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