void GetNeighborhood(const arma::Col<size_t>& users,
const size_t numUsersForSimilarity,
arma::Mat<size_t>& neighborhood,
arma::mat& similarities) const
{
// 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.
// 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));
NeighborSearchPolicy neighborSearch(stretchedH);
neighborSearch.Search(
query, numUsersForSimilarity, neighborhood, similarities);
}
double MeanShift<UseKernel, KernelType, MatType>::
EstimateRadius(const MatType& data, double ratio)
{
neighbor::KNN neighborSearch(data);
/**
* For each point in dataset, select nNeighbors nearest points and get
* nNeighbors distances. Use the maximum distance to estimate the duplicate
* threshhold.
*/
const size_t nNeighbors = size_t(data.n_cols * ratio);
arma::Mat<size_t> neighbors;
arma::mat distances;
neighborSearch.Search(nNeighbors, neighbors, distances);
// Get max distance for each point.
arma::rowvec maxDistances = max(distances);
// Calculate and return the radius.
return sum(maxDistances) / (double) data.n_cols;
}
