652 lines
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652 lines
35 KiB
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<li class="navelem"><a class="el" href="namespacemlpack.html">mlpack</a></li><li class="navelem"><a class="el" href="namespacemlpack_1_1matrix__completion.html">matrix_completion</a></li><li class="navelem"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html">MatrixCompletion</a></li> </ul>
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<a href="#pub-methods">Public Member Functions</a> |
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<div class="title">mlpack::matrix_completion::MatrixCompletion Class Reference</div> </div>
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<p>This class implements the popular nuclear norm minimization heuristic for matrix completion problems.
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<a href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#details">More...</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
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Public Member Functions</h2></td></tr>
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<tr class="memitem:ac10286ac5d7b8ca5e5dd35a35578ead8"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ac10286ac5d7b8ca5e5dd35a35578ead8">MatrixCompletion</a> (const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ab0177338a3308b55c52ec2972d93eeb1">m</a>, const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ada1f30af3dd744f73ac4e1802c2bfca2">n</a>, const arma::umat &<a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a2966b9f707643aa4775002d6a26af255">indices</a>, const arma::vec &<a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a460786684fa309192016bdfef5d4b1c9">values</a>, const size_t r)</td></tr>
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<tr class="memdesc:ac10286ac5d7b8ca5e5dd35a35578ead8"><td class="mdescLeft"> </td><td class="mdescRight">Construct a matrix completion problem, specifying the maximum rank of the solution. <a href="#ac10286ac5d7b8ca5e5dd35a35578ead8">More...</a><br /></td></tr>
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<tr class="separator:ac10286ac5d7b8ca5e5dd35a35578ead8"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae45afbffa59ab7dffe0416470b891e8c"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ae45afbffa59ab7dffe0416470b891e8c">MatrixCompletion</a> (const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ab0177338a3308b55c52ec2972d93eeb1">m</a>, const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ada1f30af3dd744f73ac4e1802c2bfca2">n</a>, const arma::umat &<a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a2966b9f707643aa4775002d6a26af255">indices</a>, const arma::vec &<a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a460786684fa309192016bdfef5d4b1c9">values</a>, const arma::mat &initialPoint)</td></tr>
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<tr class="memdesc:ae45afbffa59ab7dffe0416470b891e8c"><td class="mdescLeft"> </td><td class="mdescRight">Construct a matrix completion problem, specifying the initial point of the optimization. <a href="#ae45afbffa59ab7dffe0416470b891e8c">More...</a><br /></td></tr>
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<tr class="separator:ae45afbffa59ab7dffe0416470b891e8c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a782331f3bf9dbb03c9e5ccc69e2aa180"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a782331f3bf9dbb03c9e5ccc69e2aa180">MatrixCompletion</a> (const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ab0177338a3308b55c52ec2972d93eeb1">m</a>, const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ada1f30af3dd744f73ac4e1802c2bfca2">n</a>, const arma::umat &<a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a2966b9f707643aa4775002d6a26af255">indices</a>, const arma::vec &<a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a460786684fa309192016bdfef5d4b1c9">values</a>)</td></tr>
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<tr class="memdesc:a782331f3bf9dbb03c9e5ccc69e2aa180"><td class="mdescLeft"> </td><td class="mdescRight">Construct a matrix completion problem. <a href="#a782331f3bf9dbb03c9e5ccc69e2aa180">More...</a><br /></td></tr>
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<tr class="separator:a782331f3bf9dbb03c9e5ccc69e2aa180"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:af486903584214c283bc7354e18ce6fbd"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#af486903584214c283bc7354e18ce6fbd">Recover</a> (arma::mat &recovered)</td></tr>
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<tr class="memdesc:af486903584214c283bc7354e18ce6fbd"><td class="mdescLeft"> </td><td class="mdescRight">Solve the underlying SDP to fill in the remaining values. <a href="#af486903584214c283bc7354e18ce6fbd">More...</a><br /></td></tr>
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<tr class="separator:af486903584214c283bc7354e18ce6fbd"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a6097ff2e54766f26b0e8c33bb7f30a08"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classmlpack_1_1optimization_1_1LRSDP.html">optimization::LRSDP</a>< <a class="el" href="classmlpack_1_1optimization_1_1SDP.html">optimization::SDP</a>< arma::sp_mat > > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a6097ff2e54766f26b0e8c33bb7f30a08">Sdp</a> () const </td></tr>
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<tr class="memdesc:a6097ff2e54766f26b0e8c33bb7f30a08"><td class="mdescLeft"> </td><td class="mdescRight">Return the underlying SDP. <a href="#a6097ff2e54766f26b0e8c33bb7f30a08">More...</a><br /></td></tr>
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<tr class="separator:a6097ff2e54766f26b0e8c33bb7f30a08"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a37e28472f6e6ea283fddd41c35b9d03c"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classmlpack_1_1optimization_1_1LRSDP.html">optimization::LRSDP</a>< <a class="el" href="classmlpack_1_1optimization_1_1SDP.html">optimization::SDP</a>< arma::sp_mat > > & </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a37e28472f6e6ea283fddd41c35b9d03c">Sdp</a> ()</td></tr>
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<tr class="memdesc:a37e28472f6e6ea283fddd41c35b9d03c"><td class="mdescLeft"> </td><td class="mdescRight">Modify the underlying SDP. <a href="#a37e28472f6e6ea283fddd41c35b9d03c">More...</a><br /></td></tr>
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<tr class="separator:a37e28472f6e6ea283fddd41c35b9d03c"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-methods"></a>
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Private Member Functions</h2></td></tr>
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<tr class="memitem:a7b9e4dd2ec9b82afb04787e1cdaa90a2"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a7b9e4dd2ec9b82afb04787e1cdaa90a2">CheckValues</a> ()</td></tr>
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<tr class="memdesc:a7b9e4dd2ec9b82afb04787e1cdaa90a2"><td class="mdescLeft"> </td><td class="mdescRight">Validate the input matrices. <a href="#a7b9e4dd2ec9b82afb04787e1cdaa90a2">More...</a><br /></td></tr>
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<tr class="separator:a7b9e4dd2ec9b82afb04787e1cdaa90a2"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3145e17b0cbbfbb0a158f38ad3d4cbef"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a3145e17b0cbbfbb0a158f38ad3d4cbef">InitSDP</a> ()</td></tr>
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<tr class="memdesc:a3145e17b0cbbfbb0a158f38ad3d4cbef"><td class="mdescLeft"> </td><td class="mdescRight">Initialize the SDP. <a href="#a3145e17b0cbbfbb0a158f38ad3d4cbef">More...</a><br /></td></tr>
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<tr class="separator:a3145e17b0cbbfbb0a158f38ad3d4cbef"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-static-methods"></a>
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Static Private Member Functions</h2></td></tr>
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<tr class="memitem:a1b40157c16060090be5313913ce9a0a1"><td class="memItemLeft" align="right" valign="top">static size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a1b40157c16060090be5313913ce9a0a1">DefaultRank</a> (const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ab0177338a3308b55c52ec2972d93eeb1">m</a>, const size_t <a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ada1f30af3dd744f73ac4e1802c2bfca2">n</a>, const size_t p)</td></tr>
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<tr class="memdesc:a1b40157c16060090be5313913ce9a0a1"><td class="mdescLeft"> </td><td class="mdescRight">Select a rank of the matrix given that is of size m x n and has p known elements. <a href="#a1b40157c16060090be5313913ce9a0a1">More...</a><br /></td></tr>
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<tr class="separator:a1b40157c16060090be5313913ce9a0a1"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
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Private Attributes</h2></td></tr>
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<tr class="memitem:a2966b9f707643aa4775002d6a26af255"><td class="memItemLeft" align="right" valign="top">arma::umat </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a2966b9f707643aa4775002d6a26af255">indices</a></td></tr>
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<tr class="memdesc:a2966b9f707643aa4775002d6a26af255"><td class="mdescLeft"> </td><td class="mdescRight">Matrix containing the indices of the known entries (has two rows). <a href="#a2966b9f707643aa4775002d6a26af255">More...</a><br /></td></tr>
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<tr class="separator:a2966b9f707643aa4775002d6a26af255"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab0177338a3308b55c52ec2972d93eeb1"><td class="memItemLeft" align="right" valign="top">size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ab0177338a3308b55c52ec2972d93eeb1">m</a></td></tr>
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<tr class="memdesc:ab0177338a3308b55c52ec2972d93eeb1"><td class="mdescLeft"> </td><td class="mdescRight">Number of rows in original matrix. <a href="#ab0177338a3308b55c52ec2972d93eeb1">More...</a><br /></td></tr>
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<tr class="separator:ab0177338a3308b55c52ec2972d93eeb1"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ada1f30af3dd744f73ac4e1802c2bfca2"><td class="memItemLeft" align="right" valign="top">size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ada1f30af3dd744f73ac4e1802c2bfca2">n</a></td></tr>
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<tr class="memdesc:ada1f30af3dd744f73ac4e1802c2bfca2"><td class="mdescLeft"> </td><td class="mdescRight">Number of columns in original matrix. <a href="#ada1f30af3dd744f73ac4e1802c2bfca2">More...</a><br /></td></tr>
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<tr class="separator:ada1f30af3dd744f73ac4e1802c2bfca2"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3c30c67a9a103697f1cdbf186639d68c"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classmlpack_1_1optimization_1_1LRSDP.html">optimization::LRSDP</a>< <a class="el" href="classmlpack_1_1optimization_1_1SDP.html">optimization::SDP</a>< arma::sp_mat > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a3c30c67a9a103697f1cdbf186639d68c">sdp</a></td></tr>
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<tr class="memdesc:a3c30c67a9a103697f1cdbf186639d68c"><td class="mdescLeft"> </td><td class="mdescRight">The underlying SDP to be solved. <a href="#a3c30c67a9a103697f1cdbf186639d68c">More...</a><br /></td></tr>
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<tr class="separator:a3c30c67a9a103697f1cdbf186639d68c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a460786684fa309192016bdfef5d4b1c9"><td class="memItemLeft" align="right" valign="top">arma::mat </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a460786684fa309192016bdfef5d4b1c9">values</a></td></tr>
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<tr class="memdesc:a460786684fa309192016bdfef5d4b1c9"><td class="mdescLeft"> </td><td class="mdescRight">Vector containing the values of the known entries. <a href="#a460786684fa309192016bdfef5d4b1c9">More...</a><br /></td></tr>
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<tr class="separator:a460786684fa309192016bdfef5d4b1c9"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>This class implements the popular nuclear norm minimization heuristic for matrix completion problems. </p>
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<p>That is, given known values M_ij's, the following optimization problem (semi-definite program) is solved to fill in the remaining unknown values of X</p>
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<p>min ||X||_* subj to X_ij = M_ij</p>
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<p>where ||X||_* denotes the nuclear norm (sum of singular values of X).</p>
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<p>For a theoretical treatment of the conditions necessary for exact recovery, see the following paper:</p>
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<p>A Simpler Appoarch to Matrix Completion. Benjamin Recht. JMLR 11. <a href="http://arxiv.org/pdf/0910.0651v2.pdf">http://arxiv.org/pdf/0910.0651v2.pdf</a></p>
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<p>An example of how to use this class is shown below:</p>
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<div class="fragment"><div class="line"><span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ab0177338a3308b55c52ec2972d93eeb1">m</a>, <a class="code" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ada1f30af3dd744f73ac4e1802c2bfca2">n</a>; <span class="comment">// size of unknown matrix</span></div><div class="line">arma::umat <a class="code" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a2966b9f707643aa4775002d6a26af255">indices</a>; <span class="comment">// contains the known indices [2 x n_entries]</span></div><div class="line">arma::vec <a class="code" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#a460786684fa309192016bdfef5d4b1c9">values</a>; <span class="comment">// contains the known values [n_entries]</span></div><div class="line">arma::mat recovered; <span class="comment">// will contain the completed matrix</span></div><div class="line"></div><div class="line"><a class="code" href="classmlpack_1_1matrix__completion_1_1MatrixCompletion.html#ac10286ac5d7b8ca5e5dd35a35578ead8">MatrixCompletion</a> mc(m, n, indices, values);</div><div class="line">mc.Recover(recovered);</div></div><!-- fragment --><dl class="section see"><dt>See also</dt><dd>LRSDP </dd></dl>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00053">53</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<td class="memname">mlpack::matrix_completion::MatrixCompletion::MatrixCompletion </td>
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<td>(</td>
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<td class="paramtype">const size_t </td>
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<p>Construct a matrix completion problem, specifying the maximum rank of the solution. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">m</td><td>Number of rows of original matrix. </td></tr>
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<tr><td class="paramname">n</td><td>Number of columns of original matrix. </td></tr>
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<tr><td class="paramname">indices</td><td>Matrix containing the indices of the known entries (must be [2 x p]). </td></tr>
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<tr><td class="paramname">values</td><td>Vector containing the values of the known entries (must be length p). </td></tr>
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<td class="memname">mlpack::matrix_completion::MatrixCompletion::MatrixCompletion </td>
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<p>Construct a matrix completion problem, specifying the initial point of the optimization. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">m</td><td>Number of rows of original matrix. </td></tr>
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<tr><td class="paramname">indices</td><td>Matrix containing the indices of the known entries (must be [2 x p]). </td></tr>
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<p>Construct a matrix completion problem. </p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname">void mlpack::matrix_completion::MatrixCompletion::CheckValues </td>
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<p>Validate the input matrices. </p>
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<p>Select a rank of the matrix given that is of size m x n and has p known elements. </p>
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<td class="memname">void mlpack::matrix_completion::MatrixCompletion::InitSDP </td>
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<p>Initialize the SDP. </p>
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<p>Solve the underlying SDP to fill in the remaining values. </p>
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<td class="memname">const <a class="el" href="classmlpack_1_1optimization_1_1LRSDP.html">optimization::LRSDP</a><<a class="el" href="classmlpack_1_1optimization_1_1SDP.html">optimization::SDP</a><arma::sp_mat> >& mlpack::matrix_completion::MatrixCompletion::Sdp </td>
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<p>Return the underlying SDP. </p>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00115">115</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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<p>References <a class="el" href="matrix__completion_8hpp_source.html#l00130">sdp</a>.</p>
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<td class="memname"><a class="el" href="classmlpack_1_1optimization_1_1LRSDP.html">optimization::LRSDP</a><<a class="el" href="classmlpack_1_1optimization_1_1SDP.html">optimization::SDP</a><arma::sp_mat> >& mlpack::matrix_completion::MatrixCompletion::Sdp </td>
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<p>Modify the underlying SDP. </p>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00117">117</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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<p>References <a class="el" href="matrix__completion_8hpp_source.html#l00130">sdp</a>.</p>
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<h2 class="groupheader">Member Data Documentation</h2>
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<p>Matrix containing the indices of the known entries (has two rows). </p>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00125">125</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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<p>Number of rows in original matrix. </p>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00121">121</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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<p>Number of columns in original matrix. </p>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00123">123</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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<td class="memname"><a class="el" href="classmlpack_1_1optimization_1_1LRSDP.html">optimization::LRSDP</a><<a class="el" href="classmlpack_1_1optimization_1_1SDP.html">optimization::SDP</a><arma::sp_mat> > mlpack::matrix_completion::MatrixCompletion::sdp</td>
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<p>The underlying SDP to be solved. </p>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00130">130</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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<p>Referenced by <a class="el" href="matrix__completion_8hpp_source.html#l00115">Sdp()</a>.</p>
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<td class="memname">arma::mat mlpack::matrix_completion::MatrixCompletion::values</td>
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<p>Vector containing the values of the known entries. </p>
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<p>Definition at line <a class="el" href="matrix__completion_8hpp_source.html#l00127">127</a> of file <a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a>.</p>
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<hr/>The documentation for this class was generated from the following file:<ul>
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<li>src/mlpack/methods/matrix_completion/<a class="el" href="matrix__completion_8hpp_source.html">matrix_completion.hpp</a></li>
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