\section{N\+M\+F\+A\+L\+S\+Update Class Reference} \label{classmlpack_1_1amf_1_1NMFALSUpdate}\index{N\+M\+F\+A\+L\+S\+Update@{N\+M\+F\+A\+L\+S\+Update}} This class implements a method titled \textquotesingle{}Alternating Least Squares\textquotesingle{} described in the following paper\+: \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ N\+M\+F\+A\+L\+S\+Update} () \begin{DoxyCompactList}\small\item\em Empty constructor required for the Update\+Rule template. \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type $>$ }\\void \textbf{ Initialize} (const Mat\+Type \&, const size\+\_\+t) \begin{DoxyCompactList}\small\item\em Set initial values for the factorization. \end{DoxyCompactList}\item {\footnotesize template$<$typename Archive $>$ }\\void \textbf{ serialize} (Archive \&, const unsigned int) \begin{DoxyCompactList}\small\item\em Serialize the object (in this case, there is nothing to serialize). \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Static Public Member Functions} \begin{DoxyCompactItemize} \item {\footnotesize template$<$typename Mat\+Type $>$ }\\static void \textbf{ H\+Update} (const Mat\+Type \&V, const arma\+::mat \&W, arma\+::mat \&H) \begin{DoxyCompactList}\small\item\em The update rule for the encoding matrix H. \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type $>$ }\\static void \textbf{ W\+Update} (const Mat\+Type \&V, arma\+::mat \&W, const arma\+::mat \&H) \begin{DoxyCompactList}\small\item\em The update rule for the basis matrix W. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} This class implements a method titled \textquotesingle{}Alternating Least Squares\textquotesingle{} described in the following paper\+: \begin{DoxyCode} @article\{paatero1994positive, title=\{Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values\}, author=\{Paatero, P. and Tapper, U.\}, journal=\{Environmetrics\}, volume=\{5\}, number=\{2\}, pages=\{111--126\}, year=\{1994\} \} \end{DoxyCode} It uses the least squares projection formula to reduce the error value of $ \sqrt{\sum_i \sum_j(V-WH)^2} $ by alternately calculating W and H respectively while holding the other matrix constant. Definition at line 41 of file nmf\+\_\+als.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1amf_1_1NMFALSUpdate_a3482d9d8fc18996cee80de1f698b3a09}} \index{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}!N\+M\+F\+A\+L\+S\+Update@{N\+M\+F\+A\+L\+S\+Update}} \index{N\+M\+F\+A\+L\+S\+Update@{N\+M\+F\+A\+L\+S\+Update}!mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}} \subsubsection{N\+M\+F\+A\+L\+S\+Update()} {\footnotesize\ttfamily \textbf{ N\+M\+F\+A\+L\+S\+Update} (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Empty constructor required for the Update\+Rule template. Definition at line 45 of file nmf\+\_\+als.\+hpp. \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1amf_1_1NMFALSUpdate_ad2a433d7e149001f0f44caa8967d20a6}} \index{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}!H\+Update@{H\+Update}} \index{H\+Update@{H\+Update}!mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}} \subsubsection{H\+Update()} {\footnotesize\ttfamily static void H\+Update (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{V, }\item[{const arma\+::mat \&}]{W, }\item[{arma\+::mat \&}]{H }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}} The update rule for the encoding matrix H. The formula used is \[ H = \frac{W^T V}{W^T W} \] The function takes in all the matrices and only changes the value of the H matrix. \begin{DoxyParams}{Parameters} {\em V} & Input matrix to be factorized. \\ \hline {\em W} & Basis matrix. \\ \hline {\em H} & Encoding matrix to be updated. \\ \hline \end{DoxyParams} Definition at line 105 of file nmf\+\_\+als.\+hpp. \mbox{\label{classmlpack_1_1amf_1_1NMFALSUpdate_aac5af164b10635addd7ff7bb934a4db3}} \index{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}!Initialize@{Initialize}} \index{Initialize@{Initialize}!mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}} \subsubsection{Initialize()} {\footnotesize\ttfamily void Initialize (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{, }\item[{const size\+\_\+t}]{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Set initial values for the factorization. In this case, we don\textquotesingle{}t need to set anything. Definition at line 52 of file nmf\+\_\+als.\+hpp. \mbox{\label{classmlpack_1_1amf_1_1NMFALSUpdate_aa5b3dd8336182f751ebec27167c22415}} \index{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}} \subsubsection{serialize()} {\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{, }\item[{const unsigned}]{int }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Serialize the object (in this case, there is nothing to serialize). Definition at line 123 of file nmf\+\_\+als.\+hpp. \mbox{\label{classmlpack_1_1amf_1_1NMFALSUpdate_a79b17bfdd69326a4f9f7d17c698ee6af}} \index{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}!W\+Update@{W\+Update}} \index{W\+Update@{W\+Update}!mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update@{mlpack\+::amf\+::\+N\+M\+F\+A\+L\+S\+Update}} \subsubsection{W\+Update()} {\footnotesize\ttfamily static void W\+Update (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{V, }\item[{arma\+::mat \&}]{W, }\item[{const arma\+::mat \&}]{H }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}} The update rule for the basis matrix W. The formula used isa \[ W^T = \frac{H V^T}{H H^T} \] The function takes in all the matrices and only changes the value of the W matrix. \begin{DoxyParams}{Parameters} {\em V} & Input matrix to be factorized. \\ \hline {\em W} & Basis matrix to be updated. \\ \hline {\em H} & Encoding matrix. \\ \hline \end{DoxyParams} Definition at line 72 of file nmf\+\_\+als.\+hpp. The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize} \item /var/www/mlpack.\+ratml.\+org/mlpack.\+org/\+\_\+src/mlpack-\/3.\+3.\+2/src/mlpack/methods/amf/update\+\_\+rules/\textbf{ nmf\+\_\+als.\+hpp}\end{DoxyCompactItemize}