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Merge pull request #3413 from AdarshSantoria/bksvd
Add Block Krylov SVD method in CF
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src/mlpack/methods/cf/decomposition_policies/block_krylov_svd_method.hpp
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| /** | ||
| * @file methods/cf/decomposition_policies/block_krylov_svd_method.hpp | ||
| * @author Adarsh Santoria | ||
| * | ||
| * Implementation of the block krylov svd method for use in | ||
| * Collaborative Fitlering. | ||
| * | ||
| * mlpack is free software; you may redistribute it and/or modify it under the | ||
| * terms of the 3-clause BSD license. You should have received a copy of the | ||
| * 3-clause BSD license along with mlpack. If not, see | ||
| * http://www.opensource.org/licenses/BSD-3-Clause for more information. | ||
| */ | ||
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| #ifndef MLPACK_METHODS_CF_DECOMPOSITION_POLICIES_BLOCK_KRYLOV_SVD_METHOD_HPP | ||
| #define MLPACK_METHODS_CF_DECOMPOSITION_POLICIES_BLOCK_KRYLOV_SVD_METHOD_HPP | ||
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| #include <mlpack/prereqs.hpp> | ||
| #include <mlpack/methods/block_krylov_svd/block_krylov_svd.hpp> | ||
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| namespace mlpack { | ||
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| /** | ||
| * Implementation of the Block Krylov SVD policy to act as a wrapper when | ||
| * using Block Krylov SVD for the decomposition type of CF. | ||
| * | ||
| * An example of how to use BlockKrylovSVDPolicy in CF is shown below: | ||
| * | ||
| * @code | ||
| * extern arma::mat data; // data is a (user, item, rating) table. | ||
| * // Users for whom recommendations are generated. | ||
| * extern arma::Col<size_t> users; | ||
| * arma::Mat<size_t> recommendations; // Resulting recommendations. | ||
| * | ||
| * CFType<BlockKrylovSVDPolicy> cf(data); | ||
| * | ||
| * // Generate 10 recommendations for all users. | ||
| * cf.GetRecommendations(10, recommendations); | ||
| * @endcode | ||
| */ | ||
| class BlockKrylovSVDPolicy | ||
| { | ||
| public: | ||
| /** | ||
| * Create block krylov SVD object to use for collaborative filtering. | ||
| */ | ||
| BlockKrylovSVDPolicy() | ||
| { | ||
| /* Nothing to do here */ | ||
| } | ||
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| /** | ||
| * Apply Collaborative Filtering to the provided data set using the | ||
| * block krylov SVD. | ||
| * | ||
| * @param * (data) Data matrix: dense matrix (coordinate lists) | ||
| * or sparse matrix(cleaned). | ||
| * @param cleanedData item user table in form of sparse matrix. | ||
| * @param rank Rank parameter for matrix factorization. | ||
| * @param * (maxIterations) Maximum number of iterations. | ||
| * @param * (minResidue) Residue required to terminate. | ||
| * @param * (mit) Whether to terminate only when maxIterations is reached. | ||
| */ | ||
| 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; | ||
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| // Preprocessed data converted to mat format | ||
| arma::mat data(cleanedData); | ||
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| // Do singular value decomposition using the block krylov SVD algorithm. | ||
| RandomizedBlockKrylovSVD blockkrylovsvd; | ||
| blockkrylovsvd.Apply(data, w, sigma, h, rank); | ||
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| // Sigma matrix is multiplied to w. | ||
| w = w * arma::diagmat(sigma); | ||
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| // Take transpose of the matrix h as required by CF class. | ||
| h = arma::trans(h); | ||
| } | ||
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| /** | ||
| * Return predicted rating given user ID and item ID. | ||
| * | ||
| * @param user User ID. | ||
| * @param item Item ID. | ||
| */ | ||
| double GetRating(const size_t user, const size_t item) const | ||
| { | ||
| double rating = arma::as_scalar(w.row(item) * h.col(user)); | ||
| return rating; | ||
| } | ||
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| /** | ||
| * Get predicted ratings for a user. | ||
| * | ||
| * @param user User ID. | ||
| * @param rating Resulting rating vector. | ||
| */ | ||
| void GetRatingOfUser(const size_t user, arma::vec& rating) const | ||
| { | ||
| rating = w * h.col(user); | ||
| } | ||
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| /** | ||
| * Get the neighborhood and corresponding similarities for a set of users. | ||
| * | ||
| * @tparam NeighborSearchPolicy The policy to perform neighbor search. | ||
| * | ||
| * @param users Users whose neighborhood is to be computed. | ||
| * @param numUsersForSimilarity The number of neighbors returned for | ||
| * each user. | ||
| * @param neighborhood Neighbors represented by user IDs. | ||
| * @param similarities Similarity between each user and each of its | ||
| * neighbors. | ||
| */ | ||
| 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. | ||
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| // 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)); | ||
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| NeighborSearchPolicy neighborSearch(stretchedH); | ||
| neighborSearch.Search( | ||
| query, numUsersForSimilarity, neighborhood, similarities); | ||
| } | ||
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| //! Get the Item Matrix. | ||
| const arma::mat& W() const { return w; } | ||
| //! Get the User Matrix. | ||
| const arma::mat& H() const { return h; } | ||
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| /** | ||
| * Serialization. | ||
| */ | ||
| template<typename Archive> | ||
| void serialize(Archive& ar, const uint32_t /* version */) | ||
| { | ||
| ar(CEREAL_NVP(w)); | ||
| ar(CEREAL_NVP(h)); | ||
| } | ||
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| private: | ||
| //! Item matrix. | ||
| arma::mat w; | ||
| //! User matrix. | ||
| arma::mat h; | ||
| }; | ||
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| } // namespace mlpack | ||
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| #endif |
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