SparseWeightMatrix klle_weight_matrix(RandomAccessIterator begin, RandomAccessIterator end,
const Neighbors& neighbors, PairwiseCallback callback, DefaultScalarType shift)
{
timed_context context("KLLE weight computation");
const unsigned int k = neighbors[0].size();
SparseTriplets sparse_triplets;
sparse_triplets.reserve((k*k+2*k+1)*(end-begin));
RandomAccessIterator iter;
RandomAccessIterator iter_begin = begin, iter_end = end;
DenseMatrix gram_matrix = DenseMatrix::Zero(k,k);
DenseVector dots(k);
DenseVector rhs = DenseVector::Ones(k);
DenseVector weights;
for (RandomAccessIterator iter=iter_begin; iter!=iter_end; ++iter)
{
DefaultScalarType kernel_value = callback(*iter,*iter);
const LocalNeighbors& current_neighbors = neighbors[iter-begin];
for (unsigned int i=0; i<k; ++i)
dots[i] = callback(*iter, begin[current_neighbors[i]]);
for (unsigned int i=0; i<k; ++i)
{
for (unsigned int j=i; j<k; ++j)
gram_matrix(i,j) = kernel_value - dots(i) - dots(j) + callback(begin[current_neighbors[i]],begin[current_neighbors[j]]);
}
DefaultScalarType trace = gram_matrix.trace();
gram_matrix.diagonal().array() += 1e-3*trace;
weights = gram_matrix.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
weights /= weights.sum();
sparse_triplets.push_back(SparseTriplet(iter-begin,iter-begin,1.0+shift));
for (unsigned int i=0; i<k; ++i)
{
sparse_triplets.push_back(SparseTriplet(current_neighbors[i],iter-begin,
-weights[i]));
sparse_triplets.push_back(SparseTriplet(iter-begin,current_neighbors[i],
-weights[i]));
for (unsigned int j=0; j<k; ++j)
sparse_triplets.push_back(SparseTriplet(current_neighbors[i],current_neighbors[j],
+weights(i)*weights(j)));
}
}
SparseWeightMatrix weight_matrix(end-begin,end-begin);
weight_matrix.setFromTriplets(sparse_triplets.begin(),sparse_triplets.end());
return weight_matrix;
}
SparseWeightMatrix linear_weight_matrix(const RandomAccessIterator& begin, const RandomAccessIterator& end,
const Neighbors& neighbors, PairwiseCallback callback,
const ScalarType shift, const ScalarType trace_shift)
{
timed_context context("KLLE weight computation");
const IndexType k = neighbors[0].size();
SparseTriplets sparse_triplets;
sparse_triplets.reserve((k*k+2*k+1)*(end-begin));
#pragma omp parallel shared(begin,end,neighbors,callback,sparse_triplets) default(none)
{
IndexType index_iter;
DenseMatrix gram_matrix = DenseMatrix::Zero(k,k);
DenseVector dots(k);
DenseVector rhs = DenseVector::Ones(k);
DenseVector weights;
SparseTriplets local_triplets;
local_triplets.reserve(k*k+2*k+1);
//RESTRICT_ALLOC;
#pragma omp for nowait
for (index_iter=0; index_iter<static_cast<IndexType>(end-begin); index_iter++)
{
ScalarType kernel_value = callback.kernel(begin[index_iter],begin[index_iter]);
const LocalNeighbors& current_neighbors = neighbors[index_iter];
for (IndexType i=0; i<k; ++i)
dots[i] = callback.kernel(begin[index_iter], begin[current_neighbors[i]]);
for (IndexType i=0; i<k; ++i)
{
for (IndexType j=i; j<k; ++j)
gram_matrix(i,j) = kernel_value - dots(i) - dots(j) +
callback.kernel(begin[current_neighbors[i]],begin[current_neighbors[j]]);
}
ScalarType trace = gram_matrix.trace();
gram_matrix.diagonal().array() += trace_shift*trace;
weights = gram_matrix.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
weights /= weights.sum();
SparseTriplet diagonal_triplet(index_iter,index_iter,1.0+shift);
local_triplets.push_back(diagonal_triplet);
for (IndexType i=0; i<k; ++i)
{
SparseTriplet row_side_triplet(current_neighbors[i],index_iter,-weights[i]);
SparseTriplet col_side_triplet(index_iter,current_neighbors[i],-weights[i]);
local_triplets.push_back(row_side_triplet);
local_triplets.push_back(col_side_triplet);
for (IndexType j=0; j<k; ++j)
{
SparseTriplet cross_triplet(current_neighbors[i],current_neighbors[j],weights(i)*weights(j));
local_triplets.push_back(cross_triplet);
}
}
#pragma omp critical
{
copy(local_triplets.begin(),local_triplets.end(),back_inserter(sparse_triplets));
}
local_triplets.clear();
}
//UNRESTRICT_ALLOC;
}
return sparse_matrix_from_triplets(sparse_triplets, end-begin, end-begin);
}