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| |
| <p>Set of functions for k-means clustering. |
| <a href="#details">More...</a></p> |
| |
| <p><a href="kmeans_8sql__in_source.html">Go to the source code of this file.</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:ae8bb21bf12220aa9de82792376afab7d"><td class="memItemLeft" align="right" valign="top">kmeans_result </td><td class="memItemRight" valign="bottom"><a class="el" href="kmeans_8sql__in.html#ae8bb21bf12220aa9de82792376afab7d">kmeans</a> (varchar rel_source, varchar expr_point, float8[][] initial_centroids, varchar fn_dist="squared_dist_norm2", varchar agg_centroid="avg", integer max_num_iterations=20, float8 min_frac_reassigned=0.001)</td></tr> |
| <tr class="memdesc:ae8bb21bf12220aa9de82792376afab7d"><td class="mdescLeft"> </td><td class="mdescRight">Perform Lloyd's k-means local-search heuristic. <a href="#ae8bb21bf12220aa9de82792376afab7d">More...</a><br/></td></tr> |
| <tr class="separator:ae8bb21bf12220aa9de82792376afab7d"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:af0d5172211c83d4de4d70a84555aa68e"><td class="memItemLeft" align="right" valign="top">float8[][] </td><td class="memItemRight" valign="bottom"><a class="el" href="kmeans_8sql__in.html#af0d5172211c83d4de4d70a84555aa68e">kmeanspp_seeding</a> (varchar rel_source, varchar expr_point, integer k, varchar fn_dist="squared_dist_norm2", float8[][] initial_centroids=NULL)</td></tr> |
| <tr class="memdesc:af0d5172211c83d4de4d70a84555aa68e"><td class="mdescLeft"> </td><td class="mdescRight">k-Means++ Seeding <a href="#af0d5172211c83d4de4d70a84555aa68e">More...</a><br/></td></tr> |
| <tr class="separator:af0d5172211c83d4de4d70a84555aa68e"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:ac6c26c8e6b4643acfa79a87bd3ab0fe4"><td class="memItemLeft" align="right" valign="top">kmeans_result </td><td class="memItemRight" valign="bottom"><a class="el" href="kmeans_8sql__in.html#ac6c26c8e6b4643acfa79a87bd3ab0fe4">kmeanspp</a> (varchar rel_source, varchar expr_point, integer k, varchar fn_dist="squared_dist_norm2", varchar agg_centroid="avg", integer max_num_iterations=20, float8 min_frac_reassigned=0.001)</td></tr> |
| <tr class="memdesc:ac6c26c8e6b4643acfa79a87bd3ab0fe4"><td class="mdescLeft"> </td><td class="mdescRight">Run k-Means++. <a href="#ac6c26c8e6b4643acfa79a87bd3ab0fe4">More...</a><br/></td></tr> |
| <tr class="separator:ac6c26c8e6b4643acfa79a87bd3ab0fe4"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a01e02736e6d156240b15f7d6dae092c3"><td class="memItemLeft" align="right" valign="top">float8[][] </td><td class="memItemRight" valign="bottom"><a class="el" href="kmeans_8sql__in.html#a01e02736e6d156240b15f7d6dae092c3">kmeans_random_seeding</a> (varchar rel_source, varchar expr_point, integer k, float8[][] initial_centroids=NULL)</td></tr> |
| <tr class="memdesc:a01e02736e6d156240b15f7d6dae092c3"><td class="mdescLeft"> </td><td class="mdescRight">k-Means Random Seeding <a href="#a01e02736e6d156240b15f7d6dae092c3">More...</a><br/></td></tr> |
| <tr class="separator:a01e02736e6d156240b15f7d6dae092c3"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:aeec5efd06aca50f4830aa10d522dc5ed"><td class="memItemLeft" align="right" valign="top">kmeans_result </td><td class="memItemRight" valign="bottom"><a class="el" href="kmeans_8sql__in.html#aeec5efd06aca50f4830aa10d522dc5ed">kmeans_random</a> (varchar rel_source, varchar expr_point, integer k, varchar fn_dist="squared_dist_norm2", varchar agg_centroid="avg", integer max_num_iterations=20, float8 min_frac_reassigned=0.001)</td></tr> |
| <tr class="memdesc:aeec5efd06aca50f4830aa10d522dc5ed"><td class="mdescLeft"> </td><td class="mdescRight">Run k-Means with random seeding. <a href="#aeec5efd06aca50f4830aa10d522dc5ed">More...</a><br/></td></tr> |
| <tr class="separator:aeec5efd06aca50f4830aa10d522dc5ed"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a6e1a47f006bc0576f56eabcd6903086f"><td class="memItemLeft" align="right" valign="top">kmeans_result </td><td class="memItemRight" valign="bottom"><a class="el" href="kmeans_8sql__in.html#a6e1a47f006bc0576f56eabcd6903086f">kmeans</a> (varchar rel_source, varchar expr_point, varchar rel_initial_centroids, varchar expr_centroid, varchar fn_dist="squared_dist_norm2", varchar agg_centroid="avg", integer max_num_iterations=20, float8 min_frac_reassigned=0.001)</td></tr> |
| <tr class="memdesc:a6e1a47f006bc0576f56eabcd6903086f"><td class="mdescLeft"> </td><td class="mdescRight">Perform Lloyd's k-means local-search heuristic, but with initial centroids stored in a table. <a href="#a6e1a47f006bc0576f56eabcd6903086f">More...</a><br/></td></tr> |
| <tr class="separator:a6e1a47f006bc0576f56eabcd6903086f"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a71e7675758c99acbe7785819b6a85a8f"><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="kmeans_8sql__in.html#a71e7675758c99acbe7785819b6a85a8f">simple_silhouette</a> (varchar rel_source, varchar expr_point, float8[][] centroids, varchar fn_dist="dist_norm2")</td></tr> |
| <tr class="memdesc:a71e7675758c99acbe7785819b6a85a8f"><td class="mdescLeft"> </td><td class="mdescRight">Compute a simplified version of the silhouette coefficient. <a href="#a71e7675758c99acbe7785819b6a85a8f">More...</a><br/></td></tr> |
| <tr class="separator:a71e7675758c99acbe7785819b6a85a8f"><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 see"><dt>See Also</dt><dd>For a brief introduction to k-means clustering, see the module description <a class="el" href="group__grp__kmeans.html">k-Means Clustering</a>. </dd></dl> |
| |
| <p>Definition in file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
| </div><h2 class="groupheader">Function Documentation</h2> |
| <a class="anchor" id="ae8bb21bf12220aa9de82792376afab7d"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">kmeans_result kmeans </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_point</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>initial_centroids</em>[][], </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>fn_dist</em> = <code>"squared_dist_norm2"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>agg_centroid</em> = <code>"avg"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em> = <code>20</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>min_frac_reassigned</em> = <code>0.001</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <dl class="params"><dt>Parameters</dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">rel_source</td><td>Name of the relation containing input points </td></tr> |
| <tr><td class="paramname">expr_point</td><td>Expression evaluating to point coordinates for each tuple </td></tr> |
| <tr><td class="paramname">initial_centroids</td><td>Matrix containing the initial centroids as columns </td></tr> |
| <tr><td class="paramname">fn_dist</td><td>Name of a function with signature <code>DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION</code> that returns the distance between two points. The default is the <a class="el" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668">squared Euclidean distance</a>. </td></tr> |
| <tr><td class="paramname">agg_centroid</td><td>Name of an aggregate function with signature <code>DOUBLE PRECISION[] -> DOUBLE PRECISION[]</code> that, for each group of points, returns a centroid. In order for Lloyd's local-search heuristic to provably converge and to return a local minimum, this centroid should minimize the sum of distances between each point in the group and the centroid. The default is the <a class="el" href="linalg_8sql__in.html#a1aa37f73fb1cd8d7d106aa518dd8c0b4">average (mean/barycenter in Euclidean space)</a>, which satisfies this property if <code>fn_dist = 'squared_dist_norm2'</code>. </td></tr> |
| <tr><td class="paramname">max_num_iterations</td><td>Maximum number of iterations </td></tr> |
| <tr><td class="paramname">min_frac_reassigned</td><td>Fraction of reassigned points below which convergence is assumed and the algorithm terminates </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="section return"><dt>Returns</dt><dd>A composite value:<ul> |
| <li><code>centroids</code> - Matrix with \( k \) centroids as columns.</li> |
| <li><code>frac_reassigned</code> - Fraction of points that were assigned a different centroid in the last iteration.</li> |
| <li><code>num_iterations</code> - The number of iterations before the algorithm terminated </li> |
| </ul> |
| </dd></dl> |
| |
| <p>Definition at line <a class="el" href="kmeans_8sql__in_source.html#l00348">348</a> of file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a6e1a47f006bc0576f56eabcd6903086f"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">kmeans_result kmeans </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_point</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_initial_centroids</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_centroid</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>fn_dist</em> = <code>"squared_dist_norm2"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>agg_centroid</em> = <code>"avg"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em> = <code>20</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>min_frac_reassigned</em> = <code>0.001</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <p>This is a shortcut for running k-means with initial centroids stored in a table (as opposed to an array of centroids). It is equivalent to </p> |
| <pre>SELECT <a class="el" href="kmeans_8sql__in.html#a6e1a47f006bc0576f56eabcd6903086f">kmeans</a>( |
| rel_source, |
| expr_point, |
| (SELECT <a class="el" href="linalg_8sql__in.html#a9c439706f35d6cac89f151d553a5f111">matrix_agg</a>($expr_centroid) FROM $rel_initial_centroids), |
| fn_dist, |
| agg_centroid, |
| max_num_iterations, |
| min_frac_reassigned |
| )</pre><p> where <code>$expr_centroid</code> and <code>$rel_initial_centroids</code> denote textual substituions. </p> |
| |
| <p>Definition at line <a class="el" href="kmeans_8sql__in_source.html#l01093">1093</a> of file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aeec5efd06aca50f4830aa10d522dc5ed"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">kmeans_result kmeans_random </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_point</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>k</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>fn_dist</em> = <code>"squared_dist_norm2"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>agg_centroid</em> = <code>"avg"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em> = <code>20</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>min_frac_reassigned</em> = <code>0.001</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <p>This is a shortcut for running k-means with random seeding. It is equivalent to </p> |
| <pre>SELECT <a class="el" href="kmeans_8sql__in.html#a6e1a47f006bc0576f56eabcd6903086f">kmeans</a>( |
| rel_source, |
| expr_point, |
| <a class="el" href="kmeans_8sql__in.html#a01e02736e6d156240b15f7d6dae092c3">kmeans_random_seeding</a>( |
| rel_source, |
| expr_point, |
| k |
| ), |
| fn_dist, |
| agg_centroid, |
| max_num_iterations, |
| min_frac_reassigned |
| )</pre> |
| <p>Definition at line <a class="el" href="kmeans_8sql__in_source.html#l00910">910</a> of file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a01e02736e6d156240b15f7d6dae092c3"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 [][] kmeans_random_seeding </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_point</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>k</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>initial_centroids</em>[][] = <code>NULL</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <dl class="params"><dt>Parameters</dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">rel_source</td><td>Name of the relation containing input points </td></tr> |
| <tr><td class="paramname">expr_point</td><td>Expression evaluating to point coordinates for each tuple </td></tr> |
| <tr><td class="paramname">k</td><td>Number of centroids </td></tr> |
| <tr><td class="paramname">initial_centroids</td><td>A matrix containing up to \( k \) columns as columns. <a class="el" href="kmeans_8sql__in.html#af0d5172211c83d4de4d70a84555aa68e" title="k-Means++ Seeding ">kmeanspp_seeding()</a> proceeds exactly as if these centroids had already been generated in previous iterations. This parameter may be NULL in which all \( k \) centroids will be generated. </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="section return"><dt>Returns</dt><dd>A matrix containing \( k \) centroids as columns </dd></dl> |
| |
| <p>Definition at line <a class="el" href="kmeans_8sql__in_source.html#l00804">804</a> of file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ac6c26c8e6b4643acfa79a87bd3ab0fe4"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">kmeans_result kmeanspp </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_point</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>k</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>fn_dist</em> = <code>"squared_dist_norm2"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>agg_centroid</em> = <code>"avg"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em> = <code>20</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>min_frac_reassigned</em> = <code>0.001</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <p>This is a shortcut for running k-means++. It is equivalent to </p> |
| <pre>SELECT <a class="el" href="kmeans_8sql__in.html#a6e1a47f006bc0576f56eabcd6903086f">kmeans</a>( |
| rel_source, |
| expr_point, |
| <a class="el" href="kmeans_8sql__in.html#af0d5172211c83d4de4d70a84555aa68e">kmeanspp_seeding</a>( |
| rel_source, |
| expr_point, |
| k, |
| fn_dist |
| ), |
| fn_dist, |
| agg_centroid, |
| max_num_iterations, |
| min_frac_reassigned |
| )</pre> |
| <p>Definition at line <a class="el" href="kmeans_8sql__in_source.html#l00668">668</a> of file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="af0d5172211c83d4de4d70a84555aa68e"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 [][] kmeanspp_seeding </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_point</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>k</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>fn_dist</em> = <code>"squared_dist_norm2"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>initial_centroids</em>[][] = <code>NULL</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <dl class="params"><dt>Parameters</dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">rel_source</td><td>Name of the relation containing input points </td></tr> |
| <tr><td class="paramname">expr_point</td><td>Expression evaluating to point coordinates for each tuple </td></tr> |
| <tr><td class="paramname">k</td><td>Number of centroids </td></tr> |
| <tr><td class="paramname">fn_dist</td><td>Name of a function with signature <code>DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION</code> that returns the distance between two points </td></tr> |
| <tr><td class="paramname">initial_centroids</td><td>A matrix containing up to \( k \) columns as columns. <a class="el" href="kmeans_8sql__in.html#af0d5172211c83d4de4d70a84555aa68e" title="k-Means++ Seeding ">kmeanspp_seeding()</a> proceeds exactly as if these centroids had already been generated in previous iterations. This parameter may be NULL in which all \( k \) centroids will be generated. </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="section return"><dt>Returns</dt><dd>A matrix containing \( k \) centroids as columns </dd></dl> |
| |
| <p>Definition at line <a class="el" href="kmeans_8sql__in_source.html#l00544">544</a> of file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a71e7675758c99acbe7785819b6a85a8f"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 simple_silhouette </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>rel_source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>expr_point</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>centroids</em>[][], </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>fn_dist</em> = <code>"dist_norm2"</code> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <dl class="params"><dt>Parameters</dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">rel_source</td><td>Name of the relation containing input points </td></tr> |
| <tr><td class="paramname">expr_point</td><td>Expression evaluating to point coordinates \( x_i \) for each tuple </td></tr> |
| <tr><td class="paramname">centroids</td><td>Matrix \( M = (\vec{m_0} \dots \vec{m_{k-1}}) \in \mathbb{R}^{d \times k} \) with \( k \) columns, where column \( i \) contains the position of centroid \( i \). </td></tr> |
| <tr><td class="paramname">fn_dist</td><td>Name of a function with signature <code>DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION</code> that returns the distance between two points </td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="section return"><dt>Returns</dt><dd>For each point \( x_i \), let \( d_1( x_i ) \) and \( d_2( x_i ) \) be the distance to the closest and 2nd-closest centroid, respectively. If there is more than one closest centroids then \( d_1( x_i ) = d_2( x_i )\). The return value is the average, over all points \( x_i \), of <p class="formulaDsp"> |
| \[ \frac{d_2( x_i ) - d_1(x_i)}{d_2(x_i)}, \] |
| </p> |
| where 0/0 is interpreted as 0. Clearly, the simplified silhouette coefficient assumes values in \( [0,1] \). </dd></dl> |
| |
| <p>Definition at line <a class="el" href="kmeans_8sql__in_source.html#l01230">1230</a> of file <a class="el" href="kmeans_8sql__in_source.html">kmeans.sql_in</a>.</p> |
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