inline force_inline // Absolutely MUST be inline so optimizations can happen.
double NeighborSearchRules<SortPolicy, MetricType, TreeType>::
BaseCase(const size_t queryIndex, const size_t referenceIndex)
{
// If the datasets are the same, then this search is only using one dataset
// and we should not return identical points.
if ((&querySet == &referenceSet) && (queryIndex == referenceIndex))
return 0.0;
// If we have already performed this base case, then do not perform it again.
if ((lastQueryIndex == queryIndex) && (lastReferenceIndex == referenceIndex))
return lastBaseCase;
double distance = metric.Evaluate(querySet.col(queryIndex),
referenceSet.col(referenceIndex));
++baseCases;
// If this distance is better than any of the current candidates, the
// SortDistance() function will give us the position to insert it into.
arma::vec queryDist = distances.unsafe_col(queryIndex);
arma::Col<size_t> queryIndices = neighbors.unsafe_col(queryIndex);
const size_t insertPosition = SortPolicy::SortDistance(queryDist,
queryIndices, distance);
// SortDistance() returns (size_t() - 1) if we shouldn't add it.
if (insertPosition != (size_t() - 1))
InsertNeighbor(queryIndex, insertPosition, referenceIndex, distance);
// Cache this information for the next time BaseCase() is called.
lastQueryIndex = queryIndex;
lastReferenceIndex = referenceIndex;
lastBaseCase = distance;
return distance;
}
inline force_inline
double LSHSearch<SortPolicy>::BaseCase(arma::mat& distances,
arma::Mat<size_t>& neighbors,
const size_t queryIndex,
const size_t referenceIndex)
{
// If the datasets are the same, then this search is only using one dataset
// and we should not return identical points.
if ((&querySet == &referenceSet) && (queryIndex == referenceIndex))
return 0.0;
const double distance = metric::EuclideanDistance::Evaluate(
querySet.unsafe_col(queryIndex), referenceSet.unsafe_col(referenceIndex));
// If this distance is better than any of the current candidates, the
// SortDistance() function will give us the position to insert it into.
arma::vec queryDist = distances.unsafe_col(queryIndex);
arma::Col<size_t> queryIndices = neighbors.unsafe_col(queryIndex);
size_t insertPosition = SortPolicy::SortDistance(queryDist, queryIndices,
distance);
// SortDistance() returns (size_t() - 1) if we shouldn't add it.
if (insertPosition != (size_t() - 1))
InsertNeighbor(distances, neighbors, queryIndex, insertPosition,
referenceIndex, distance);
return distance;
}
inline force_inline
double FastMKSRules<KernelType, TreeType>::BaseCase(
const size_t queryIndex,
const size_t referenceIndex)
{
// Score() always happens before BaseCase() for a given node combination. For
// cover trees, the kernel evaluation between the two centroid points already
// happened. So we don't need to do it. Note that this optimizes out if the
// first conditional is false (its result is known at compile time).
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
{
if ((queryIndex == lastQueryIndex) &&
(referenceIndex == lastReferenceIndex))
return lastKernel;
// Store new values.
lastQueryIndex = queryIndex;
lastReferenceIndex = referenceIndex;
}
++baseCases;
double kernelEval = kernel.Evaluate(querySet.unsafe_col(queryIndex),
referenceSet.unsafe_col(referenceIndex));
// Update the last kernel value, if we need to.
if (tree::TreeTraits<TreeType>::FirstPointIsCentroid)
lastKernel = kernelEval;
// If the reference and query sets are identical, we still need to compute the
// base case (so that things can be bounded properly), but we won't add it to
// the results.
if ((&querySet == &referenceSet) && (queryIndex == referenceIndex))
return kernelEval;
// If this is a better candidate, insert it into the list.
if (kernelEval < products(products.n_rows - 1, queryIndex))
return kernelEval;
size_t insertPosition = 0;
for ( ; insertPosition < products.n_rows; ++insertPosition)
if (kernelEval >= products(insertPosition, queryIndex))
break;
InsertNeighbor(queryIndex, insertPosition, referenceIndex, kernelEval);
return kernelEval;
}
inline force_inline // Absolutely MUST be inline so optimizations can happen.
double NeighborSearchRules<SortPolicy, MetricType, TreeType>::
BaseCase(const size_t queryIndex, const size_t referenceIndex)
{
// If the datasets are the same, then this search is only using one dataset
// and we should not return identical points.
if ((&querySet == &referenceSet) && (queryIndex == referenceIndex))
return 0.0;
double distance = metric.Evaluate(querySet.unsafe_col(queryIndex),
referenceSet.unsafe_col(referenceIndex));
// If this distance is better than any of the current candidates, the
// SortDistance() function will give us the position to insert it into.
arma::vec queryDist = distances.unsafe_col(queryIndex);
size_t insertPosition = SortPolicy::SortDistance(queryDist, distance);
// SortDistance() returns (size_t() - 1) if we shouldn't add it.
if (insertPosition != (size_t() - 1))
InsertNeighbor(queryIndex, insertPosition, referenceIndex, distance);
return distance;
}
void CF<FactorizerType>::GetRecommendations(const size_t numRecs,
arma::Mat<size_t>& recommendations,
arma::Col<size_t>& users)
{
// Generate new table by multiplying approximate values.
rating = w * h;
// Now, we will use the decomposed w and h matrices to estimate what the user
// would have rated items as, and then pick the best items.
// Temporarily store feature vector of queried users.
arma::mat query(rating.n_rows, users.n_elem);
// Select feature vectors of queried users.
for (size_t i = 0; i < users.n_elem; i++)
query.col(i) = rating.col(users(i));
// Temporary storage for neighborhood of the queried users.
arma::Mat<size_t> neighborhood;
// Calculate the neighborhood of the queried users.
// This should be a templatized option.
neighbor::AllkNN a(rating);
arma::mat resultingDistances; // Temporary storage.
a.Search(query, numUsersForSimilarity, neighborhood, resultingDistances);
// Temporary storage for storing the average rating for each user in their
// neighborhood.
arma::mat averages = arma::zeros<arma::mat>(rating.n_rows, query.n_cols);
// Iterate over each query user.
for (size_t i = 0; i < neighborhood.n_cols; ++i)
{
// Iterate over each neighbor of the query user.
for (size_t j = 0; j < neighborhood.n_rows; ++j)
averages.col(i) += rating.col(neighborhood(j, i));
// Normalize average.
averages.col(i) /= neighborhood.n_rows;
}
// Generate recommendations for each query user by finding the maximum numRecs
// elements in the averages matrix.
recommendations.set_size(numRecs, users.n_elem);
recommendations.fill(cleanedData.n_rows); // Invalid item number.
arma::mat values(numRecs, users.n_elem);
values.fill(-DBL_MAX); // The smallest possible value.
for (size_t i = 0; i < users.n_elem; i++)
{
// Look through the averages column corresponding to the current user.
for (size_t j = 0; j < averages.n_rows; ++j)
{
// Ensure that the user hasn't already rated the item.
if (cleanedData(j, users(i)) != 0.0)
continue; // The user already rated the item.
// Is the estimated value better than the worst candidate?
const double value = averages(j, i);
if (value > values(values.n_rows - 1, i))
{
// It should be inserted. Which position?
size_t insertPosition = values.n_rows - 1;
while (insertPosition > 0)
{
if (value <= values(insertPosition - 1, i))
break; // The current value is the right one.
insertPosition--;
}
// Now insert it into the list.
InsertNeighbor(i, insertPosition, j, value, recommendations,
values);
}
}
// If we were not able to come up with enough recommendations, issue a
// warning.
if (recommendations(values.n_rows - 1, i) == cleanedData.n_rows + 1)
Log::Warn << "Could not provide " << values.n_rows << " recommendations "
<< "for user " << users(i) << " (not enough un-rated items)!"
<< std::endl;
}
}
void CF::GetRecommendations(const size_t numRecs,
arma::Mat<size_t>& recommendations,
arma::Col<size_t>& users)
{
// We want to avoid calculating the full rating matrix, so we will do nearest
// neighbor search only on the H matrix, using the observation that if the
// rating matrix X = W*H, then d(X.col(i), X.col(j)) = d(W H.col(i), W
// H.col(j)). This can be seen as nearest neighbor search on the H matrix
// with the Mahalanobis distance where M^{-1} = W^T W. So, we'll decompose
// M^{-1} = L L^T (the Cholesky decomposition), and then multiply H by L^T.
// Then we can perform nearest neighbor search.
arma::mat l = arma::chol(w.t() * w);
arma::mat stretchedH = l * h; // Due to the Armadillo API, l is L^T.
// Now, we will use the decomposed w and h matrices to estimate what the user
// would have rated items as, and then pick the best items.
// Temporarily store feature vector of queried users.
arma::mat query(stretchedH.n_rows, users.n_elem);
// Select feature vectors of queried users.
for (size_t i = 0; i < users.n_elem; i++)
query.col(i) = stretchedH.col(users(i));
// Temporary storage for neighborhood of the queried users.
arma::Mat<size_t> neighborhood;
// Calculate the neighborhood of the queried users.
// This should be a templatized option.
neighbor::KNN a(stretchedH);
arma::mat resultingDistances; // Temporary storage.
a.Search(query, numUsersForSimilarity, neighborhood, resultingDistances);
// Generate recommendations for each query user by finding the maximum numRecs
// elements in the averages matrix.
recommendations.set_size(numRecs, users.n_elem);
recommendations.fill(cleanedData.n_rows); // Invalid item number.
arma::mat values(numRecs, users.n_elem);
values.fill(-DBL_MAX); // The smallest possible value.
for (size_t i = 0; i < users.n_elem; i++)
{
// First, calculate average of neighborhood values.
arma::vec averages;
averages.zeros(cleanedData.n_rows);
for (size_t j = 0; j < neighborhood.n_rows; ++j)
averages += w * h.col(neighborhood(j, i));
averages /= neighborhood.n_rows;
// Look through the averages column corresponding to the current user.
for (size_t j = 0; j < averages.n_rows; ++j)
{
// Ensure that the user hasn't already rated the item.
if (cleanedData(j, users(i)) != 0.0)
continue; // The user already rated the item.
// Is the estimated value better than the worst candidate?
const double value = averages[j];
if (value > values(values.n_rows - 1, i))
{
// It should be inserted. Which position?
size_t insertPosition = values.n_rows - 1;
while (insertPosition > 0)
{
if (value <= values(insertPosition - 1, i))
break; // The current value is the right one.
insertPosition--;
}
// Now insert it into the list.
InsertNeighbor(i, insertPosition, j, value, recommendations,
values);
}
}
// If we were not able to come up with enough recommendations, issue a
// warning.
if (recommendations(values.n_rows - 1, i) == cleanedData.n_rows + 1)
Log::Warn << "Could not provide " << values.n_rows << " recommendations "
<< "for user " << users(i) << " (not enough un-rated items)!"
<< std::endl;
}
}
void FastMKS<KernelType, TreeType>::Search(
const typename TreeType::Mat& querySet,
const size_t k,
arma::Mat<size_t>& indices,
arma::mat& kernels)
{
Timer::Start("computing_products");
// No remapping will be necessary because we are using the cover tree.
indices.set_size(k, querySet.n_cols);
kernels.set_size(k, querySet.n_cols);
// Naive implementation.
if (naive)
{
// Fill kernels.
kernels.fill(-DBL_MAX);
// Simple double loop. Stupid, slow, but a good benchmark.
for (size_t q = 0; q < querySet.n_cols; ++q)
{
for (size_t r = 0; r < referenceSet.n_cols; ++r)
{
const double eval = metric.Kernel().Evaluate(querySet.col(q),
referenceSet.col(r));
size_t insertPosition;
for (insertPosition = 0; insertPosition < indices.n_rows;
++insertPosition)
if (eval > kernels(insertPosition, q))
break;
if (insertPosition < indices.n_rows)
InsertNeighbor(indices, kernels, q, insertPosition, r, eval);
}
}
Timer::Stop("computing_products");
return;
}
// Single-tree implementation.
if (singleMode)
{
// Fill kernels.
kernels.fill(-DBL_MAX);
// Create rules object (this will store the results). This constructor
// precalculates each self-kernel value.
typedef FastMKSRules<KernelType, TreeType> RuleType;
RuleType rules(referenceSet, querySet, indices, kernels, metric.Kernel());
typename TreeType::template SingleTreeTraverser<RuleType> traverser(rules);
for (size_t i = 0; i < querySet.n_cols; ++i)
traverser.Traverse(i, *referenceTree);
Log::Info << rules.BaseCases() << " base cases." << std::endl;
Log::Info << rules.Scores() << " scores." << std::endl;
Timer::Stop("computing_products");
return;
}
// Dual-tree implementation. First, we need to build the query tree. We are
// assuming it doesn't map anything...
Timer::Stop("computing_products");
Timer::Start("tree_building");
TreeType queryTree(querySet);
Timer::Stop("tree_building");
Search(&queryTree, k, indices, kernels);
}
void FastMKS<KernelType, TreeType>::Search(const size_t k,
arma::Mat<size_t>& indices,
arma::mat& kernels)
{
// No remapping will be necessary because we are using the cover tree.
Timer::Start("computing_products");
indices.set_size(k, referenceSet.n_cols);
kernels.set_size(k, referenceSet.n_cols);
kernels.fill(-DBL_MAX);
// Naive implementation.
if (naive)
{
// Simple double loop. Stupid, slow, but a good benchmark.
for (size_t q = 0; q < referenceSet.n_cols; ++q)
{
for (size_t r = 0; r < referenceSet.n_cols; ++r)
{
if (q == r)
continue; // Don't return the point as its own candidate.
const double eval = metric.Kernel().Evaluate(referenceSet.col(q),
referenceSet.col(r));
size_t insertPosition;
for (insertPosition = 0; insertPosition < indices.n_rows;
++insertPosition)
if (eval > kernels(insertPosition, q))
break;
if (insertPosition < indices.n_rows)
InsertNeighbor(indices, kernels, q, insertPosition, r, eval);
}
}
Timer::Stop("computing_products");
return;
}
// Single-tree implementation.
if (singleMode)
{
// Create rules object (this will store the results). This constructor
// precalculates each self-kernel value.
typedef FastMKSRules<KernelType, TreeType> RuleType;
RuleType rules(referenceSet, referenceSet, indices, kernels,
metric.Kernel());
typename TreeType::template SingleTreeTraverser<RuleType> traverser(rules);
for (size_t i = 0; i < referenceSet.n_cols; ++i)
traverser.Traverse(i, *referenceTree);
// Save the number of pruned nodes.
const size_t numPrunes = traverser.NumPrunes();
Log::Info << "Pruned " << numPrunes << " nodes." << std::endl;
Log::Info << rules.BaseCases() << " base cases." << std::endl;
Log::Info << rules.Scores() << " scores." << std::endl;
Timer::Stop("computing_products");
return;
}
// Dual-tree implementation.
Timer::Stop("computing_products");
Search(referenceTree, k, indices, kernels);
}
