docs/v1.9.1/group__grp__correlation.html - madlib-site - Git at Google

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 <title>MADlib: Pearson&#39;s Correlation</title>
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 <div class="header">
   <div class="headertitle">
 <div class="title">Pearson's Correlation<div class="ingroups"><a class="el" href="group__grp__stats.html">Statistics</a> &raquo; <a class="el" href="group__grp__desc__stats.html">Descriptive Statistics</a></div></div>  </div>
 </div><!--header-->
 <div class="contents">
 <div class="toc"><b>Contents</b> </p><ul>
 <li>
 <a href="#usage">Correlation Function</a> </li>
 <li>
 <a href="#examples">Examples</a> </li>
 <li>
 <a href="#seealso">See Also</a> </li>
 </ul>
 </div><p>A correlation function is the degree and direction of association of two variables&mdash;how well one random variable can be predicted from the other. The coefficient of correlation varies from -1 to 1. A coefficient of 1 implies perfect correlation, 0 means no correlation, and -1 means perfect anti-correlation.</p>
 <p>This function provides a cross-correlation matrix for all pairs of numeric columns in a <em>source_table</em>. A correlation matrix describes correlation among <img class="formulaInl" alt="$ M $" src="form_174.png"/> variables. It is a square symmetrical <img class="formulaInl" alt="$ M $" src="form_174.png"/>x <img class="formulaInl" alt="$M $" src="form_380.png"/> matrix with the <img class="formulaInl" alt="$ (ij) $" src="form_381.png"/>th element equal to the correlation coefficient between the <img class="formulaInl" alt="$i$" src="form_128.png"/>th and the <img class="formulaInl" alt="$j$" src="form_129.png"/>th variable. The diagonal elements (correlations of variables with themselves) are always equal to 1.0.</p>
 <p><a class="anchor" id="usage"></a></p><dl class="section user"><dt>Correlation Function</dt><dd></dd></dl>
 <p>The correlation function has the following syntax: </p><pre class="syntax">
 correlation( source_table,
              output_table,
              target_cols,
              verbose
            )
 </pre><p>The covariance function, with a similar syntax, can be used to compute the covariance between features. </p><pre class="syntax">
 covariance( source_table,
              output_table,
              target_cols,
              verbose
            )
 </pre><dl class="arglist">
 <dt>source_table </dt>
 <dd><p class="startdd">TEXT. The name of the data containing the input data.</p>
 <p class="enddd"></p>
 </dd>
 <dt>output_table </dt>
 <dd><p class="startdd">TEXT. The name of the table where the cross-correlation matrix will be saved. The output is a table with N+2 columns and N rows, where N is the number of target columns. It contains the following columns. </p><table  class="output">
 <tr>
 <th>column_position </th><td>The first column is a sequential counter indicating the position of the variable in the '<em>output_table</em>'.  </td></tr>
 <tr>
 <th>variable </th><td>The second column contains the row-header for the variables.  </td></tr>
 <tr>
 <th>&lt;...&gt; </th><td>The remainder of the table is the NxN correlation matrix for the pairs of numeric 'source_table' columns.  </td></tr>
 </table>
 <p>The output table is arranged as a lower-triangular matrix with the upper triangle set to NULL and the diagonal elements set to 1.0. To obtain the result from the '<em>output_table</em>' in this matrix format ensure to order the elements using the '<em>column_position</em>', as shown in the example below. </p><pre class="example">
 SELECT * FROM output_table ORDER BY column_position;
 </pre><p>In addition to output table, a summary table named &lt;output_table&gt;_summary is also created at the same time, which has the following columns: </p><table  class="output">
 <tr>
 <th>method</th><td>'correlation' </td></tr>
 <tr>
 <th>source_table</th><td>VARCHAR. The data source table name. </td></tr>
 <tr>
 <th>output_table</th><td>VARCHAR. The output table name. </td></tr>
 <tr>
 <th>column_names</th><td>VARCHAR. Column names used for correlation computation, comma-separated string. </td></tr>
 <tr>
 <th>mean_vector</th><td>FLOAT8[]. Vector where each is the mean of a column. </td></tr>
 <tr>
 <th>total_rows_processed </th><td>BIGINT. Total numbers of rows processed.  </td></tr>
 <tr>
 <th>total_rows_skipped </th><td>BIGINT. Total numbers of rows skipped due to missing values.  </td></tr>
 </table>
 <p class="enddd"></p>
 </dd>
 <dt>target_cols (optional) </dt>
 <dd><p class="startdd">TEXT, default: '*'. A comma-separated list of the columns to correlate. If NULL or <code>'*'</code>, results are produced for all numeric columns.</p>
 <p class="enddd"></p>
 </dd>
 <dt>verbose (optional) </dt>
 <dd><p class="startdd">BOOLEAN, default: FALSE. Print verbose debugging information if TRUE.</p>
 <p class="enddd"></p>
 </dd>
 </dl>
 <p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
 <ol type="1">
 <li>View online help for the correlation function. <pre class="example">
 SELECT madlib.correlation();
 </pre></li>
 <li>Create an input data set. <pre class="example">
 DROP TABLE IF EXISTS example_data;
 CREATE TABLE example_data(
     id SERIAL, outlook TEXT,
     temperature FLOAT8, humidity FLOAT8,
     windy TEXT, class TEXT);
 INSERT INTO example_data VALUES
 (1, 'sunny', 85, 85, 'false', 'Dont Play'),
 (2, 'sunny', 80, 90, 'true', 'Dont Play'),
 (3, 'overcast', 83, 78, 'false', 'Play'),
 (4, 'rain', 70, 96, 'false', 'Play'),
 (5, 'rain', 68, 80, 'false', 'Play'),
 (6, 'rain', 65, 70, 'true', 'Dont Play'),
 (7, 'overcast', 64, 65, 'true', 'Play'),
 (8, 'sunny', 72, 95, 'false', 'Dont Play'),
 (9, 'sunny', 69, 70, 'false', 'Play'),
 (10, 'rain', 75, 80, 'false', 'Play'),
 (11, 'sunny', 75, 70, 'true', 'Play'),
 (12, 'overcast', 72, 90, 'true', 'Play'),
 (13, 'overcast', 81, 75, 'false', 'Play'),
 (14, 'rain', 71, 80, 'true', 'Dont Play'),
 (15, NULL, 100, 100, 'true', NULL),
 (16, NULL, 110, 100, 'true', NULL);
 </pre></li>
 <li>Run the <a class="el" href="correlation_8sql__in.html#ada17a10ea8a6c4580e7413c86ae5345e">correlation()</a> function on the data set. <pre class="example">
 -- Correlate all numeric columns
 SELECT madlib.correlation( 'example_data',
                            'example_data_output'
                          );
 -- Setting target_cols to NULL or '*' also correlates all numeric columns
 SELECT madlib.correlation( 'example_data',
                            'example_data_output',
                            '*'
                          );
 -- Correlate only the temperature and humidity columns
 SELECT madlib.correlation( 'example_data',
                            'example_data_output',
                            'temperature, humidity'
                          );
 </pre></li>
 <li>View the correlation matrix. <pre class="example">
 SELECT * FROM example_data_output ORDER BY column_position;
 </pre> Result: <pre class="result">
  column_position |  variable   |    temperature    | humidity
 -----------------+-------------+-------------------+----------
                1 | temperature |               1.0 |
                2 | humidity    | 0.616876934548786 |      1.0
 (2 rows)
 </pre></li>
 <li>Compute the covariance of features in the data set. <pre class="example">
 SELECT madlib.covariance( 'example_data',
                           'cov_output'
                          );
 </pre></li>
 <li>View the covariance matrix. <pre class="example">
 SELECT * FROM cov_output ORDER BY column_position;
 </pre> Result: <pre class="result">
  column_position |  variable   |    temperature    | humidity
 -----------------+-------------+-------------------+----------
                1 | temperature |      146.25       |
                2 | humidity    |      82.125       | 121.1875
 (2 rows)
 </pre></li>
 </ol>
 <dl class="section user"><dt>Notes</dt><dd>Current implementation ignores a row that contains NULL entirely. This means any correlation in such a row (with NULLs) does not contribute to the final answer.</dd></dl>
 <p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl>
 <p>File <a class="el" href="correlation_8sql__in.html" title="SQL functions for correlation computation. ">correlation.sql_in</a> documenting the SQL functions</p>
 <p><a class="el" href="group__grp__summary.html">Summary</a> for general descriptive statistics for a table </p>
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	<div class="header">
	<div class="headertitle">
	<div class="title">Pearson's Correlation<div class="ingroups"><a class="el" href="group__grp__stats.html">Statistics</a> » <a class="el" href="group__grp__desc__stats.html">Descriptive Statistics</a></div></div> </div>
	</div><!--header-->
	<div class="contents">
	<div class="toc"><b>Contents</b> </p><ul>
	<li>
	<a href="#usage">Correlation Function</a> </li>
	<li>
	<a href="#examples">Examples</a> </li>
	<li>
	<a href="#seealso">See Also</a> </li>
	</ul>
	</div><p>A correlation function is the degree and direction of association of two variables—how well one random variable can be predicted from the other. The coefficient of correlation varies from -1 to 1. A coefficient of 1 implies perfect correlation, 0 means no correlation, and -1 means perfect anti-correlation.</p>
	<p>This function provides a cross-correlation matrix for all pairs of numeric columns in a <em>source_table</em>. A correlation matrix describes correlation among <img class="formulaInl" alt="$ M $" src="form_174.png"/> variables. It is a square symmetrical <img class="formulaInl" alt="$ M $" src="form_174.png"/>x <img class="formulaInl" alt="$M $" src="form_380.png"/> matrix with the <img class="formulaInl" alt="$ (ij) $" src="form_381.png"/>th element equal to the correlation coefficient between the <img class="formulaInl" alt="$i$" src="form_128.png"/>th and the <img class="formulaInl" alt="$j$" src="form_129.png"/>th variable. The diagonal elements (correlations of variables with themselves) are always equal to 1.0.</p>
	<p><a class="anchor" id="usage"></a></p><dl class="section user"><dt>Correlation Function</dt><dd></dd></dl>
	<p>The correlation function has the following syntax: </p><pre class="syntax">
	correlation( source_table,
	output_table,
	target_cols,
	verbose
	)
	</pre><p>The covariance function, with a similar syntax, can be used to compute the covariance between features. </p><pre class="syntax">
	covariance( source_table,
	output_table,
	target_cols,
	verbose
	)
	</pre><dl class="arglist">
	<dt>source_table </dt>
	<dd><p class="startdd">TEXT. The name of the data containing the input data.</p>
	<p class="enddd"></p>
	</dd>
	<dt>output_table </dt>
	<dd><p class="startdd">TEXT. The name of the table where the cross-correlation matrix will be saved. The output is a table with N+2 columns and N rows, where N is the number of target columns. It contains the following columns. </p><table class="output">
	<tr>
	<th>column_position </th><td>The first column is a sequential counter indicating the position of the variable in the '<em>output_table</em>'. </td></tr>
	<tr>
	<th>variable </th><td>The second column contains the row-header for the variables. </td></tr>
	<tr>
	<th><...> </th><td>The remainder of the table is the NxN correlation matrix for the pairs of numeric 'source_table' columns. </td></tr>
	</table>
	<p>The output table is arranged as a lower-triangular matrix with the upper triangle set to NULL and the diagonal elements set to 1.0. To obtain the result from the '<em>output_table</em>' in this matrix format ensure to order the elements using the '<em>column_position</em>', as shown in the example below. </p><pre class="example">
	SELECT * FROM output_table ORDER BY column_position;
	</pre><p>In addition to output table, a summary table named <output_table>_summary is also created at the same time, which has the following columns: </p><table class="output">
	<tr>
	<th>method</th><td>'correlation' </td></tr>
	<tr>
	<th>source_table</th><td>VARCHAR. The data source table name. </td></tr>
	<tr>
	<th>output_table</th><td>VARCHAR. The output table name. </td></tr>
	<tr>
	<th>column_names</th><td>VARCHAR. Column names used for correlation computation, comma-separated string. </td></tr>
	<tr>
	<th>mean_vector</th><td>FLOAT8[]. Vector where each is the mean of a column. </td></tr>
	<tr>
	<th>total_rows_processed </th><td>BIGINT. Total numbers of rows processed. </td></tr>
	<tr>
	<th>total_rows_skipped </th><td>BIGINT. Total numbers of rows skipped due to missing values. </td></tr>
	</table>
	<p class="enddd"></p>
	</dd>
	<dt>target_cols (optional) </dt>
	<dd><p class="startdd">TEXT, default: ''. A comma-separated list of the columns to correlate. If NULL or <code>''</code>, results are produced for all numeric columns.</p>
	<p class="enddd"></p>
	</dd>
	<dt>verbose (optional) </dt>
	<dd><p class="startdd">BOOLEAN, default: FALSE. Print verbose debugging information if TRUE.</p>
	<p class="enddd"></p>
	</dd>
	</dl>
	<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
	<ol type="1">
	<li>View online help for the correlation function. <pre class="example">
	SELECT madlib.correlation();
	</pre></li>
	<li>Create an input data set. <pre class="example">
	DROP TABLE IF EXISTS example_data;
	CREATE TABLE example_data(
	id SERIAL, outlook TEXT,
	temperature FLOAT8, humidity FLOAT8,
	windy TEXT, class TEXT);
	INSERT INTO example_data VALUES
	(1, 'sunny', 85, 85, 'false', 'Dont Play'),
	(2, 'sunny', 80, 90, 'true', 'Dont Play'),
	(3, 'overcast', 83, 78, 'false', 'Play'),
	(4, 'rain', 70, 96, 'false', 'Play'),
	(5, 'rain', 68, 80, 'false', 'Play'),
	(6, 'rain', 65, 70, 'true', 'Dont Play'),
	(7, 'overcast', 64, 65, 'true', 'Play'),
	(8, 'sunny', 72, 95, 'false', 'Dont Play'),
	(9, 'sunny', 69, 70, 'false', 'Play'),
	(10, 'rain', 75, 80, 'false', 'Play'),
	(11, 'sunny', 75, 70, 'true', 'Play'),
	(12, 'overcast', 72, 90, 'true', 'Play'),
	(13, 'overcast', 81, 75, 'false', 'Play'),
	(14, 'rain', 71, 80, 'true', 'Dont Play'),
	(15, NULL, 100, 100, 'true', NULL),
	(16, NULL, 110, 100, 'true', NULL);
	</pre></li>
	<li>Run the <a class="el" href="correlation_8sql__in.html#ada17a10ea8a6c4580e7413c86ae5345e">correlation()</a> function on the data set. <pre class="example">
	-- Correlate all numeric columns
	SELECT madlib.correlation( 'example_data',
	'example_data_output'
	);
	-- Setting target_cols to NULL or '*' also correlates all numeric columns
	SELECT madlib.correlation( 'example_data',
	'example_data_output',
	'*'
	);
	-- Correlate only the temperature and humidity columns
	SELECT madlib.correlation( 'example_data',
	'example_data_output',
	'temperature, humidity'
	);
	</pre></li>
	<li>View the correlation matrix. <pre class="example">
	SELECT * FROM example_data_output ORDER BY column_position;
	</pre> Result: <pre class="result">
	column_position \| variable \| temperature \| humidity
	-----------------+-------------+-------------------+----------
	1 \| temperature \| 1.0 \|
	2 \| humidity \| 0.616876934548786 \| 1.0
	(2 rows)
	</pre></li>
	<li>Compute the covariance of features in the data set. <pre class="example">
	SELECT madlib.covariance( 'example_data',
	'cov_output'
	);
	</pre></li>
	<li>View the covariance matrix. <pre class="example">
	SELECT * FROM cov_output ORDER BY column_position;
	</pre> Result: <pre class="result">
	column_position \| variable \| temperature \| humidity
	-----------------+-------------+-------------------+----------
	1 \| temperature \| 146.25 \|
	2 \| humidity \| 82.125 \| 121.1875
	(2 rows)
	</pre></li>
	</ol>
	<dl class="section user"><dt>Notes</dt><dd>Current implementation ignores a row that contains NULL entirely. This means any correlation in such a row (with NULLs) does not contribute to the final answer.</dd></dl>
	<p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl>
	<p>File <a class="el" href="correlation_8sql__in.html" title="SQL functions for correlation computation. ">correlation.sql_in</a> documenting the SQL functions</p>
	<p><a class="el" href="group__grp__summary.html">Summary</a> for general descriptive statistics for a table </p>
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