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

# mlpack\_amf\_AMF(3)

This class implements AMF (alternating matrix factorization) on the given matrix V.

## NAME

mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \> -

This class implements **AMF** (alternating matrix factorization) on the given matrix V.

## SYNOPSIS

### Public Member Functions

**AMF** (const TerminationPolicyType &**terminationPolicy**=TerminationPolicyType(), const InitializationRuleType &initializeRule=InitializationRuleType(), const UpdateRuleType &**update**=UpdateRuleType())\
 *Create the* **AMF** *object and (optionally) set the parameters which* **AMF** *will run with.*  template\<typename MatType \> double **Apply** (const MatType &V, const size\_t r, arma::mat &W, arma::mat &H)\
 *Apply Alternating Matrix Factorization to the provided matrix.*  const InitializationRuleType & **InitializeRule** () const \
 *Access the initialization rule.*  InitializationRuleType & **InitializeRule** ()\
 *Modify the initialization rule.*  const TerminationPolicyType & **TerminationPolicy** () const \
 *Access the termination policy.*  TerminationPolicyType & **TerminationPolicy** ()\
 *Modify the termination policy.*  const UpdateRuleType & **Update** () const \
 *Access the update rule.*  UpdateRuleType & **Update** ()\
 *Modify the update rule.*

### Private Attributes

InitializationRuleType **initializationRule**\
 *Instantiated initialization Rule.*  TerminationPolicyType **terminationPolicy**\
 *Termination policy.*  UpdateRuleType **update**\
 *Instantiated update rule.*

## Detailed Description

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\>class mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>

This class implements **AMF** (alternating matrix factorization) on the given matrix V.

Alternating matrix factorization decomposes V in the form $ V  pprox WH $ where W is called the basis matrix and H is called the encoding matrix. V is taken to be of size n x m and the obtained W is n x r and H is r x m. The size r is called the rank of the factorization.

The implementation requires three template types; the first contains the policy used to determine when the algorithm has converged; the second contains the initialization rule for the W and H matrix; the last contains the update rule to be used during each iteration. This templatization allows the user to try various update rules, initialization rules, and termination policies (including ones not supplied with MLPACK) for factorization. By default, the template parameters to **AMF** implement non-negative matrix factorization with the multiplicative distance update.

A simple example of how to run **AMF** (or NMF) is shown below.

```
extern arma::mat V; // Matrix that we want to perform LMF on.
size_t r = 10; // Rank of decomposition
arma::mat W; // Basis matrix
arma::mat H; // Encoding matrix
AMF<> amf; // Default options: NMF with multiplicative distance update rules.
amf.Apply(V, W, H, r);
```

**Template Parameters:**

*TerminationPolicy* The policy to use for determining when the factorization has converged. \
 *InitializationRule* The initialization rule for initializing W and H matrix. \
 *UpdateRule* The update rule for calculating W and H matrix at each iteration.

**See also:**

NMF\_MultiplicativeDistanceUpdate

Definition at line 77 of file amf.hpp.

## Constructor & Destructor Documentation

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::AMF (const TerminationPolicyType &terminationPolicy = `TerminationPolicyType()`, const InitializationRuleType &initializeRule = `InitializationRuleType()`, const UpdateRuleType &update = `UpdateRuleType()`)

Create the **AMF** object and (optionally) set the parameters which **AMF** will run with. The minimum residue refers to the root mean square of the difference between two subsequent iterations of the product W \* H. A low residue indicates that subsequent iterations are not producing much change in W and H. Once the residue goes below the specified minimum residue, the algorithm terminates.

**Parameters:**

*initializationRule* Optional instantiated InitializationRule object for initializing the W and H matrices. \
 *updateRule* Optional instantiated UpdateRule object; this parameter is useful when the update rule for the W and H vector has state that it needs to store (i.e. HUpdate() and WUpdate() are not static functions). \
 *terminationPolicy* Optional instantiated TerminationPolicy object.

## Member Function Documentation

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> template\<typename MatType \> double mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::Apply (const MatType &V, const size\_tr, arma::mat &W, arma::mat &H)

Apply Alternating Matrix Factorization to the provided matrix.

**Parameters:**

*V* Input matrix to be factorized. \
 *W* Basis matrix to be output. \
 *H* Encoding matrix to output. \
 *r* Rank r of the factorization.

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> const InitializationRuleType& mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::InitializeRule () const` [inline]`

Access the initialization rule.

Definition at line 121 of file amf.hpp.

References mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::initializationRule.

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> InitializationRuleType& mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::InitializeRule ()` [inline]`

Modify the initialization rule.

Definition at line 124 of file amf.hpp.

References mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::initializationRule.

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> const TerminationPolicyType& mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::TerminationPolicy () const` [inline]`

Access the termination policy.

Definition at line 115 of file amf.hpp.

References mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::terminationPolicy.

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> TerminationPolicyType& mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::TerminationPolicy ()` [inline]`

Modify the termination policy.

Definition at line 118 of file amf.hpp.

References mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::terminationPolicy.

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> const UpdateRuleType& mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::Update () const` [inline]`

Access the update rule.

Definition at line 127 of file amf.hpp.

References mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::update.

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> UpdateRuleType& mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::Update ()` [inline]`

Modify the update rule.

Definition at line 129 of file amf.hpp.

References mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::update.

## Member Data Documentation

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> InitializationRuleType mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::initializationRule` [private]`

Instantiated initialization Rule.

Definition at line 135 of file amf.hpp.

Referenced by mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::InitializeRule().

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> TerminationPolicyType mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::terminationPolicy` [private]`

Termination policy.

Definition at line 133 of file amf.hpp.

Referenced by mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::TerminationPolicy().

### template\<typename TerminationPolicyType = SimpleResidueTermination, typename InitializationRuleType = RandomInitialization, typename UpdateRuleType = NMFMultiplicativeDistanceUpdate\> UpdateRuleType mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::update` [private]`

Instantiated update rule.

Definition at line 137 of file amf.hpp.

Referenced by mlpack::amf::AMF\< TerminationPolicyType, InitializationRuleType, UpdateRuleType \>::Update().

## Author

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