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mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >(3) | MLPACK | mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >(3) |
NAME¶
mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer > - An implementation of Local Coordinate Coding (LCC) that codes data which approximately lives on a manifold using a variation of l1-norm regularized sparse coding; in LCC, the penalty on the absolute value of each point's coefficient for each atom is weighted by the squared distance of that point to that atom.SYNOPSIS¶
Public Member Functions¶
LocalCoordinateCoding (const arma::mat &data, const size_t atoms, const double lambda)
Private Attributes¶
size_t atoms
Detailed Description¶
template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer>class mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >¶
An implementation of Local Coordinate Coding (LCC) that codes data which approximately lives on a manifold using a variation of l1-norm regularized sparse coding; in LCC, the penalty on the absolute value of each point's coefficient for each atom is weighted by the squared distance of that point to that atom. Let d be the number of dimensions in the original space, m the number of training points, and k the number of atoms in the dictionary (the dimension of the learned feature space). The training data X is a d-by-m matrix where each column is a point and each row is a dimension. The dictionary D is a d-by-k matrix, and the sparse codes matrix Z is a k-by-m matrix. This program seeks to minimize the objective: min_{D,Z} ||X - D Z||_{Fro}^2- •
- lambda sum_{i=1}^m sum_{j=1}^k dist(X_i,D_j)^2 Z_i^j where lambda > 0.
@incollection{NIPS2009_0719, title = {Nonlinear Learning using Local Coordinate Coding}, author = {Kai Yu and Tong Zhang and Yihong Gong}, booktitle = {Advances in Neural Information Processing Systems 22}, editor = {Y. Bengio and D. Schuurmans and J. Lafferty and C. K. I. Williams and A. Culotta}, pages = {2223--2231}, year = {2009} }
@article{efron2004least, title={Least angle regression}, author={Efron, B. and Hastie, T. and Johnstone, I. and Tibshirani, R.}, journal={The Annals of statistics}, volume={32}, number={2}, pages={407--499}, year={2004}, publisher={Institute of Mathematical Statistics} }Definition at line 91 of file lcc.hpp.
Constructor & Destructor Documentation¶
template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >:: LocalCoordinateCoding (const arma::mat &data, const size_tatoms, const doublelambda)¶
Set the parameters to LocalCoordinateCoding. Parameters:data Data matrix.
atoms Number of atoms in dictionary.
lambda Regularization parameter for weighted l1-norm penalty.
Member Function Documentation¶
template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> const arma::mat& mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Codes () const [inline]¶
Accessor the codes. Definition at line 144 of file lcc.hpp. References mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::codes.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> arma::mat& mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Codes () [inline]¶
Modify the codes. Definition at line 146 of file lcc.hpp. References mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::codes.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> const arma::mat& mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Data () const [inline]¶
Access the data. Definition at line 136 of file lcc.hpp. References mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::data.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> const arma::mat& mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Dictionary () const [inline]¶
Accessor for dictionary. Definition at line 139 of file lcc.hpp. References mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::dictionary.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> arma::mat& mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Dictionary () [inline]¶
Mutator for dictionary. Definition at line 141 of file lcc.hpp. References mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::dictionary.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> void mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Encode (const size_tmaxIterations = 0, const doubleobjTolerance = 0.01)¶
Run local coordinate coding. Parameters:nIterations Maximum number of iterations to run
algorithm.
objTolerance Tolerance of objective function. When the objective function
changes by a value lower than this tolerance, the optimization
terminates.
template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> double mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Objective (arma::uvecadjacencies) const¶
Compute objective function given the list of adjacencies.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> void mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::OptimizeCode ()¶
Code each point via distance-weighted LARS.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> void mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::OptimizeDictionary (arma::uvecadjacencies)¶
Learn dictionary by solving linear system. Parameters:adjacencies Indices of entries (unrolled column by
column) of the coding matrix Z that are non-zero (the adjacency matrix for the
bipartite graph of points and atoms)
template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> std::string mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::ToString () const¶
Member Data Documentation¶
template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> size_t mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::atoms [private]¶
Number of atoms in dictionary. Definition at line 153 of file lcc.hpp.template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> arma::mat mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::codes [private]¶
Codes (columns are points). Definition at line 162 of file lcc.hpp. Referenced by mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Codes().template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> const arma::mat& mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::data [private]¶
Data matrix (columns are points). Definition at line 156 of file lcc.hpp. Referenced by mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Data().template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> arma::mat mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::dictionary [private]¶
Dictionary (columns are atoms). Definition at line 159 of file lcc.hpp. Referenced by mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::Dictionary().template<typename DictionaryInitializer = sparse_coding::DataDependentRandomInitializer> double mlpack::lcc::LocalCoordinateCoding< DictionaryInitializer >::lambda [private]¶
l1 regularization term. Definition at line 165 of file lcc.hpp.Author¶
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