---
name: "mlpack_lcc_LocalCoordinateCoding"
section: "3"
platform: "linux"
package: "mlpack-doc"
version: "1.0.10-1"
release: "Debian 8 (Jessie)"
platforms: ["linux"]
url: "https://new.carta.tech/mlpack_lcc_LocalCoordinateCoding"
---

# mlpack\_lcc\_LocalCoordinateCoding(3)

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.

## 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**)\
 *Set the parameters to* **LocalCoordinateCoding***.*  const arma::mat & **Codes** () const \
 *Accessor the codes.*  arma::mat & **Codes** ()\
 *Modify the codes.*  const arma::mat & **Data** () const \
 *Access the data.*  const arma::mat & **Dictionary** () const \
 *Accessor for dictionary.*  arma::mat & **Dictionary** ()\
 *Mutator for dictionary.*  void **Encode** (const size\_t maxIterations=0, const double objTolerance=0.01)\
 *Run local coordinate coding.*  double **Objective** (arma::uvec adjacencies) const \
 *Compute objective function given the list of adjacencies.*  void **OptimizeCode** ()\
 *Code each point via distance-weighted LARS.*  void **OptimizeDictionary** (arma::uvec adjacencies)\
 *Learn dictionary by solving linear system.*  std::string **ToString** () const \

### Private Attributes

size\_t **atoms**\
 *Number of atoms in dictionary.*  arma::mat **codes**\
 *Codes (columns are points).*  const arma::mat & **data**\
 *Data matrix (columns are points).*  arma::mat **dictionary**\
 *Dictionary (columns are atoms).*  double **lambda**\
 *l1 regularization term.*

## 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.

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 by solving a linear system (note that the objective is a positive definite quadratic program). The sparse coding step involves solving a large number of weighted l1-norm regularized linear regression problems problems; this can be done efficiently using LARS, an algorithm that can solve the LASSO (paper below).

The papers are listed below.

```
@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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