MLPACK
1.0.11
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An implementation of Sparse Coding with Dictionary Learning that achieves sparsity via an l1-norm regularizer on the codes (LASSO) or an (l1+l2)-norm regularizer on the codes (the Elastic Net). More...
Public Member Functions | |
SparseCoding (const arma::mat &data, const size_t atoms, const double lambda1, const double lambda2=0) | |
Set the parameters to SparseCoding. More... | |
const arma::mat & | Codes () const |
Access the sparse codes. More... | |
arma::mat & | Codes () |
Modify the sparse codes. More... | |
const arma::mat & | Data () const |
Access the data. More... | |
const arma::mat & | Dictionary () const |
Access the dictionary. More... | |
arma::mat & | Dictionary () |
Modify the dictionary. More... | |
void | Encode (const size_t maxIterations=0, const double objTolerance=0.01, const double newtonTolerance=1e-6) |
Run Sparse Coding with Dictionary Learning. More... | |
double | Objective () const |
Compute the objective function. More... | |
void | OptimizeCode () |
Sparse code each point via LARS. More... | |
double | OptimizeDictionary (const arma::uvec &adjacencies, const double newtonTolerance=1e-6, const size_t maxIterations=50) |
Learn dictionary via Newton method based on Lagrange dual. More... | |
void | ProjectDictionary () |
Project each atom of the dictionary back onto the unit ball, if necessary. More... | |
std::string | ToString () const |
Private Attributes | |
size_t | atoms |
Number of atoms. More... | |
arma::mat | codes |
Sparse codes (columns are points). More... | |
const arma::mat & | data |
Data matrix (columns are points). More... | |
arma::mat | dictionary |
Dictionary (columns are atoms). More... | |
double | lambda1 |
l1 regularization term. More... | |
double | lambda2 |
l2 regularization term. More... | |
An implementation of Sparse Coding with Dictionary Learning that achieves sparsity via an l1-norm regularizer on the codes (LASSO) or an (l1+l2)-norm regularizer on the codes (the Elastic Net).
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:
subject to for
where typically
and
.
This problem is solved by an algorithm that alternates between a dictionary learning step and a sparse coding step. The dictionary learning step updates the dictionary D using a Newton method based on the Lagrange dual (see the paper below for details). The sparse coding step involves solving a large number of sparse linear regression problems; this can be done efficiently using LARS, an algorithm that can solve the LASSO or the Elastic Net (papers below).
Here are those papers:
Before the method is run, the dictionary is initialized using the DictionaryInitializationPolicy class. Possible choices include the RandomInitializer, which provides an entirely random dictionary, the DataDependentRandomInitializer, which provides a random dictionary based loosely on characteristics of the dataset, and the NothingInitializer, which does not initialize the dictionary – instead, the user should set the dictionary using the Dictionary() mutator method.
DictionaryInitializationPolicy | The class to use to initialize the dictionary; must have 'void Initialize(const arma::mat& data, arma::mat& dictionary)' function. |
Definition at line 119 of file sparse_coding.hpp.
mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::SparseCoding | ( | const arma::mat & | data, |
const size_t | atoms, | ||
const double | lambda1, | ||
const double | lambda2 = 0 |
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Set the parameters to SparseCoding.
lambda2 defaults to 0.
data | Data matrix |
atoms | Number of atoms in dictionary |
lambda1 | Regularization parameter for l1-norm penalty |
lambda2 | Regularization parameter for l2-norm penalty |
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Access the sparse codes.
Definition at line 190 of file sparse_coding.hpp.
References mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::codes.
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Modify the sparse codes.
Definition at line 192 of file sparse_coding.hpp.
References mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::codes, and mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::ToString().
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Access the data.
Definition at line 182 of file sparse_coding.hpp.
References mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::data.
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Access the dictionary.
Definition at line 185 of file sparse_coding.hpp.
References mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::dictionary.
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Modify the dictionary.
Definition at line 187 of file sparse_coding.hpp.
References mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::dictionary.
void mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::Encode | ( | const size_t | maxIterations = 0 , |
const double | objTolerance = 0.01 , |
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const double | newtonTolerance = 1e-6 |
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Run Sparse Coding with Dictionary Learning.
maxIterations | Maximum number of iterations to run algorithm. If 0, the algorithm will run until convergence (or forever). |
objTolerance | Tolerance for objective function. When an iteration of the algorithm produces an improvement smaller than this, the algorithm will terminate. |
newtonTolerance | Tolerance for the Newton's method dictionary optimization step. |
double mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::Objective | ( | ) | const |
Compute the objective function.
void mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::OptimizeCode | ( | ) |
Sparse code each point via LARS.
double mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::OptimizeDictionary | ( | const arma::uvec & | adjacencies, |
const double | newtonTolerance = 1e-6 , |
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const size_t | maxIterations = 50 |
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Learn dictionary via Newton method based on Lagrange dual.
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). |
newtonTolerance | Tolerance of the Newton's method optimizer. |
maxIterations | Maximum number of iterations to run the Newton's method. If 0, the method will run until convergence (or forever). |
void mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::ProjectDictionary | ( | ) |
Project each atom of the dictionary back onto the unit ball, if necessary.
std::string mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::ToString | ( | ) | const |
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Number of atoms.
Definition at line 199 of file sparse_coding.hpp.
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Sparse codes (columns are points).
Definition at line 208 of file sparse_coding.hpp.
Referenced by mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::Codes().
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Data matrix (columns are points).
Definition at line 202 of file sparse_coding.hpp.
Referenced by mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::Data().
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Dictionary (columns are atoms).
Definition at line 205 of file sparse_coding.hpp.
Referenced by mlpack::sparse_coding::SparseCoding< DictionaryInitializer >::Dictionary().
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l1 regularization term.
Definition at line 211 of file sparse_coding.hpp.
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l2 regularization term.
Definition at line 214 of file sparse_coding.hpp.