R: Local Coordinate Coding

local_coordinate_coding {mlpack} | R Documentation

## Local Coordinate Coding

### Description

An implementation of Local Coordinate Coding (LCC), a data transformation technique. Given input data, this transforms each point to be expressed as a linear combination of a few points in the dataset; once an LCC model is trained, it can be used to transform points later also.

### Usage

    local_coordinate_coding(
      atoms = NA,
      initial_dictionary = NA,
      input_model = NA,
      lambda = NA,
      max_iterations = NA,
      normalize = FALSE,
      seed = NA,
      test = NA,
      tolerance = NA,
      training = NA,
      verbose = FALSE
    )

### Arguments

`atoms` | Number of atoms in the dictionary. Default value "0" (integer).
`initial_dictionary` | Optional initial dictionary (numeric matrix).
`input_model` | Input LCC model (LocalCoordinateCoding).
`lambda` | Weighted l1-norm regularization parameter. Default value "0" (numeric).
`max_iterations` | Maximum number of iterations for LCC (0 indicates no limit). Default value "0" (integer).
`normalize` | If set, the input data matrix will be normalized before coding. Default value "FALSE" (logical).
`seed` | Random seed. If 0, 'std::time(NULL)' is used. Default value "0" (integer).
`test` | Test points to encode (numeric matrix).
`tolerance` | Tolerance for objective function. Default value "0.01" (numeric).
`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 Local Coordinate Coding (LCC), which codes data that approximately lives on a manifold using a variation of l1-norm regularized sparse coding. Given a dense data matrix X with n points and d dimensions, LCC seeks to find a dense dictionary matrix D with k atoms in d dimensions, and a coding matrix Z with n points in k dimensions. Because of the regularization method used, the atoms in D should lie close to the manifold on which the data points lie.

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

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

To run this program, the input matrix X must be specified (with -i), along with the number of atoms in the dictionary (-k). An initial dictionary may also be specified with the "initial_dictionary" parameter. The l1-norm regularization parameter is specified with the "lambda" parameter.

### Value

A list with several components:

`codes` | Output codes matrix (numeric matrix).
`dictionary` | Output dictionary matrix (numeric matrix).
`output_model` | Output for trained LCC model (LocalCoordinateCoding).

### Author(s)

mlpack developers

### Examples

    # For example, to run LCC on the dataset "data" using 200 atoms and an
    # l1-regularization parameter of 0.1, saving the dictionary "dictionary" and
    # the codes into "codes", use

    ## Not run:
    output <- local_coordinate_coding(training=data, atoms=200, lambda=0.1)
    dict <- output$dictionary
    codes <- output$codes

    ## End(Not run)

    # The maximum number of iterations may be specified with the "max_iterations"
    # parameter. Optionally, the input data matrix X can be normalized before
    # coding with the "normalize" parameter.
    #
    # An LCC model may be saved using the "output_model" output parameter.  Then,
    # to encode new points from the dataset "points" with the previously saved
    # model "lcc_model", saving the new codes to "new_codes", the following
    # command can be used:

    ## Not run:
    output <- local_coordinate_coding(input_model=lcc_model, test=points)
    new_codes <- output$codes

    ## End(Not run)

[Package mlpack version 3.4.2.1 Index]