
}
DenseMatrix B1 = operation(Y);
DenseMatrix B = Y.householderQr().solve(B1);
DenseSelfAdjointEigenSolver eigenOfB(B);
if (eigenOfB.info() == Eigen::Success)
{
DenseMatrix embedding = (Y*eigenOfB.eigenvectors()).block(0, skip, wm.cols(), target_dimension);
return EmbeddingResult(embedding,eigenOfB.eigenvalues());
}
else
{
throw eigendecomposition_error("eigendecomposition failed");
}
return EmbeddingResult();
}
EmbeddingResult embed(const LMatrixType& lhs, const RMatrixType& rhs, unsigned int target_dimension, unsigned int skip)
{
timed_context context("ARPACK DSXUPD generalized eigendecomposition");
#ifndef TAPKEE_NO_ARPACK
ArpackGeneralizedSelfAdjointEigenSolver<LMatrixType, RMatrixType, MatrixTypeOperation> arpack(lhs,rhs,target_dimension+skip,"SM");
DenseMatrix embedding_feature_matrix = (arpack.eigenvectors()).block(0,skip,lhs.cols(),target_dimension);
return EmbeddingResult(embedding_feature_matrix,arpack.eigenvalues().tail(target_dimension));
#else
return EmbeddingResult();
#endif
}
EmbeddingResult embed(const MatrixType& wm, IndexType target_dimension, unsigned int skip)
{
timed_context context("Eigen library dense eigendecomposition");
DenseMatrix dense_wm = wm;
DenseSelfAdjointEigenSolver solver(dense_wm);
if (solver.info() == Eigen::Success)
{
DenseMatrix embedding_feature_matrix = (solver.eigenvectors()).block(0,skip,wm.cols(),target_dimension);
return EmbeddingResult(embedding_feature_matrix,solver.eigenvalues().tail(target_dimension));
}
else
{
throw eigendecomposition_error("eigendecomposition failed");
}
return EmbeddingResult();
}
EmbeddingResult embed(const LMatrixType& lhs, const RMatrixType& rhs, IndexType target_dimension, unsigned int skip)
{
timed_context context("Eigen dense generalized eigendecomposition");
DenseMatrix dense_lhs = lhs;
DenseMatrix dense_rhs = rhs;
Eigen::GeneralizedSelfAdjointEigenSolver<DenseMatrix> solver(dense_lhs, dense_rhs);
if (solver.info() == Eigen::Success)
{
DenseMatrix embedding_feature_matrix = (solver.eigenvectors()).block(0,skip,lhs.cols(),target_dimension);
return EmbeddingResult(embedding_feature_matrix,solver.eigenvalues().tail(target_dimension));
}
else
{
throw eigendecomposition_error("eigendecomposition failed");
}
return EmbeddingResult();
}
EmbeddingResult generalized_eigen_embedding(TAPKEE_EIGEN_EMBEDDING_METHOD method, const LMatrixType& lhs,
const RMatrixType& rhs,
unsigned int target_dimension, unsigned int skip)
{
switch (method)
{
case ARPACK:
return generalized_eigen_embedding_impl<LMatrixType, RMatrixType, MatrixTypeOperation,
ARPACK>().embed(lhs, rhs, target_dimension, skip);
case EIGEN_DENSE_SELFADJOINT_SOLVER:
return generalized_eigen_embedding_impl<LMatrixType, RMatrixType, MatrixTypeOperation,
EIGEN_DENSE_SELFADJOINT_SOLVER>().embed(lhs, rhs, target_dimension, skip);
case RANDOMIZED:
// TODO fail here
return EmbeddingResult();
default: break;
}
return EmbeddingResult();
};
EmbeddingResult generalized_eigen_embedding(TAPKEE_EIGEN_EMBEDDING_METHOD method, const LMatrixType& lhs,
const RMatrixType& rhs,
IndexType target_dimension, unsigned int skip)
{
switch (method)
{
#ifdef TAPKEE_WITH_ARPACK
case ARPACK:
return generalized_eigen_embedding_impl<LMatrixType, RMatrixType, MatrixOperationType,
ARPACK>().embed(lhs, rhs, target_dimension, skip);
#endif
case EIGEN_DENSE_SELFADJOINT_SOLVER:
return generalized_eigen_embedding_impl<LMatrixType, RMatrixType, MatrixOperationType,
EIGEN_DENSE_SELFADJOINT_SOLVER>().embed(lhs, rhs, target_dimension, skip);
case RANDOMIZED:
throw unsupported_method_error("Randomized method is not supported for generalized eigenproblems");
return EmbeddingResult();
default: break;
}
return EmbeddingResult();
}
EmbeddingResult embed(const LMatrixType& lhs, const RMatrixType& rhs, unsigned int target_dimension, unsigned int skip)
{
timed_context context("Eigen dense generalized eigendecomposition");
DenseMatrix dense_lhs = lhs;
DenseMatrix dense_rhs = rhs;
Eigen::GeneralizedSelfAdjointEigenSolver<DenseMatrix> solver(dense_lhs, dense_rhs);
DenseMatrix embedding_feature_matrix = (solver.eigenvectors()).block(0,skip,lhs.cols(),target_dimension);
return EmbeddingResult(embedding_feature_matrix,solver.eigenvalues().tail(target_dimension));
}
EmbeddingResult project(const ProjectionResult& projection_result, RandomAccessIterator begin,
RandomAccessIterator end, FeatureVectorCallback callback, unsigned int dimension)
{
timed_context context("Data projection");
DenseVector current_vector(dimension);
const DenseSymmetricMatrix& projection_matrix = projection_result.first;
DenseMatrix embedding = DenseMatrix::Zero((end-begin),projection_matrix.cols());
for (RandomAccessIterator iter=begin; iter!=end; ++iter)
{
callback(*iter,current_vector);
embedding.row(iter-begin) = projection_matrix.transpose()*current_vector;
}
return EmbeddingResult(embedding,DenseVector());
}
EmbeddingResult eigen_embedding(TAPKEE_EIGEN_EMBEDDING_METHOD method, const MatrixType& m,
IndexType target_dimension, unsigned int skip)
{
LoggingSingleton::instance().message_info("Using " + get_eigen_embedding_name(method) +
" eigendecomposition.");
switch (method)
{
case ARPACK:
return eigen_embedding_impl<MatrixType, MatrixTypeOperation,
ARPACK>().embed(m, target_dimension, skip);
case RANDOMIZED:
return eigen_embedding_impl<MatrixType, MatrixTypeOperation,
RANDOMIZED>().embed(m, target_dimension, skip);
case EIGEN_DENSE_SELFADJOINT_SOLVER:
return eigen_embedding_impl<MatrixType, MatrixTypeOperation,
EIGEN_DENSE_SELFADJOINT_SOLVER>().embed(m, target_dimension, skip);
default: break;
}
return EmbeddingResult();
};
EmbeddingResult spe_embedding(RandomAccessIterator begin, RandomAccessIterator end,
PairwiseCallback callback, const Neighbors& neighbors,
unsigned int target_dimension, bool global_strategy,
DefaultScalarType tolerance, int nupdates)
{
timed_context context("SPE embedding computation");
unsigned int k = 0;
if (!global_strategy)
k = neighbors[0].size();
// The number of data points
int N = end-begin;
while (nupdates > N/2)
nupdates = N/2;
// Look for the maximum distance
DefaultScalarType max = 0.0;
for (RandomAccessIterator i_iter=begin; i_iter!=end; ++i_iter)
{
for (RandomAccessIterator j_iter=i_iter+1; j_iter!=end; ++j_iter)
{
max = std::max(max, callback(*i_iter,*j_iter));
}
}
// Distances normalizer used in global strategy
DefaultScalarType alpha = 0.0;
if (global_strategy)
alpha = 1.0 / max * std::sqrt(2.0);
// Random embedding initialization, Y is the short for embedding_feature_matrix
std::srand(std::time(0));
DenseMatrix Y = (DenseMatrix::Random(target_dimension,N)
+ DenseMatrix::Ones(target_dimension,N)) / 2;
// Auxiliary diffference embedding feature matrix
DenseMatrix Yd(target_dimension,nupdates);
// SPE's main loop
typedef std::vector<int> Indices;
typedef std::vector<int>::iterator IndexIterator;
// Maximum number of iterations
int max_iter = 2000 + round(0.04 * N*N);
if (!global_strategy)
max_iter *= 3;
// Learning parameter
DefaultScalarType lambda = 1.0;
// Vector of indices used for shuffling
Indices indices(N);
for (int i=0; i<N; ++i)
indices[i] = i;
// Vector with distances in the original space of the points to update
DenseVector Rt(nupdates);
DenseVector scale(nupdates);
DenseVector D(nupdates);
// Pointers to the indices of the elements to update
IndexIterator ind1;
IndexIterator ind2;
// Helper used in local strategy
Indices ind1Neighbors;
if (!global_strategy)
ind1Neighbors.resize(k*nupdates);
for (int i=0; i<max_iter; ++i)
{
// Shuffle to select the vectors to update in this iteration
std::random_shuffle(indices.begin(),indices.end());
ind1 = indices.begin();
ind2 = indices.begin()+nupdates;
// With local strategy, the seecond set of indices is selected among
// neighbors of the first set
if (!global_strategy)
{
// Neighbors of interest
for(int j=0; j<nupdates; ++j)
{
const LocalNeighbors& current_neighbors =
neighbors[*ind1++];
for(unsigned int kk=0; kk<k; ++kk)
ind1Neighbors[kk + j*k] = current_neighbors[kk];
}
// Restore ind1
ind1 = indices.begin();
// Generate pseudo-random indices and select final indices
for(int j=0; j<nupdates; ++j)
{
unsigned int r = round( std::rand()*1.0/RAND_MAX*(k-1) ) + k*j;
indices[nupdates+j] = ind1Neighbors[r];
}
}
// Compute distances between the selected points in the embedded space
for(int j=0; j<nupdates; ++j)
{
//FIXME it seems that here Euclidean distance is forced
D[j] = (Y.col(*ind1) - Y.col(*ind2)).norm();
++ind1, ++ind2;
}
// Get the corresponding distances in the original space
if (global_strategy)
Rt.fill(alpha);
else // local_strategy
Rt.fill(1);
ind1 = indices.begin();
ind2 = indices.begin()+nupdates;
for (int j=0; j<nupdates; ++j)
Rt[j] *= callback(*(begin + *ind1++), *(begin + *ind2++));
// Compute some terms for update
// Scale factor
D.array() += tolerance;
scale = (Rt-D).cwiseQuotient(D);
ind1 = indices.begin();
ind2 = indices.begin()+nupdates;
// Difference matrix
for (int j=0; j<nupdates; ++j)
{
Yd.col(j).noalias() = Y.col(*ind1) - Y.col(*ind2);
++ind1, ++ind2;
}
ind1 = indices.begin();
ind2 = indices.begin()+nupdates;
// Update the location of the vectors in the embedded space
for (int j=0; j<nupdates; ++j)
{
Y.col(*ind1) += lambda / 2 * scale[j] * Yd.col(j);
Y.col(*ind2) -= lambda / 2 * scale[j] * Yd.col(j);
++ind1, ++ind2;
}
// Update the learning parameter
lambda = lambda - ( lambda / max_iter );
}
return EmbeddingResult(Y.transpose(),DenseVector());
};