This class implements AMF (alternating matrix factorization) on the given matrix V. More...
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. More...  
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. More...  
const InitializationRuleType &  InitializeRule () const 
Access the initialization rule. More...  
InitializationRuleType &  InitializeRule () 
Modify the initialization rule. More...  
const TerminationPolicyType &  TerminationPolicy () const 
Access the termination policy. More...  
TerminationPolicyType &  TerminationPolicy () 
Modify the termination policy. More...  
const UpdateRuleType &  Update () const 
Access the update rule. More...  
UpdateRuleType &  Update () 
Modify the update rule. More...  
This class implements AMF (alternating matrix factorization) on the given matrix V.
Alternating matrix factorization decomposes V in the form 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 nonnegative matrix factorization with the multiplicative distance update.
A simple example of how to run AMF (or NMF) is shown below.
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. 
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.
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. 
double Apply  (  const MatType &  V, 
const size_t  r,  
arma::mat &  W,  
arma::mat &  H  
) 
Apply Alternating Matrix Factorization to the provided matrix.
V  Input matrix to be factorized. 
W  Basis matrix to be output. 
H  Encoding matrix to output. 
r  Rank r of the factorization. 
Referenced by NMFPolicy::Apply(), BatchSVDPolicy::Apply(), SVDCompletePolicy::Apply(), and SVDIncompletePolicy::Apply().

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