sparse_coding: Sparse Coding

In mlpack: 'Rcpp' Integration for the 'mlpack' Library

Sparse Coding

Description

An implementation of Sparse Coding with Dictionary Learning. Given a dataset, this will decompose the dataset into a sparse combination of a few dictionary elements, where the dictionary is learned during computation; a dictionary can be reused for future sparse coding of new points.

Usage

sparse_coding(
  atoms = NA,
  initial_dictionary = NA,
  input_model = NA,
  lambda1 = NA,
  lambda2 = NA,
  max_iterations = NA,
  newton_tolerance = NA,
  normalize = FALSE,
  objective_tolerance = NA,
  seed = NA,
  test = NA,
  training = NA,
  verbose = FALSE
)

Arguments

atoms	Number of atoms in the dictionary. Default value "15" (integer).
initial_dictionary	Optional initial dictionary matrix (numeric matrix).
input_model	File containing input sparse coding model (SparseCoding).
lambda1	Sparse coding l1-norm regularization parameter. Default value "0" (numeric).
lambda2	Sparse coding l2-norm regularization parameter. Default value "0" (numeric).
max_iterations	Maximum number of iterations for sparse coding (0 indicates no limit). Default value "0" (integer).
newton_tolerance	Tolerance for convergence of Newton method. Default value "1e-06" (numeric).
normalize	If set, the input data matrix will be normalized before coding. Default value "FALSE" (logical).
objective_tolerance	Tolerance for convergence of the objective function. Default value "0.01" (numeric).
seed	Random seed. If 0, 'std::time(NULL)' is used. Default value "0" (integer).
test	Optional matrix to be encoded by trained model (numeric matrix).
training	Matrix of training data (X) (numeric matrix).
verbose	Display informational messages and the full list of parameters and timers at the end of execution. Default value "FALSE" (logical).

Details

An implementation of Sparse Coding with Dictionary Learning, which achieves sparsity via an l1-norm regularizer on the codes (LASSO) or an (l1+l2)-norm regularizer on the codes (the Elastic Net). Given a dense data matrix X with d dimensions and n points, sparse coding seeks to find a dense dictionary matrix D with k atoms in d dimensions, and a sparse coding matrix Z with n points in k dimensions.

The original data matrix X can then be reconstructed as Z * D. Therefore, this program finds a representation of each point in X as a sparse linear combination of atoms in the dictionary D.

The sparse coding is found with an algorithm which alternates between a dictionary step, which updates the dictionary D, and a sparse coding step, which updates the sparse coding matrix.

Once a dictionary D is found, the sparse coding model may be used to encode other matrices, and saved for future usage.

To run this program, either an input matrix or an already-saved sparse coding model must be specified. An input matrix may be specified with the "training" option, along with the number of atoms in the dictionary (specified with the "atoms" parameter). It is also possible to specify an initial dictionary for the optimization, with the "initial_dictionary" parameter. An input model may be specified with the "input_model" parameter.

Value

A list with several components:

codes	Matrix to save the output sparse codes of the test matrix (–test_file) to (numeric matrix).
dictionary	Matrix to save the output dictionary to (numeric matrix).
output_model	File to save trained sparse coding model to (SparseCoding).

Author(s)

mlpack developers

Examples

# As an example, to build a sparse coding model on the dataset "data" using
# 200 atoms and an l1-regularization parameter of 0.1, saving the model into
# "model", use 

## Not run: 
output <- sparse_coding(training=data, atoms=200, lambda1=0.1)
model <- output$output_model

## End(Not run)

# Then, this model could be used to encode a new matrix, "otherdata", and
# save the output codes to "codes": 

## Not run: 
output <- sparse_coding(input_model=model, test=otherdata)
codes <- output$codes

## End(Not run)

mlpack documentation built on Sept. 27, 2023, 1:07 a.m.