randomized_svd_method.hpp

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#ifndef MLPACK_METHODS_CF_DECOMPOSITION_POLICIES_RANDOMIZED_SVD_METHOD_HPP
#define MLPACK_METHODS_CF_DECOMPOSITION_POLICIES_RANDOMIZED_SVD_METHOD_HPP

#include <mlpack/prereqs.hpp>
#include <mlpack/methods/randomized_svd/randomized_svd.hpp>

namespace mlpack {
namespace cf {

class RandomizedSVDPolicy
{
 public:
  RandomizedSVDPolicy(const size_t iteratedPower = 0,
                      const size_t maxIterations = 2) :
      iteratedPower(iteratedPower),
      maxIterations(maxIterations)
  {
    /* Nothing to do here */
  }

  template<typename MatType>
  void Apply(const MatType& /* data */,
             const arma::sp_mat& cleanedData,
             const size_t rank,
             const size_t maxIterations,
             const double /* minResidue */,
             const bool /* mit */)
  {
    arma::vec sigma;

    // Do singular value decomposition using the randomized SVD algorithm.
    svd::RandomizedSVD rsvd(iteratedPower, maxIterations);
    rsvd.Apply(cleanedData, w, sigma, h, rank);

    // Sigma matrix is multiplied to w.
    w = w * arma::diagmat(sigma);

    // Take transpose of the matrix h as required by CF class.
    h = arma::trans(h);
  }

  double GetRating(const size_t user, const size_t item) const
  {
    double rating = arma::as_scalar(w.row(item) * h.col(user));
    return rating;
  }

  void GetRatingOfUser(const size_t user, arma::vec& rating) const
  {
    rating = w * h.col(user);
  }

  template<typename NeighborSearchPolicy>
  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);
  }

  const arma::mat& W() const { return w; }
  const arma::mat& H() const { return h; }

  size_t IteratedPower() const { return iteratedPower; }
  size_t& IteratedPower() { return iteratedPower; }

  size_t MaxIterations() const { return maxIterations; }
  size_t& MaxIterations() { return maxIterations; }

  template<typename Archive>
  void serialize(Archive& ar, const uint32_t /* version */)
  {
    ar(CEREAL_NVP(w));
    ar(CEREAL_NVP(h));
  }

 private:
  size_t iteratedPower;
  size_t maxIterations;
  arma::mat w;
  arma::mat h;
};

} // namespace cf
} // namespace mlpack

#endif