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+            <!-- ! Licensed to the Apache Software Foundation (ASF) under one
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+ ! --><h1>AsterixDB Support of Similarity Queries</h1>
+<div class="section">
+<h2><a name="Table_of_Contents"></a><a name="toc" id="toc">Table of Contents</a></h2>
+
+<ul>
+  
+<li><a href="#Motivation">Motivation</a></li>
+  
+<li><a href="#DataTypesAndSimilarityFunctions">Data Types and Similarity Functions</a></li>
+  
+<li><a href="#SimilaritySelectionQueries">Similarity Selection Queries</a></li>
+  
+<li><a href="#SimilarityJoinQueries">Similarity Join Queries</a></li>
+  
+<li><a href="#UsingIndexesToSupportSimilarityQueries">Using Indexes to Support Similarity Queries</a></li>
+</ul></div>
+<div class="section">
+<h2><a name="Motivation_Back_to_TOC"></a><a name="Motivation" id="Motivation">Motivation</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
+<p>Similarity queries are widely used in applications where users need to find objects that satisfy a similarity predicate, while exact matching is not sufficient. These queries are especially important for social and Web applications, where errors, abbreviations, and inconsistencies are common. As an example, we may want to find all the movies starring Schwarzenegger, while we don&#x2019;t know the exact spelling of his last name (despite his popularity in both the movie industry and politics :-)). As another example, we want to find all the Facebook users who have similar friends. To meet this type of needs, AsterixDB supports similarity queries using efficient indexes and algorithms.</p></div>
+<div class="section">
+<h2><a name="Data_Types_and_Similarity_Functions_Back_to_TOC"></a><a name="DataTypesAndSimilarityFunctions" id="DataTypesAndSimilarityFunctions">Data Types and Similarity Functions</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
+<p>AsterixDB supports <a class="externalLink" href="http://en.wikipedia.org/wiki/Levenshtein_distance">edit distance</a> (on strings) and <a class="externalLink" href="http://en.wikipedia.org/wiki/Jaccard_index">Jaccard</a> (on sets). For instance, in our <a href="primer.html#ADM:_Modeling_Semistructed_Data_in_AsterixDB">TinySocial</a> example, the <tt>friend-ids</tt> of a Facebook user forms a set of friends, and we can define a similarity between the sets of friends of two users. We can also convert a string to a set of grams of a length &#x201c;n&#x201d; (called &#x201c;n-grams&#x201d;) and define the Jaccard similarity between the two gram sets of the two strings. Formally, the &#x201c;n-grams&#x201d; of a string are its substrings of length &#x201c;n&#x201d;. For instance, the 3-grams of the string <tt>schwarzenegger</tt> are <tt>sch</tt>, <tt>chw</tt>, <tt>hwa</tt>, &#x2026;, <tt>ger</tt>.</p>
+<p>AsterixDB provides <a href="functions.html#Tokenizing_Functions">tokenization functions</a> to convert strings to sets, and the <a href="functions.html#Similarity_Functions">similarity functions</a>.</p></div>
+<div class="section">
+<h2><a name="Similarity_Selection_Queries_Back_to_TOC"></a><a name="SimilaritySelectionQueries" id="SimilaritySelectionQueries">Similarity Selection Queries</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
+<p>The following query asks for all the Facebook users whose name is similar to <tt>Suzanna Tilson</tt>, i.e., their edit distance is at most 2.</p>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    for $user in dataset('FacebookUsers')
+    let $ed := edit-distance($user.name, &quot;Suzanna Tilson&quot;)
+    where $ed &lt;= 2
+    return $user
+</pre></div></div>
+<p>The following query asks for all the Facebook users whose set of friend ids is similar to <tt>[1,5,9,10]</tt>, i.e., their Jaccard similarity is at least 0.6.</p>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    for $user in dataset('FacebookUsers')
+    let $sim := similarity-jaccard($user.friend-ids, [1,5,9,10])
+    where $sim &gt;= 0.6f
+    return $user
+</pre></div></div>
+<p>AsterixDB allows a user to use a similarity operator <tt>~=</tt> to express a condition by defining the similarity function and threshold using &#x201c;set&#x201d; statements earlier. For instance, the above query can be equivalently written as:</p>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    set simfunction &quot;jaccard&quot;;
+    set simthreshold &quot;0.6f&quot;;
+
+    for $user in dataset('FacebookUsers')
+    where $user.friend-ids ~= [1,5,9,10]
+    return $user
+</pre></div></div>
+<p>In this query, we first declare Jaccard as the similarity function using <tt>simfunction</tt> and then specify the threshold <tt>0.6f</tt> using <tt>simthreshold</tt>.</p></div>
+<div class="section">
+<h2><a name="Similarity_Join_Queries_Back_to_TOC"></a><a name="SimilarityJoinQueries" id="SimilarityJoinQueries">Similarity Join Queries</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
+<p>AsterixDB supports fuzzy joins between two sets. The following <a href="primer.html#Query_5_-_Fuzzy_Join">query</a> finds, for each Facebook user, all Twitter users with names similar to their name based on the edit distance.</p>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    set simfunction &quot;edit-distance&quot;;
+    set simthreshold &quot;3&quot;;
+
+    for $fbu in dataset FacebookUsers
+    return {
+        &quot;id&quot;: $fbu.id,
+        &quot;name&quot;: $fbu.name,
+        &quot;similar-users&quot;: for $t in dataset TweetMessages
+                            let $tu := $t.user
+                            where $tu.name ~= $fbu.name
+                            return {
+                            &quot;twitter-screenname&quot;: $tu.screen-name,
+                            &quot;twitter-name&quot;: $tu.name
+                            }
+    };
+</pre></div></div></div>
+<div class="section">
+<h2><a name="Using_Indexes_to_Support_Similarity_Queries_Back_to_TOC"></a><a name="UsingIndexesToSupportSimilarityQueries" id="UsingIndexesToSupportSimilarityQueries">Using Indexes to Support Similarity Queries</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
+<p>AsterixDB uses two types of indexes to support similarity queries, namely &#x201c;ngram index&#x201d; and &#x201c;keyword index&#x201d;.</p>
+<div class="section">
+<h3><a name="NGram_Index"></a>NGram Index</h3>
+<p>An &#x201c;ngram index&#x201d; is constructed on a set of strings. We generate n-grams for each string, and build an inverted list for each n-gram that includes the ids of the strings with this gram. A similarity query can be answered efficiently by accessing the inverted lists of the grams in the query and counting the number of occurrences of the string ids on these inverted lists. The similar idea can be used to answer queries with Jaccard similarity. A detailed description of these techniques is available at this <a class="externalLink" href="http://www.ics.uci.edu/~chenli/pub/icde2009-memreducer.pdf">paper</a>.</p>
+<p>For instance, the following DDL statements create an ngram index on the <tt>FacebookUsers.name</tt> attribute using an inverted index of 3-grams.</p>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    create index fbUserIdx on FacebookUsers(name) type ngram(3);
+</pre></div></div>
+<p>The number &#x201c;3&#x201d; in &#x201c;ngram(3)&#x201d; is the length &#x201c;n&#x201d; in the grams. This index can be used to optimize similarity queries on this attribute using <a href="functions.html#edit-distance">edit-distance</a>, <a href="functions.html#edit-distance-check">edit-distance-check</a>, <a href="functions.html#similarity-jaccard">similarity-jaccard</a>, or <a href="functions.html#similarity-jaccard-check">similarity-jaccard-check</a> queries on this attribute where the similarity is defined on sets of 3-grams. This index can also be used to optimize queries with the &#x201c;<a href="functions.html#contains">contains()</a>&#x201d; predicate (i.e., substring matching) since it can be also be solved by counting on the inverted lists of the grams in the query string.</p>
+<div class="section">
+<h4><a name="NGram_Index_usage_case_-_edit-distance"></a>NGram Index usage case - <a href="functions.html#edit-distance">edit-distance</a></h4>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    for $user in dataset('FacebookUsers')
+    let $ed := edit-distance($user.name, &quot;Suzanna Tilson&quot;)
+    where $ed &lt;= 2
+    return $user
+</pre></div></div></div>
+<div class="section">
+<h4><a name="NGram_Index_usage_case_-_edit-distance-check"></a>NGram Index usage case - <a href="functions.html#edit-distance-check">edit-distance-check</a></h4>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    for $user in dataset('FacebookUsers')
+    let $ed := edit-distance-check($user.name, &quot;Suzanna Tilson&quot;, 2)
+    where $ed[0]
+    return $ed[1]
+</pre></div></div></div>
+<div class="section">
+<h4><a name="NGram_Index_usage_case_-_similarity-jaccard"></a>NGram Index usage case - <a href="functions.html#similarity-jaccard">similarity-jaccard</a></h4>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    for $user in dataset('FacebookUsers')
+    let $sim := similarity-jaccard($user.friend-ids, [1,5,9,10])
+    where $sim &gt;= 0.6f
+    return $user
+</pre></div></div></div>
+<div class="section">
+<h4><a name="NGram_Index_usage_case_-_similarity-jaccard-check"></a>NGram Index usage case - <a href="functions.html#similarity-jaccard-check">similarity-jaccard-check</a></h4>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    for $user in dataset('FacebookUsers')
+    let $sim := similarity-jaccard-check($user.friend-ids, [1,5,9,10], 0.6f)
+    where $sim[0]
+    return $user
+</pre></div></div></div>
+<div class="section">
+<h4><a name="NGram_Index_usage_case_-_contains"></a>NGram Index usage case - <a href="functions.html#contains">contains()</a></h4>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    for $i in dataset('FacebookMessages')
+    where contains($i.message, &quot;phone&quot;)
+    return {&quot;mid&quot;: $i.message-id, &quot;message&quot;: $i.message}
+</pre></div></div></div></div>
+<div class="section">
+<h3><a name="Keyword_Index"></a>Keyword Index</h3>
+<p>A &#x201c;keyword index&#x201d; is constructed on a set of strings or sets (e.g., OrderedList, UnorderedList). Instead of generating grams as in an ngram index, we generate tokens (e.g., words) and for each token, construct an inverted list that includes the ids of the objects with this token. The following two examples show how to create keyword index on two different types:</p>
+<div class="section">
+<h4><a name="Keyword_Index_on_String_Type"></a>Keyword Index on String Type</h4>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    drop index FacebookMessages.fbMessageIdx if exists;
+    create index fbMessageIdx on FacebookMessages(message) type keyword;
+
+    for $o in dataset('FacebookMessages')
+    let $jacc := similarity-jaccard-check(word-tokens($o.message), word-tokens(&quot;love like ccast&quot;), 0.2f)
+    where $jacc[0]
+    return $o
+</pre></div></div></div>
+<div class="section">
+<h4><a name="Keyword_Index_on_UnorderedList_Type"></a>Keyword Index on UnorderedList Type</h4>
+
+<div class="source">
+<div class="source">
+<pre>    use dataverse TinySocial;
+
+    create index fbUserIdx_fids on FacebookUsers(friend-ids) type keyword;
+
+    for $c in dataset('FacebookUsers')
+    let $jacc := similarity-jaccard-check($c.friend-ids, {{3,10}}, 0.5f)
+    where $jacc[0]
+    return $c
+</pre></div></div>
+<p>As shown above, keyword index can be used to optimize queries with token-based similarity predicates, including <a href="functions.html#similarity-jaccard">similarity-jaccard</a> and <a href="functions.html#similarity-jaccard-check">similarity-jaccard-check</a>.</p></div></div></div>
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