\section{Randomized\+S\+VD Class Reference} \label{classmlpack_1_1svd_1_1RandomizedSVD}\index{Randomized\+S\+VD@{Randomized\+S\+VD}} Randomized S\+VD is a matrix factorization that is based on randomized matrix approximation techniques, developed in in \char`\"{}\+Finding structure with randomness\+: \+Probabilistic algorithms for constructing approximate matrix decompositions\char`\"{}. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ Randomized\+S\+VD} (const arma\+::mat \&data, arma\+::mat \&u, arma\+::vec \&s, arma\+::mat \&v, const size\+\_\+t iterated\+Power=0, const size\+\_\+t max\+Iterations=2, const size\+\_\+t rank=0, const double eps=1e-\/7) \begin{DoxyCompactList}\small\item\em Create object for the randomized S\+VD method. \end{DoxyCompactList}\item \textbf{ Randomized\+S\+VD} (const size\+\_\+t iterated\+Power=0, const size\+\_\+t max\+Iterations=2, const double eps=1e-\/7) \begin{DoxyCompactList}\small\item\em Create object for the randomized S\+VD method. \end{DoxyCompactList}\item void \textbf{ Apply} (const arma\+::sp\+\_\+mat \&data, arma\+::mat \&u, arma\+::vec \&s, arma\+::mat \&v, const size\+\_\+t rank) \begin{DoxyCompactList}\small\item\em Center the data to apply Principal Component Analysis on given sparse matrix dataset using randomized S\+VD. \end{DoxyCompactList}\item void \textbf{ Apply} (const arma\+::mat \&data, arma\+::mat \&u, arma\+::vec \&s, arma\+::mat \&v, const size\+\_\+t rank) \begin{DoxyCompactList}\small\item\em Center the data to apply Principal Component Analysis on given matrix dataset using randomized S\+VD. \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type $>$ }\\void \textbf{ Apply} (const Mat\+Type \&data, arma\+::mat \&u, arma\+::vec \&s, arma\+::mat \&v, const size\+\_\+t rank, Mat\+Type row\+Mean) \begin{DoxyCompactList}\small\item\em Apply Principal Component Analysis to the provided matrix data set using the randomized S\+VD. \end{DoxyCompactList}\item double \textbf{ Epsilon} () const \begin{DoxyCompactList}\small\item\em Get the value used for decomposition stability. \end{DoxyCompactList}\item double \& \textbf{ Epsilon} () \begin{DoxyCompactList}\small\item\em Modify the value used for decomposition stability. \end{DoxyCompactList}\item size\+\_\+t \textbf{ Iterated\+Power} () const \begin{DoxyCompactList}\small\item\em Get the size of the normalized power iterations. \end{DoxyCompactList}\item size\+\_\+t \& \textbf{ Iterated\+Power} () \begin{DoxyCompactList}\small\item\em Modify the size of the normalized power iterations. \end{DoxyCompactList}\item size\+\_\+t \textbf{ Max\+Iterations} () const \begin{DoxyCompactList}\small\item\em Get the number of iterations for the power method. \end{DoxyCompactList}\item size\+\_\+t \& \textbf{ Max\+Iterations} () \begin{DoxyCompactList}\small\item\em Modify the number of iterations for the power method. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} Randomized S\+VD is a matrix factorization that is based on randomized matrix approximation techniques, developed in in \char`\"{}\+Finding structure with randomness\+: \+Probabilistic algorithms for constructing approximate matrix decompositions\char`\"{}. For more information, see the following. \begin{DoxyCode} @article\{Halko2011, author = \{Halko, N. and Martinsson, P. G. and Tropp, J. A.\}, title = \{Finding Structure with Randomness: Probabilistic Algorithms \textcolor{keywordflow}{for} Constructing Approximate Matrix Decompositions\}, journal = \{SIAM Rev.\}, volume = \{53\}, year = \{2011\}, \} \end{DoxyCode} \begin{DoxyCode} @article\{Szlam2014, author = \{Arthur Szlam Yuval Kluger and Mark Tygert\}, title = \{An implementation of a randomized algorithm \textcolor{keywordflow}{for} principal component analysis\}, journal = \{CoRR\}, volume = \{abs/1412.3510\}, year = \{2014\}, \} \end{DoxyCode} An example of how to use the interface is shown below\+: \begin{DoxyCode} arma::mat data; \textcolor{comment}{// Rating data in the form of coordinate list.} \textcolor{keyword}{const} \textcolor{keywordtype}{size\_t} rank = 20; \textcolor{comment}{// Rank used for the decomposition.} \textcolor{comment}{// Make a RandomizedSVD object.} RandomizedSVD rSVD(); arma::mat u, s, v; \textcolor{comment}{// Use the Apply() method to get a factorization.} rSVD.Apply(data, u, s, v, rank); \end{DoxyCode} Definition at line 66 of file randomized\+\_\+svd.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_af70e8f0a731005cb119a615c99057f66}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Randomized\+S\+VD@{Randomized\+S\+VD}} \index{Randomized\+S\+VD@{Randomized\+S\+VD}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Randomized\+S\+V\+D()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily \textbf{ Randomized\+S\+VD} (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{data, }\item[{arma\+::mat \&}]{u, }\item[{arma\+::vec \&}]{s, }\item[{arma\+::mat \&}]{v, }\item[{const size\+\_\+t}]{iterated\+Power = {\ttfamily 0}, }\item[{const size\+\_\+t}]{max\+Iterations = {\ttfamily 2}, }\item[{const size\+\_\+t}]{rank = {\ttfamily 0}, }\item[{const double}]{eps = {\ttfamily 1e-\/7} }\end{DoxyParamCaption})} Create object for the randomized S\+VD method. \begin{DoxyParams}{Parameters} {\em data} & Data matrix. \\ \hline {\em u} & First unitary matrix. \\ \hline {\em v} & Second unitary matrix. \\ \hline {\em sigma} & Diagonal matrix of singular values. \\ \hline {\em iterated\+Power} & Size of the normalized power iterations (Default\+: rank + 2). \\ \hline {\em max\+Iterations} & Number of iterations for the power method (Default\+: 2). \\ \hline {\em rank} & Rank of the approximation (Default\+: number of rows.) \\ \hline {\em eps} & The eps coefficient to avoid division by zero (numerical stability). \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_aade248977ba80c862ec357d2c33f5ddf}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Randomized\+S\+VD@{Randomized\+S\+VD}} \index{Randomized\+S\+VD@{Randomized\+S\+VD}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Randomized\+S\+V\+D()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily \textbf{ Randomized\+S\+VD} (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{iterated\+Power = {\ttfamily 0}, }\item[{const size\+\_\+t}]{max\+Iterations = {\ttfamily 2}, }\item[{const double}]{eps = {\ttfamily 1e-\/7} }\end{DoxyParamCaption})} Create object for the randomized S\+VD method. \begin{DoxyParams}{Parameters} {\em iterated\+Power} & Size of the normalized power iterations (Default\+: rank + 2). \\ \hline {\em max\+Iterations} & Number of iterations for the power method (Default\+: 2). \\ \hline {\em eps} & The eps coefficient to avoid division by zero (numerical stability). \\ \hline \end{DoxyParams} \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_ab1a789d5811597b03ad838edcfab055a}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Apply@{Apply}} \index{Apply@{Apply}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Apply()\hspace{0.1cm}{\footnotesize\ttfamily [1/3]}} {\footnotesize\ttfamily void Apply (\begin{DoxyParamCaption}\item[{const arma\+::sp\+\_\+mat \&}]{data, }\item[{arma\+::mat \&}]{u, }\item[{arma\+::vec \&}]{s, }\item[{arma\+::mat \&}]{v, }\item[{const size\+\_\+t}]{rank }\end{DoxyParamCaption})} Center the data to apply Principal Component Analysis on given sparse matrix dataset using randomized S\+VD. \begin{DoxyParams}{Parameters} {\em data} & Sparse data matrix. \\ \hline {\em u} & First unitary matrix. \\ \hline {\em v} & Second unitary matrix. \\ \hline {\em sigma} & Diagonal matrix of singular values. \\ \hline {\em rank} & Rank of the approximation. \\ \hline \end{DoxyParams} Referenced by Randomized\+S\+V\+D\+Policy\+::\+Apply(). \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_a880f86693b7d486206c2f69ad8d9c59a}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Apply@{Apply}} \index{Apply@{Apply}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Apply()\hspace{0.1cm}{\footnotesize\ttfamily [2/3]}} {\footnotesize\ttfamily void Apply (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{data, }\item[{arma\+::mat \&}]{u, }\item[{arma\+::vec \&}]{s, }\item[{arma\+::mat \&}]{v, }\item[{const size\+\_\+t}]{rank }\end{DoxyParamCaption})} Center the data to apply Principal Component Analysis on given matrix dataset using randomized S\+VD. \begin{DoxyParams}{Parameters} {\em data} & Data matrix. \\ \hline {\em u} & First unitary matrix. \\ \hline {\em v} & Second unitary matrix. \\ \hline {\em sigma} & Diagonal matrix of singular values. \\ \hline {\em rank} & Rank of the approximation. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_adf076c4f0e7c5f7587da9a00f656e5b2}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Apply@{Apply}} \index{Apply@{Apply}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Apply()\hspace{0.1cm}{\footnotesize\ttfamily [3/3]}} {\footnotesize\ttfamily void Apply (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{data, }\item[{arma\+::mat \&}]{u, }\item[{arma\+::vec \&}]{s, }\item[{arma\+::mat \&}]{v, }\item[{const size\+\_\+t}]{rank, }\item[{Mat\+Type}]{row\+Mean }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Apply Principal Component Analysis to the provided matrix data set using the randomized S\+VD. \begin{DoxyParams}{Parameters} {\em data} & Data matrix. \\ \hline {\em u} & First unitary matrix. \\ \hline {\em v} & Second unitary matrix. \\ \hline {\em sigma} & Diagonal matrix of singular values. \\ \hline {\em rank} & Rank of the approximation. \\ \hline {\em row\+Mean} & Centered mean value matrix. \\ \hline \end{DoxyParams} Definition at line 151 of file randomized\+\_\+svd.\+hpp. \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_af6d960193bb5db37e51416e12bf720de}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Epsilon@{Epsilon}} \index{Epsilon@{Epsilon}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Epsilon()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Epsilon (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the value used for decomposition stability. Definition at line 245 of file randomized\+\_\+svd.\+hpp. \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_ab6a080993b32456443eced5df2f8b9b9}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Epsilon@{Epsilon}} \index{Epsilon@{Epsilon}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Epsilon()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double\& Epsilon (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the value used for decomposition stability. Definition at line 247 of file randomized\+\_\+svd.\+hpp. \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_aa8e59edf3732bcceec0a214f9d049488}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Iterated\+Power@{Iterated\+Power}} \index{Iterated\+Power@{Iterated\+Power}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Iterated\+Power()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily size\+\_\+t Iterated\+Power (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the size of the normalized power iterations. Definition at line 235 of file randomized\+\_\+svd.\+hpp. \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_aa06eded3fc0ec2f6bae88acc0395da57}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Iterated\+Power@{Iterated\+Power}} \index{Iterated\+Power@{Iterated\+Power}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Iterated\+Power()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily size\+\_\+t\& Iterated\+Power (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the size of the normalized power iterations. Definition at line 237 of file randomized\+\_\+svd.\+hpp. \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_a420770944a5b0c7a852c4ec372c4a2d1}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Max\+Iterations@{Max\+Iterations}} \index{Max\+Iterations@{Max\+Iterations}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Max\+Iterations()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily size\+\_\+t Max\+Iterations (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the number of iterations for the power method. Definition at line 240 of file randomized\+\_\+svd.\+hpp. \mbox{\label{classmlpack_1_1svd_1_1RandomizedSVD_acda675ab4ab86b95c92bc33bc391a61b}} \index{mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}!Max\+Iterations@{Max\+Iterations}} \index{Max\+Iterations@{Max\+Iterations}!mlpack\+::svd\+::\+Randomized\+S\+VD@{mlpack\+::svd\+::\+Randomized\+S\+VD}} \subsubsection{Max\+Iterations()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily size\+\_\+t\& Max\+Iterations (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the number of iterations for the power method. Definition at line 242 of file randomized\+\_\+svd.\+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.\+1/src/mlpack/methods/randomized\+\_\+svd/\textbf{ randomized\+\_\+svd.\+hpp}\end{DoxyCompactItemize}