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 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);
arma::mat values(numRecs, users.n_elem);
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;
// Let's build the list of candidate recomendations for the given user.
// Default candidate: the smallest possible value and invalid item number.
const Candidate def = std::make_pair(-DBL_MAX, cleanedData.n_rows);
std::vector<Candidate> vect(numRecs, def);
typedef std::priority_queue<Candidate, std::vector<Candidate>, CandidateCmp>
CandidateList;
CandidateList pqueue(CandidateCmp(), std::move(vect));
// 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?
if (averages[i] > pqueue.top().first)
{
Candidate c = std::make_pair(averages[j], j);
pqueue.pop();
pqueue.push(c);
}
}
for (size_t p = 1; p <= numRecs; p++)
{
recommendations(numRecs - p, i) = pqueue.top().second;
values(numRecs - p, i) = pqueue.top().first;
pqueue.pop();
}
// If we were not able to come up with enough recommendations, issue a
// warning.
if (recommendations(numRecs - 1, i) == def.second)
Log::Warn << "Could not provide " << numRecs << " recommendations "
<< "for user " << users(i) << " (not enough un-rated items)!"
<< std::endl;
}
}
