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+ <!-- ! 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
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+ ! "License"); you may not use this file except in compliance
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+ ! specific language governing permissions and limitations
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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’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 “n” (called
“n-grams”) and define the Jaccard similarity between the two gram
sets of the two strings. Formally, the “n-grams” of a string are
its substrings of length “n”. For instance, the 3-grams of the
string <tt>schwarzenegger</tt> are <tt>sch</tt>, <tt>chw</tt>, <tt>hwa</tt>,
…, <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, "Suzanna Tilson")
+ where $ed <= 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 >= 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
“set” 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 "jaccard";
+ set simthreshold "0.6f";
+
+ 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 "edit-distance";
+ set simthreshold "3";
+
+ for $fbu in dataset FacebookUsers
+ return {
+ "id": $fbu.id,
+ "name": $fbu.name,
+ "similar-users": for $t in dataset TweetMessages
+ let $tu := $t.user
+ where $tu.name ~= $fbu.name
+ return {
+ "twitter-screenname": $tu.screen-name,
+ "twitter-name": $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
“ngram index” and “keyword index”.</p>
+<div class="section">
+<h3><a name="NGram_Index"></a>NGram Index</h3>
+<p>An “ngram index” 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 “3” in “ngram(3)” is the length
“n” 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 “<a
href="functions.html#contains">contains()</a>” 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, "Suzanna Tilson")
+ where $ed <= 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, "Suzanna Tilson", 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 >= 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, "phone")
+ return {"mid": $i.message-id, "message": $i.message}
+</pre></div></div></div></div>
+<div class="section">
+<h3><a name="Keyword_Index"></a>Keyword Index</h3>
+<p>A “keyword index” 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("love like verizon"), 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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