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96<h1>AsterixDB Support of Similarity Queries</h1>
97<div class="section">
98<h2><a name="Table_of_Contents"></a><a name="toc" id="toc">Table of Contents</a></h2>
99<ul>
100
101<li><a href="#Motivation">Motivation</a></li>
102<li><a href="#DataTypesAndSimilarityFunctions">Data Types and Similarity Functions</a></li>
103<li><a href="#SimilaritySelectionQueries">Similarity Selection Queries</a></li>
104<li><a href="#SimilarityJoinQueries">Similarity Join Queries</a></li>
105<li><a href="#UsingIndexesToSupportSimilarityQueries">Using Indexes to Support Similarity Queries</a></li>
106</ul></div>
107<div class="section">
108<h2><a name="Motivation_.5BBack_to_TOC.5D"></a><a name="Motivation" id="Motivation">Motivation</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
109<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>
110<div class="section">
111<h2><a name="Data_Types_and_Similarity_Functions_.5BBack_to_TOC.5D"></a><a name="DataTypesAndSimilarityFunctions" id="DataTypesAndSimilarityFunctions">Data Types and Similarity Functions</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
112<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="../sqlpp/primer-sqlpp.html#ADM:_Modeling_Semistructured_Data_in_AsterixDB">TinySocial</a> example, the <tt>friendIds</tt> of a Gleambook 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>
113<p>AsterixDB provides <a href="../sqlpp/builtins.html#Tokenizing_Functions">tokenization functions</a> to convert strings to sets, and the <a href="../sqlpp/builtins.html#Similarity_Functions">similarity functions</a>.</p></div>
114<div class="section">
115<h2><a name="Similarity_Selection_Queries_.5BBack_to_TOC.5D"></a><a name="SimilaritySelectionQueries" id="SimilaritySelectionQueries">Similarity Selection Queries</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
116<p>The following query asks for all the Gleambook users whose name is similar to <tt>Suzanna Tilson</tt>, i.e., their edit distance is at most 2.</p>
117
118<div>
119<div>
120<pre class="source"> use TinySocial;
121
122 select u
123 from GleambookUsers u
124 where edit_distance(u.name, &quot;Suzanna Tilson&quot;) &lt;= 2;
125</pre></div></div>
126
127<p>The following query asks for all the Gleambook 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>
128
129<div>
130<div>
131<pre class="source"> use TinySocial;
132
133 select u
134 from GleambookUsers u
135 where similarity_jaccard(u.friendIds, [1,5,9,10]) &gt;= 0.6f;
136</pre></div></div>
137
138<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>
139
140<div>
141<div>
142<pre class="source"> use TinySocial;
143
144 set simfunction &quot;jaccard&quot;;
145 set simthreshold &quot;0.6f&quot;;
146
147 select u
148 from GleambookUsers u
149 where u.friendIds ~= [1,5,9,10];
150</pre></div></div>
151
152<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>
153<div class="section">
154<h2><a name="Similarity_Join_Queries_.5BBack_to_TOC.5D"></a><a name="SimilarityJoinQueries" id="SimilarityJoinQueries">Similarity Join Queries</a> <font size="4"><a href="#toc">[Back to TOC]</a></font></h2>
155<p>AsterixDB supports fuzzy joins between two sets. The following <a href="../sqlpp/primer-sqlpp.html#Query_5_-_Fuzzy_Join">query</a> finds, for each Gleambook user, all Chirp users with names similar to their name based on the edit distance.</p>
156
157<div>
158<div>
159<pre class="source"> use TinySocial;
160
161 set simfunction &quot;edit-distance&quot;;
162 set simthreshold &quot;3&quot;;
163
164 select gbu.id, gbu.name, (select cu.screenName, cu.name
165 from ChirpUsers cu
166 where cu.name ~= gbu.name) as similar_users
167 from GleambookUsers gbu;
168</pre></div></div>
169</div>
170<div class="section">
171<h2><a name="Using_Indexes_to_Support_Similarity_Queries_.5BBack_to_TOC.5D"></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>
172<p>AsterixDB uses two types of indexes to support similarity queries, namely &#x201c;ngram index&#x201d; and &#x201c;keyword index&#x201d;.</p>
173<div class="section">
174<h3><a name="NGram_Index"></a>NGram Index</h3>
175<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>
176<p>For instance, the following DDL statements create an ngram index on the <tt>GleambookUsers.name</tt> attribute using an inverted index of 3-grams.</p>
177
178<div>
179<div>
180<pre class="source"> use TinySocial;
181
182 create index gbUserIdx on GleambookUsers(name) type ngram(3);
183</pre></div></div>
184
185<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="../sqlpp/builtins.html#edit_distance">edit_distance</a>, <a href="../sqlpp/builtins.html#edit_distance_check">edit_distance_check</a>, <a href="../sqlpp/builtins.html#similarity_jaccard">similarity_jaccard</a>, or <a href="../sqlpp/builtins.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="(../sqlpp/builtins.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>
186<div class="section">
187<h4><a name="NGram_Index_usage_case_-_edit_distance"></a>NGram Index usage case - <a href="../sqlpp/builtins.html#edit-distance">edit_distance</a></h4>
188
189<div>
190<div>
191<pre class="source"> use TinySocial;
192
193 select u
194 from GleambookUsers u
195 where edit_distance(u.name, &quot;Suzanna Tilson&quot;) &lt;= 2;
196</pre></div></div>
197</div>
198<div class="section">
199<h4><a name="NGram_Index_usage_case_-_edit_distance_check"></a>NGram Index usage case - <a href="../sqlpp/builtins.html#edit_distance_check">edit_distance_check</a></h4>
200
201<div>
202<div>
203<pre class="source"> use TinySocial;
204
205 select u
206 from GleambookUsers u
207 where edit_distance_check(u.name, &quot;Suzanna Tilson&quot;, 2)[0];
208</pre></div></div>
209</div>
210<div class="section">
211<h4><a name="NGram_Index_usage_case_-_contains.28.29"></a>NGram Index usage case - <a href="(../sqlpp/builtins.html#contains">contains()</a></h4>
212
213<div>
214<div>
215<pre class="source"> use TinySocial;
216
217 select m
218 from GleambookMessages m
219 where contains(m.message, &quot;phone&quot;);
220</pre></div></div>
221</div></div>
222<div class="section">
223<h3><a name="Keyword_Index"></a>Keyword Index</h3>
224<p>A &#x201c;keyword index&#x201d; is constructed on a set of strings or sets (e.g., array, multiset). 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>
225<div class="section">
226<h4><a name="Keyword_Index_on_String_Type"></a>Keyword Index on String Type</h4>
227
228<div>
229<div>
230<pre class="source"> use TinySocial;
231
232 drop index GleambookMessages.gbMessageIdx if exists;
233 create index gbMessageIdx on GleambookMessages(message) type keyword;
234
235 select m
236 from GleambookMessages m
237 where similarity_jaccard_check(word_tokens(m.message), word_tokens(&quot;love like ccast&quot;), 0.2f)[0];
238</pre></div></div>
239</div>
240<div class="section">
241<h4><a name="Keyword_Index_on_Multiset_Type"></a>Keyword Index on Multiset Type</h4>
242
243<div>
244<div>
245<pre class="source"> use TinySocial;
246
247 create index gbUserIdxFIds on GleambookUsers(friendIds) type keyword;
248
249 select u
250 from GleambookUsers u
251 where similarity_jaccard_check(u.friendIds, {{3,10}}, 0.5f)[0];
252</pre></div></div>
253
254<p>As shown above, keyword index can be used to optimize queries with token-based similarity predicates, including <a href="../sqlpp/builtins.html#similarity_jaccard">similarity_jaccard</a> and <a href="../sqlpp/builtins.html#similarity_jaccard_check">similarity_jaccard_check</a>.</p></div>
255<div class="section">
256<h4><a name="Keyword_Index_usage_case_-_similarity_jaccard"></a>Keyword Index usage case - <a href="../sqlpp/builtins.html#similarity_jaccard">similarity_jaccard</a></h4>
257
258<div>
259<div>
260<pre class="source"> use TinySocial;
261
262 select u
263 from GleambookUsers u
264 where similarity_jaccard(u.friendIds, [1,5,9,10]) &gt;= 0.6f;
265</pre></div></div>
266</div>
267<div class="section">
268<h4><a name="Keyword_Index_usage_case_-_similarity_jaccard_check"></a>Keyword Index usage case - <a href="../sqlpp/builtins.html#similarity_jaccard_check">similarity_jaccard_check</a></h4>
269
270<div>
271<div>
272<pre class="source"> use TinySocial;
273
274 select u
275 from GleambookUsers u
276 where similarity_jaccard_check(u.friendIds, [1,5,9,10], 0.6f)[0];
277</pre></div></div></div></div></div>
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