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| |
| <p>SQL functions for SVD Matrix Factorization. |
| <a href="#details">More...</a></p> |
| <table class="memberdecls"> |
| <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a> |
| Functions</h2></td></tr> |
| <tr class="memitem:a6cff34415cca23aa0a826cc08a6283f5"><td class="memItemLeft" align="right" valign="top">text </td><td class="memItemRight" valign="bottom"><a class="el" href="svdmf_8sql__in.html#a6cff34415cca23aa0a826cc08a6283f5">svdmf_run</a> (text input_table, text col_name, text row_name, text value, int num_features)</td></tr> |
| <tr class="memdesc:a6cff34415cca23aa0a826cc08a6283f5"><td class="mdescLeft"> </td><td class="mdescRight">Partial SVD decomposition of a sparse matrix into U and V components. <a href="#a6cff34415cca23aa0a826cc08a6283f5">More...</a><br/></td></tr> |
| <tr class="separator:a6cff34415cca23aa0a826cc08a6283f5"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a456119a507138326cdfda4f402de196f"><td class="memItemLeft" align="right" valign="top">text </td><td class="memItemRight" valign="bottom"><a class="el" href="svdmf_8sql__in.html#a456119a507138326cdfda4f402de196f">svdmf_run</a> (text input_table, text col_name, text row_name, text value, int num_features, int num_iterations, float min_error)</td></tr> |
| <tr class="memdesc:a456119a507138326cdfda4f402de196f"><td class="mdescLeft"> </td><td class="mdescRight">Partial SVD decomposition of a sparse matrix into U and V components. <a href="#a456119a507138326cdfda4f402de196f">More...</a><br/></td></tr> |
| <tr class="separator:a456119a507138326cdfda4f402de196f"><td class="memSeparator" colspan="2"> </td></tr> |
| </table> |
| <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2> |
| <div class="textblock"><dl class="section date"><dt>Date</dt><dd>January 2011</dd></dl> |
| <dl class="section see"><dt>See Also</dt><dd>For a brief introduction to <a class="el" href="svd_8sql__in.html#a9ccd79db12f3a1640003c94aa01d6540">SVD</a> Matrix Factorization, see the module description grp_svdmf. </dd></dl> |
| </div><h2 class="groupheader">Function Documentation</h2> |
| <a class="anchor" id="a6cff34415cca23aa0a826cc08a6283f5"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">text svdmf_run </td> |
| <td>(</td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>input_table</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>col_name</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>row_name</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>value</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int </td> |
| <td class="paramname"><em>num_features</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <dl class="section warning"><dt>Warning</dt><dd><em> This is an old implementation of Singular Value Decomposition and has been deprecated. For the latest version of SVD, please see <a class="el" href="group__grp__svd.html">Singular Value Decomposition</a></em></dd></dl> |
| <div class="toc"><b>Contents</b> </p> |
| <ul> |
| <li> |
| <a href="#syntax">SVD Function Syntax</a> </li> |
| <li> |
| <a href="#xamples">Examples</a> </li> |
| <li> |
| <a href="#literature">Literature Related Topics</a> </li> |
| </ul> |
| </div><dl class="section warning"><dt>Warning</dt><dd><em> This is an old implementation of Support Vector Decomposition and has been deprecated. For the latest version of SVD, please see <a class="el" href="group__grp__svd.html">Singular Value Decomposition</a></em></dd></dl> |
| <p>This module implements "partial SVD decomposition" method for representing a sparse matrix using a low-rank approximation. Mathematically, this algorithm seeks to find matrices U and V that, for any given A, minimizes:<br/> |
| </p> |
| <p class="formulaDsp"> |
| \[ ||\boldsymbol A - \boldsymbol UV ||_2 \] |
| </p> |
| <p> subject to \( rank(\boldsymbol UV) \leq k \), where \( ||\cdot||_2 \) denotes the Frobenius norm and \( k \leq rank(\boldsymbol A)\). If A is \( m \times n \), then U will be \( m \times k \) and V will be \( k \times n \).</p> |
| <p>This algorithm is not intended to do the full decomposition, or to be used as part of inverse procedure. It effectively computes the SVD of a low-rank approximation of A (preferably sparse), with the singular values absorbed in U and V. Code is based on the write-up as appears at [1], with some modifications.</p> |
| <p><a class="anchor" id="syntax"></a></p> |
| <dl class="section user"><dt>Function Syntax</dt><dd></dd></dl> |
| <p>The SVD function is called as follows: </p> |
| <pre class="syntax"> |
| svdmf_run( input_table, |
| col_name, |
| row_name, |
| value, num_features) |
| </pre><p>The <b>input matrix</b> is expected to be of the following form: </p> |
| <pre>{TABLE|VIEW} <em>input_table</em> ( |
| <em>col_num</em> INTEGER, |
| <em>row_num</em> INTEGER, |
| <em>value</em> FLOAT |
| )</pre><p>Input is contained in a table where column number and row number for each cell are sequential; that is to say that if the data was written as a matrix, those values would be the actual row and column numbers and not some random identifiers. All rows and columns must be associated with a value. There should not be any missing row, columns or values.</p> |
| <p>The function returns two tables <code>matrix_u</code> and <code>matrix_v</code>, which represent the matrices U and V in table format.</p> |
| <p><a class="anchor" id="examples"></a></p> |
| <dl class="section user"><dt>Examples</dt><dd><ol type="1"> |
| <li>Prepare an input table/view. <pre class="example"> |
| CREATE TABLE svd_test ( col INT, |
| row INT, |
| val FLOAT |
| ); |
| </pre></li> |
| <li>Populate the input table with some data. <pre class="example"> |
| INSERT INTO svd_test SELECT ( g.a%1000)+1, g.a/1000+1, random() |
| FROM generate_series(1,1000) AS g(a); |
| </pre></li> |
| <li><p class="startli">Call the <a class="el" href="svdmf_8sql__in.html#a6cff34415cca23aa0a826cc08a6283f5" title="Partial SVD decomposition of a sparse matrix into U and V components. ">svdmf_run()</a> stored procedure. </p> |
| <pre class="example"> |
| SELECT madlib.svdmf_run( 'svd_test', |
| 'col', |
| 'row', |
| 'val', |
| 3); |
| </pre><p> Example result: </p> |
| <pre class="result"> |
| INFO: ('Started <a class="el" href="svdmf_8sql__in.html#a6cff34415cca23aa0a826cc08a6283f5" title="Partial SVD decomposition of a sparse matrix into U and V components. ">svdmf_run()</a> with parameters:',) |
| INFO: (' * input_matrix = madlib_svdsparse_test.test',) |
| INFO: (' * col_name = col_num',) |
| INFO: (' * row_name = row_num',) |
| INFO: (' * value = val',) |
| INFO: (' * num_features = 3',) |
| INFO: ('Copying the source data into a temporary table...',) |
| INFO: ('Estimating feature: 1',) |
| INFO: ('...Iteration 1: residual_error = 33345014611.1, step_size = 4.9997500125e-10, min_improvement = 1.0',) |
| INFO: ('...Iteration 2: residual_error = 33345014557.6, step_size = 5.49972501375e-10, min_improvement = 1.0',) |
| INFO: ('...Iteration 3: residual_error = 33345014054.3, step_size = 6.04969751512e-10, min_improvement = 1.0',) |
| ... |
| INFO: ('...Iteration 78: residual_error = 2.02512133868, step_size = 5.78105354457e-10, min_improvement = 1.0',) |
| INFO: ('...Iteration 79: residual_error = 0.893810181282, step_size = 6.35915889903e-10, min_improvement = 1.0',) |
| INFO: ('...Iteration 80: residual_error = 0.34496773222, step_size = 6.99507478893e-10, min_improvement = 1.0',) |
| INFO: ('Swapping residual error matrix...',) |
| svdmf_run |
|  -------------------------------------------------------------------------------------------</pre><pre class="result"> Finished SVD matrix factorisation for madlib_svdsparse_test.test (row_num, col_num, val). |
| Results: |
| total error = 0.34496773222 |
| number of estimated features = 1 |
| Output: |
| table : madlib.matrix_u |
| table : madlib.matrix_v |
| Time elapsed: 4 minutes 47.86839 seconds. |
| </pre></li> |
| </ol> |
| </dd></dl> |
| <p><a class="anchor" id="literature"></a></p> |
| <dl class="section user"><dt>Literature</dt><dd></dd></dl> |
| <p>[1] Simon Funk, Netflix Update: Try This at Home, December 11 2006, <a href="http://sifter.org/~simon/journal/20061211.html">http://sifter.org/~simon/journal/20061211.html</a></p> |
| <p><a class="anchor" id="related"></a></p> |
| <dl class="section user"><dt>Related Topics</dt><dd>File <a class="el" href="svdmf_8sql__in.html" title="SQL functions for SVD Matrix Factorization. ">svdmf.sql_in</a> documenting the SQL functions. This function takes as input the table representation of a sparse matrix and decomposes it into the specified set of most significant features of matrices of U and V matrix.</dd></dl> |
| <dl class="params"><dt>Parameters</dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">input_table</td><td>Name of the table/view with the source data </td></tr> |
| <tr><td class="paramname">col_name</td><td>Name of the column containing cell column number </td></tr> |
| <tr><td class="paramname">row_name</td><td>Name of the column containing cell row number </td></tr> |
| <tr><td class="paramname">value</td><td>Name of the column containing cell value </td></tr> |
| <tr><td class="paramname">num_features</td><td>Rank of desired approximation </td></tr> |
| </table> |
| </dd> |
| </dl> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a456119a507138326cdfda4f402de196f"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">text svdmf_run </td> |
| <td>(</td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>input_table</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>col_name</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>row_name</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">text </td> |
| <td class="paramname"><em>value</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int </td> |
| <td class="paramname"><em>num_features</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">int </td> |
| <td class="paramname"><em>num_iterations</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float </td> |
| <td class="paramname"><em>min_error</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <p>This function takes as input the table representation of a sparse matrix and decomposes it into the specified set of most significant features of matrices of U and V matrix.</p> |
| <dl class="params"><dt>Parameters</dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">input_table</td><td>Name of the table/view with the source data </td></tr> |
| <tr><td class="paramname">col_name</td><td>Name of the column containing cell column number </td></tr> |
| <tr><td class="paramname">row_name</td><td>Name of the column containing cell row number </td></tr> |
| <tr><td class="paramname">value</td><td>Name of the column containing cell value </td></tr> |
| <tr><td class="paramname">num_features</td><td>Rank of desired approximation </td></tr> |
| <tr><td class="paramname">num_iterations</td><td>Maximum number if iterations to perform regardless of convergence </td></tr> |
| <tr><td class="paramname">min_error</td><td>Acceptable level of error in convergence. </td></tr> |
| </table> |
| </dd> |
| </dl> |
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