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93<h1>AsterixDB Support of Similarity Queries</h1>
94<div class="section">
95<h2><a name="Table_of_Contents"></a><a name="toc" id="toc">Table of Contents</a></h2>
96<ul>
97
98<li><a href="#Motivation">Motivation</a></li>
99<li><a href="#DataTypesAndSimilarityFunctions">Data Types and Similarity Functions</a></li>
100<li><a href="#SimilaritySelectionQueries">Similarity Selection Queries</a></li>
101<li><a href="#SimilarityJoinQueries">Similarity Join Queries</a></li>
102<li><a href="#UsingIndexesToSupportSimilarityQueries">Using Indexes to Support Similarity Queries</a></li>
103</ul></div>
104<div class="section">
105<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>
106<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>
107<div class="section">
108<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>
109<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_Semistructed_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>
110<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>
111<div class="section">
112<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>
113<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>
114
115<div>
116<div>
117<pre class="source"> use TinySocial;
118
119 select u
120 from GleambookUsers u
121 where edit_distance(u.name, &quot;Suzanna Tilson&quot;) &lt;= 2;
122</pre></div></div>
123
124<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>
125
126<div>
127<div>
128<pre class="source"> use TinySocial;
129
130 select u
131 from GleambookUsers u
132 where similarity_jaccard(u.friendIds, [1,5,9,10]) &gt;= 0.6f;
133</pre></div></div>
134
135<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>
136
137<div>
138<div>
139<pre class="source"> use TinySocial;
140
141 set simfunction &quot;jaccard&quot;;
142 set simthreshold &quot;0.6f&quot;;
143
144 select u
145 from GleambookUsers u
146 where u.friendIds ~= [1,5,9,10];
147</pre></div></div>
148
149<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>
150<div class="section">
151<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>
152<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>
153
154<div>
155<div>
156<pre class="source"> use TinySocial;
157
158 set simfunction &quot;edit-distance&quot;;
159 set simthreshold &quot;3&quot;;
160
161 select gbu.id, gbu.name, (select cu.screenName, cu.name
162 from ChirpUsers cu
163 where cu.name ~= gbu.name) as similar_users
164 from GleambookUsers gbu;
165</pre></div></div>
166</div>
167<div class="section">
168<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>
169<p>AsterixDB uses two types of indexes to support similarity queries, namely &#x201c;ngram index&#x201d; and &#x201c;keyword index&#x201d;.</p>
170<div class="section">
171<h3><a name="NGram_Index"></a>NGram Index</h3>
172<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>
173<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>
174
175<div>
176<div>
177<pre class="source"> use TinySocial;
178
179 create index gbUserIdx on GleambookUsers(name) type ngram(3);
180</pre></div></div>
181
182<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>
183<div class="section">
184<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>
185
186<div>
187<div>
188<pre class="source"> use TinySocial;
189
190 select u
191 from GleambookUsers u
192 where edit_distance(u.name, &quot;Suzanna Tilson&quot;) &lt;= 2;
193</pre></div></div>
194</div>
195<div class="section">
196<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>
197
198<div>
199<div>
200<pre class="source"> use TinySocial;
201
202 select u
203 from GleambookUsers u
204 where edit_distance_check(u.name, &quot;Suzanna Tilson&quot;, 2)[0];
205</pre></div></div>
206</div>
207<div class="section">
208<h4><a name="NGram_Index_usage_case_-_contains.28.29"></a>NGram Index usage case - <a href="(../sqlpp/builtins.html#contains">contains()</a></h4>
209
210<div>
211<div>
212<pre class="source"> use TinySocial;
213
214 select m
215 from GleambookMessages m
216 where contains(m.message, &quot;phone&quot;);
217</pre></div></div>
218</div></div>
219<div class="section">
220<h3><a name="Keyword_Index"></a>Keyword Index</h3>
221<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>
222<div class="section">
223<h4><a name="Keyword_Index_on_String_Type"></a>Keyword Index on String Type</h4>
224
225<div>
226<div>
227<pre class="source"> use TinySocial;
228
229 drop index GleambookMessages.gbMessageIdx if exists;
230 create index gbMessageIdx on GleambookMessages(message) type keyword;
231
232 select m
233 from GleambookMessages m
234 where similarity_jaccard_check(word_tokens(m.message), word_tokens(&quot;love like ccast&quot;), 0.2f)[0];
235</pre></div></div>
236</div>
237<div class="section">
238<h4><a name="Keyword_Index_on_Multiset_Type"></a>Keyword Index on Multiset Type</h4>
239
240<div>
241<div>
242<pre class="source"> use TinySocial;
243
244 create index gbUserIdxFIds on GleambookUsers(friendIds) type keyword;
245
246 select u
247 from GleambookUsers u
248 where similarity_jaccard_check(u.friendIds, {{3,10}}, 0.5f)[0];
249</pre></div></div>
250
251<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>
252<div class="section">
253<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>
254
255<div>
256<div>
257<pre class="source"> use TinySocial;
258
259 select u
260 from GleambookUsers u
261 where similarity_jaccard(u.friendIds, [1,5,9,10]) &gt;= 0.6f;
262</pre></div></div>
263</div>
264<div class="section">
265<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>
266
267<div>
268<div>
269<pre class="source"> use TinySocial;
270
271 select u
272 from GleambookUsers u
273 where similarity_jaccard_check(u.friendIds, [1,5,9,10], 0.6f)[0];
274</pre></div></div></div></div></div>
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