Repository: incubator-hivemall-site Updated Branches: refs/heads/asf-site fc345a565 -> 542ae788e
Added usage of each_top_k Project: http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/repo Commit: http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/commit/542ae788 Tree: http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/tree/542ae788 Diff: http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/diff/542ae788 Branch: refs/heads/asf-site Commit: 542ae788e2ac292fa54c54462362cbe7dadbb1eb Parents: fc345a5 Author: myui <[email protected]> Authored: Wed Nov 16 17:41:55 2016 +0900 Committer: myui <[email protected]> Committed: Wed Nov 16 17:41:55 2016 +0900 ---------------------------------------------------------------------- userguide/misc/topk.html | 586 ++++++++++++++++++++++++++++++++++++++---- 1 file changed, 529 insertions(+), 57 deletions(-) ---------------------------------------------------------------------- http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/blob/542ae788/userguide/misc/topk.html ---------------------------------------------------------------------- diff --git a/userguide/misc/topk.html b/userguide/misc/topk.html index 6ab13c2..92a9d2f 100644 --- a/userguide/misc/topk.html +++ b/userguide/misc/topk.html @@ -1651,17 +1651,133 @@ --> <p><code>each_top_k(int k, ANY group, double value, arg1, arg2, ..., argN)</code> returns a top-k records for each <code>group</code>. It returns a relation consists of <code>(int rank, double value, arg1, arg2, .., argN)</code>.</p> <p>This function is particularly useful for applying a similarity/distance function where the computation complexity is <strong>O(nm)</strong>.</p> -<p><code>each_top_k</code> is very fast when compared to other methods running top-k queries (e.g., <a href="https://ragrawal.wordpress.com/2011/11/18/extract-top-n-records-in-each-group-in-hadoophive/"; target="_blank"><code>rank/distributed by</code></a>) in Hive.</p> +<p><code>each_top_k</code> is very fast when compared to other methods running top-k queries (e.g., <a href="https://ragrawal.wordpress.com/2011/11/18/extract-top-n-records-in-each-group-in-hadoophive/"; target="_blank"><code>rank/distribute by</code></a>) in Hive.</p> <h2 id="caution">Caution</h2> <ul> <li><code>each_top_k</code> is supported from Hivemall v0.3.2-3 or later.</li> -<li>This UDTF assumes that input records are sorted by <code>group</code>. Use <code>DISTRIBUTED BY group SORTED BY group</code> to ensure that. Or, you can use <code>LEFT OUTER JOIN</code> for certain cases.</li> +<li>This UDTF assumes that input records are sorted by <code>group</code>. Use <code>DISTRIBUTE BY group SORT BY group</code> to ensure that. Or, you can use <code>LEFT OUTER JOIN</code> for certain cases.</li> <li>It takes variable lengths arguments in <code>argN</code>. </li> <li>The third argument <code>value</code> is used for the comparison.</li> <li><code>Any number types</code> or <code>timestamp</code> are accepted for the type of <code>value</code>.</li> <li>If k is less than 0, reverse order is used and <code>tail-K</code> records are returned for each <code>group</code>.</li> <li>Note that this function returns <a href="http://www.michaelpollmeier.com/selecting-top-k-items-from-a-list-efficiently-in-java-groovy/"; target="_blank">a pseudo ranking</a> for top-k. It always returns <code>at-most K</code> records for each group. The ranking scheme is similar to <code>dense_rank</code> but slightly different in certain cases.</li> </ul> +<h1 id="efficient-top-k-query-processing-using-eachtopk">Efficient Top-k Query Processing using <code>each_top_k</code></h1> +<p>Efficient processing of Top-k queries is a crucial requirement in many interactive environments that involve massive amounts of data. +Our Hive extension <code>each_top_k</code> helps running Top-k processing efficiently.</p> +<ul> +<li>Suppose the following table as the input</li> +</ul> +<table> +<thead> +<tr> +<th style="text-align:center">student</th> +<th style="text-align:center">class</th> +<th style="text-align:center">score</th> +</tr> +</thead> +<tbody> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">b</td> +<td style="text-align:center">70</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">a</td> +<td style="text-align:center">80</td> +</tr> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">a</td> +<td style="text-align:center">90</td> +</tr> +<tr> +<td style="text-align:center">4</td> +<td style="text-align:center">b</td> +<td style="text-align:center">50</td> +</tr> +<tr> +<td style="text-align:center">5</td> +<td style="text-align:center">a</td> +<td style="text-align:center">70</td> +</tr> +<tr> +<td style="text-align:center">6</td> +<td style="text-align:center">b</td> +<td style="text-align:center">60</td> +</tr> +</tbody> +</table> +<ul> +<li>Then, list top-2 students for each class</li> +</ul> +<table> +<thead> +<tr> +<th style="text-align:center">student</th> +<th style="text-align:center">class</th> +<th style="text-align:center">score</th> +<th style="text-align:center">rank</th> +</tr> +</thead> +<tbody> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">a</td> +<td style="text-align:center">90</td> +<td style="text-align:center">1</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">a</td> +<td style="text-align:center">80</td> +<td style="text-align:center">2</td> +</tr> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">b</td> +<td style="text-align:center">70</td> +<td style="text-align:center">1</td> +</tr> +<tr> +<td style="text-align:center">6</td> +<td style="text-align:center">b</td> +<td style="text-align:center">60</td> +<td style="text-align:center">2</td> +</tr> +</tbody> +</table> +<p>The standard way using SQL window function would be as follows:</p> +<pre><code class="lang-sql"><span class="hljs-keyword">SELECT</span> + student, <span class="hljs-keyword">class</span>, score, <span class="hljs-keyword">rank</span> +<span class="hljs-keyword">FROM</span> ( + <span class="hljs-keyword">SELECT</span> + student, <span class="hljs-keyword">class</span>, score, + <span class="hljs-keyword">rank</span>() <span class="hljs-keyword">over</span> (<span class="hljs-keyword">PARTITION</span> <span class="hljs-keyword">BY</span> <span class="hljs-keyword">class</span> <span class="hljs-keyword">ORDER</span> <span class="hljs-keyword">BY</span> score <span class="hljs-keyword">DESC</span>) <span class="hljs-keyword">as</span> <span class="hljs-keyword">rank</span> + <span class="hljs-keyword">FROM</span> + <span class="hljs-keyword">table</span> +) t +WHRE <span class="hljs-keyword">rank</span> <= <span class="hljs-number">2</span> +</code></pre> +<p>An alternative and efficient way to compute top-k items using <code>each_top_k</code> is as follows:</p> +<pre><code class="lang-sql"><span class="hljs-keyword">SELECT</span> + each_top_k( + <span class="hljs-number">2</span>, <span class="hljs-keyword">class</span>, score, + <span class="hljs-keyword">class</span>, student <span class="hljs-comment">-- output columns other in addition to rank and score</span> + ) <span class="hljs-keyword">as</span> (<span class="hljs-keyword">rank</span>, score, <span class="hljs-keyword">class</span>, student) +<span class="hljs-keyword">FROM</span> ( + <span class="hljs-keyword">SELECT</span> * <span class="hljs-keyword">FROM</span> <span class="hljs-keyword">table</span> + CLUSTER <span class="hljs-keyword">BY</span> <span class="hljs-keyword">class</span> <span class="hljs-comment">-- Mandatory for `each_top_k`</span> +) t +</code></pre> +<div class="panel panel-primary"><div class="panel-heading"><h3 class="panel-title" id="note"><i class="fa fa-edit"></i> Note</h3></div><div class="panel-body"><p><code>CLUSTER BY x</code> is a synonym of <code>DISTRIBUTE BY x CLASS SORT BY x</code> and required when using <code>each_top_k</code>.</p></div></div> +<p>The function signature of <code>each_top_k</code> is <code>each_top_k(int k, ANY group, double value, arg1, arg2, ..., argN)</code> and it returns a relation <code>(int rank, double value, arg1, arg2, .., argN)</code>.</p> +<p>Any number types or timestamp are accepted for the type of <code>value</code> but it MUST be not NULL. +Do null hanlding like <code>if(value is null, -1, value)</code> to avoid null.</p> +<p>If <code>k</code> is less than 0, reverse order is used and tail-K records are returned for each <code>group</code>.</p> +<p>The ranking semantics of <code>each_top_k</code> follows SQL's <code>dense_rank</code> and then limits results by <code>k</code>. </p> +<div class="panel panel-warning"><div class="panel-heading"><h3 class="panel-title" id="caution"><i class="fa fa-exclamation-triangle"></i> Caution</h3></div><div class="panel-body"><p><code>each_top_k</code> is benefical where the number of grouping keys are large. If the number of grouping keys are not so large (e.g., less than 100), consider using <code>rank() over</code> instead.</p></div></div> <h1 id="usage">Usage</h1> <h2 id="top-k-clicks">top-k clicks</h2> <p><a href="http://stackoverflow.com/questions/9390698/hive-getting-top-n-records-in-group-by-query/32559050#32559050"; target="_blank">http://stackoverflow.com/questions/9390698/hive-getting-top-n-records-in-group-by-query/32559050#32559050</a></p> @@ -1699,33 +1815,202 @@ test_hivemall t2 <span class="hljs-keyword">LEFT</span> <span class="hljs-keyword">OUTER</span> <span class="hljs-keyword">JOIN</span> train_hivemall t1; </code></pre> -<pre><code>1 0.8594650626182556 12 10514 0 -2 0.8585299849510193 12 11719 0 -3 0.856602132320404 12 21009 0 -4 0.8562054634094238 12 17582 0 -5 0.8516314029693604 12 22006 0 -6 0.8499397039413452 12 25364 0 -7 0.8467264771461487 12 900 0 -8 0.8463355302810669 12 8018 0 -9 0.8439178466796875 12 7041 0 -10 0.8438876867294312 12 21595 0 -1 0.8390793800354004 25 21125 0 -2 0.8344510793685913 25 14073 0 -3 0.8340602517127991 25 9008 0 -4 0.8328862190246582 25 6598 0 -5 0.8301891088485718 25 943 0 -6 0.8271955251693726 25 20400 0 -7 0.8255619406700134 25 10922 0 -8 0.8241575956344604 25 8477 0 -9 0.822281539440155 25 25977 0 -10 0.8205751180648804 25 21115 0 -1 0.9761330485343933 34 2513 0 -2 0.9536819458007812 34 8697 0 -3 0.9531533122062683 34 7326 0 -4 0.9493276476860046 34 15173 0 -5 0.9480557441711426 34 19468 0 -... -</code></pre><h3 id="explicit-grouping-using-distribute-by-and-sort-by">Explicit grouping using <code>distribute by</code> and <code>sort by</code></h3> +<table> +<thead> +<tr> +<th style="text-align:center">rank</th> +<th style="text-align:center">similarity</th> +<th style="text-align:center">base_id</th> +<th style="text-align:center">neighbor_id</th> +<th style="text-align:center">y</th> +</tr> +</thead> +<tbody> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">0.8594650626182556</td> +<td style="text-align:center">12</td> +<td style="text-align:center">10514</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">0.8585299849510193</td> +<td style="text-align:center">12</td> +<td style="text-align:center">11719</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">0.856602132320404</td> +<td style="text-align:center">12</td> +<td style="text-align:center">21009</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">4</td> +<td style="text-align:center">0.8562054634094238</td> +<td style="text-align:center">12</td> +<td style="text-align:center">17582</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">5</td> +<td style="text-align:center">0.8516314029693604</td> +<td style="text-align:center">12</td> +<td style="text-align:center">22006</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">6</td> +<td style="text-align:center">0.8499397039413452</td> +<td style="text-align:center">12</td> +<td style="text-align:center">25364</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">7</td> +<td style="text-align:center">0.8467264771461487</td> +<td style="text-align:center">12</td> +<td style="text-align:center">900</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">8</td> +<td style="text-align:center">0.8463355302810669</td> +<td style="text-align:center">12</td> +<td style="text-align:center">8018</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">9</td> +<td style="text-align:center">0.8439178466796875</td> +<td style="text-align:center">12</td> +<td style="text-align:center">7041</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">10</td> +<td style="text-align:center">0.8438876867294312</td> +<td style="text-align:center">12</td> +<td style="text-align:center">21595</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">0.8390793800354004</td> +<td style="text-align:center">25</td> +<td style="text-align:center">21125</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">0.8344510793685913</td> +<td style="text-align:center">25</td> +<td style="text-align:center">14073</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">0.8340602517127991</td> +<td style="text-align:center">25</td> +<td style="text-align:center">9008</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">4</td> +<td style="text-align:center">0.8328862190246582</td> +<td style="text-align:center">25</td> +<td style="text-align:center">6598</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">5</td> +<td style="text-align:center">0.8301891088485718</td> +<td style="text-align:center">25</td> +<td style="text-align:center">943</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">6</td> +<td style="text-align:center">0.8271955251693726</td> +<td style="text-align:center">25</td> +<td style="text-align:center">20400</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">7</td> +<td style="text-align:center">0.8255619406700134</td> +<td style="text-align:center">25</td> +<td style="text-align:center">10922</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">8</td> +<td style="text-align:center">0.8241575956344604</td> +<td style="text-align:center">25</td> +<td style="text-align:center">8477</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">9</td> +<td style="text-align:center">0.822281539440155</td> +<td style="text-align:center">25</td> +<td style="text-align:center">25977</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">10</td> +<td style="text-align:center">0.8205751180648804</td> +<td style="text-align:center">25</td> +<td style="text-align:center">21115</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">0.9761330485343933</td> +<td style="text-align:center">34</td> +<td style="text-align:center">2513</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">0.9536819458007812</td> +<td style="text-align:center">34</td> +<td style="text-align:center">8697</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">0.9531533122062683</td> +<td style="text-align:center">34</td> +<td style="text-align:center">7326</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">4</td> +<td style="text-align:center">0.9493276476860046</td> +<td style="text-align:center">34</td> +<td style="text-align:center">15173</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">5</td> +<td style="text-align:center">0.9480557441711426</td> +<td style="text-align:center">34</td> +<td style="text-align:center">19468</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +</tr> +</tbody> +</table> +<h3 id="explicit-grouping-using-distribute-by-and-sort-by">Explicit grouping using <code>distribute by</code> and <code>sort by</code></h3> <pre><code class="lang-sql"><span class="hljs-keyword">SELECT</span> each_top_k( <span class="hljs-number">10</span>, id1, angular_similarity(features1, features2), @@ -1887,33 +2172,220 @@ s05 <span class="hljs-keyword">as</span> ( <span class="hljs-keyword">LEFT</span> <span class="hljs-keyword">OUTER</span> <span class="hljs-keyword">JOIN</span> train_hivemall t1 <span class="hljs-comment">-- limit 25</span> </code></pre> -<pre><code>1 0.4383084177970886 1 7503 0 -2 0.44166821241378784 1 10143 0 -3 0.4424300789833069 1 11073 0 -4 0.44254064559936523 1 17782 0 -5 0.4442034363746643 1 18556 0 -6 0.45163780450820923 1 3786 0 -7 0.45244503021240234 1 10242 0 -8 0.4525672197341919 1 21657 0 -9 0.4527127146720886 1 17218 0 -10 0.45314133167266846 1 25141 0 -1 0.44030147790908813 2 3786 0 -2 0.4408798813819885 2 23386 0 -3 0.44112563133239746 2 11073 0 -4 0.4415401816368103 2 22853 0 -5 0.4422193765640259 2 21657 0 -6 0.4429032802581787 2 10143 0 -7 0.4435907006263733 2 24413 0 -8 0.44569307565689087 2 7503 0 -9 0.4460843801498413 2 25141 0 -10 0.4464914798736572 2 24289 0 -1 0.43862903118133545 3 23150 1 -2 0.4398220181465149 3 9881 1 -3 0.44283604621887207 3 27121 0 -4 0.4432108402252197 3 26220 1 -5 0.44323229789733887 3 18541 0 -... -</code></pre><p><div id="page-footer"><hr><p><sub><font color="gray"> +<table> +<thead> +<tr> +<th style="text-align:center">rank</th> +<th style="text-align:center">similarity</th> +<th style="text-align:center">base_id</th> +<th style="text-align:center">neighbor_id</th> +<th style="text-align:center">y</th> +</tr> +</thead> +<tbody> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">0.4383084177970886</td> +<td style="text-align:center">1</td> +<td style="text-align:center">7503</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">0.44166821241378784</td> +<td style="text-align:center">1</td> +<td style="text-align:center">10143</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">0.4424300789833069</td> +<td style="text-align:center">1</td> +<td style="text-align:center">11073</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">4</td> +<td style="text-align:center">0.44254064559936523</td> +<td style="text-align:center">1</td> +<td style="text-align:center">17782</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">5</td> +<td style="text-align:center">0.4442034363746643</td> +<td style="text-align:center">1</td> +<td style="text-align:center">18556</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">6</td> +<td style="text-align:center">0.45163780450820923</td> +<td style="text-align:center">1</td> +<td style="text-align:center">3786</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">7</td> +<td style="text-align:center">0.45244503021240234</td> +<td style="text-align:center">1</td> +<td style="text-align:center">10242</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">8</td> +<td style="text-align:center">0.4525672197341919</td> +<td style="text-align:center">1</td> +<td style="text-align:center">21657</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">9</td> +<td style="text-align:center">0.4527127146720886</td> +<td style="text-align:center">1</td> +<td style="text-align:center">17218</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">10</td> +<td style="text-align:center">0.45314133167266846</td> +<td style="text-align:center">1</td> +<td style="text-align:center">25141</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">0.44030147790908813</td> +<td style="text-align:center">2</td> +<td style="text-align:center">3786</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">0.4408798813819885</td> +<td style="text-align:center">2</td> +<td style="text-align:center">23386</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">0.44112563133239746</td> +<td style="text-align:center">2</td> +<td style="text-align:center">11073</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">4</td> +<td style="text-align:center">0.4415401816368103</td> +<td style="text-align:center">2</td> +<td style="text-align:center">22853</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">5</td> +<td style="text-align:center">0.4422193765640259</td> +<td style="text-align:center">2</td> +<td style="text-align:center">21657</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">6</td> +<td style="text-align:center">0.4429032802581787</td> +<td style="text-align:center">2</td> +<td style="text-align:center">10143</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">7</td> +<td style="text-align:center">0.4435907006263733</td> +<td style="text-align:center">2</td> +<td style="text-align:center">24413</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">8</td> +<td style="text-align:center">0.44569307565689087</td> +<td style="text-align:center">2</td> +<td style="text-align:center">7503</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">9</td> +<td style="text-align:center">0.4460843801498413</td> +<td style="text-align:center">2</td> +<td style="text-align:center">25141</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">10</td> +<td style="text-align:center">0.4464914798736572</td> +<td style="text-align:center">2</td> +<td style="text-align:center">24289</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">1</td> +<td style="text-align:center">0.43862903118133545</td> +<td style="text-align:center">3</td> +<td style="text-align:center">23150</td> +<td style="text-align:center">1</td> +</tr> +<tr> +<td style="text-align:center">2</td> +<td style="text-align:center">0.4398220181465149</td> +<td style="text-align:center">3</td> +<td style="text-align:center">9881</td> +<td style="text-align:center">1</td> +</tr> +<tr> +<td style="text-align:center">3</td> +<td style="text-align:center">0.44283604621887207</td> +<td style="text-align:center">3</td> +<td style="text-align:center">27121</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">4</td> +<td style="text-align:center">0.4432108402252197</td> +<td style="text-align:center">3</td> +<td style="text-align:center">26220</td> +<td style="text-align:center">1</td> +</tr> +<tr> +<td style="text-align:center">5</td> +<td style="text-align:center">0.44323229789733887</td> +<td style="text-align:center">3</td> +<td style="text-align:center">18541</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +<td style="text-align:center">..</td> +</tr> +</tbody> +</table> +<p><div id="page-footer"><hr><!-- + Licensed to the Apache Software Foundation (ASF) under one + or more contributor license agreements. See the NOTICE file + distributed with this work for additional information + regarding copyright ownership. The ASF licenses this file + to you under the Apache License, Version 2.0 (the + "License"); you may not use this file except in compliance + with the License. You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, + software distributed under the License is distributed on an + "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + KIND, either express or implied. See the License for the + specific language governing permissions and limitations + under the License. +--> +<p><sub><font color="gray"> Apache Hivemall is an effort undergoing incubation at The Apache Software Foundation (ASF), sponsored by the Apache Incubator. </font></sub></p> </div></p> @@ -1950,7 +2422,7 @@ Apache Hivemall is an effort undergoing incubation at The Apache Software Founda <script> var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Efficient Top-K query processing","level":"2.2","depth":1,"next":{"title":"English/Japanese Text Tokenizer","level":"2.3","depth":1,"path":"misc/tokenizer.md","ref":"misc/tokenizer.md","articles":[]},"previous":{"title":"List of generic Hivemall functions","level":"2.1","depth":1,"path":"misc/generic_funcs.md","ref":"misc/generic_funcs.md","articles":[]},"dir":"ltr"},"config":{"plugins":["theme-api","edit-link","github","splitter","sitemap","etoc","callouts","toggle-chapters","anchorjs","codeblock-filename","expandable-chapters","multipart","codeblock-filename","katex","emphasize","localized-footer"],"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"emphasize":{},"callouts":{},"etoc":{"maxdepth":3,"mindepth":1,"notoc":true},"github":{"url":"https://github.com/apache/incubator-hivemall/"},"splitt er":{},"search":{},"downloadpdf":{"base":"https://github.com/apache/incubator-hivemall/docs/gitbook","label":"PDF","multilingual":false},"multipart":{},"localized-footer":{"filename":"FOOTER.md"},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"katex":{},"fontsettings":{"theme":"white","family":"sans","size":2,"font":"sans"},"highlight":{},"codeblock-filename":{},"sitemap":{"hostname":"http://hivemall.incubator.apache.org/"},"theme-api":{"languages":[],"split":false,"theme":"dark"},"sharing":{"facebook":true,"twitter":true,"google":false,"weibo":false,"instapaper":false,"vk":false,"all":["facebook","google","twitter","weibo","instapaper"]},"edit-link":{"label":"Edit","base":"https://github.com/apache/incubator-hivemall/docs/gitbook"},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":true},"anchorjs":{"selector":"h1,h2,h3, *:not(.callout) > h4,h5"},"toggle-chapters":{},"expandable-chapters":{}},"theme":"default","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56}},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"variables":{},"title":"Hivemall User Manual","links":{"sidebar":{"<i class=\"fa fa-home\"></i> Home":"http://hivemall.incubator.apache.org/"}},"gitbook":"3.x.x","description":"User Manual for Apache Hivemall"},"file":{"path":"misc/topk.md","mtime":"2016-11-12T07:18:00.000Z","type":"markdown"},"gitbook":{"version":"3.2.2","time":"2016-11-14T10:40:22.987Z"},"basePath":"..","book":{"language":""}}); 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