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Similarity Function Examples (#804)
* explaining how to use pearson function * update result * Add cosine function example * typo * jaccard examples * update jaccard examples * euclidean + better explanatory text on the others * address david's feedback
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‎doc/asciidoc/scripts/similarity-cosine.cypher‎

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@@ -43,6 +43,23 @@ MERGE (karin)-[:LIKES {score: 10}]->(portuguese)
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// end::create-sample-graph[]
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// tag::function-cypher[]
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MATCH (p1:Person {name: 'Michael'})-[likes1:LIKES]->(cuisine)
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MATCH (p2:Person {name: "Arya"})-[likes2:LIKES]->(cuisine)
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.cosine(collect(likes1.score), collect(likes2.score)) AS similarity
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// end::function-cypher[]
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// tag::function-cypher-all[]
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MATCH (p1:Person {name: 'Michael'})-[likes1:LIKES]->(cuisine)
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MATCH (p2:Person)-[likes2:LIKES]->(cuisine) WHERE p2 <> p1
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.cosine(collect(likes1.score), collect(likes2.score)) AS similarity
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ORDER BY similarity DESC
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// end::function-cypher-all[]
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// tag::stream[]
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MATCH (p:Person), (c:Cuisine)
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OPTIONAL MATCH (p)-[likes:LIKES]->(c)

‎doc/asciidoc/scripts/similarity-euclidean.cypher‎

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@@ -9,6 +9,8 @@ MERGE (italian:Cuisine {name:'Italian'})
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MERGE (indian:Cuisine {name:'Indian'})
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MERGE (lebanese:Cuisine {name:'Lebanese'})
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MERGE (portuguese:Cuisine {name:'Portuguese'})
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MERGE (british:Cuisine {name:'British'})
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MERGE (mauritian:Cuisine {name:'Mauritian'})
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MERGE (zhen:Person {name: "Zhen"})
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MERGE (praveena:Person {name: "Praveena"})
@@ -18,23 +20,46 @@ MERGE (karin:Person {name: "Karin"})
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MERGE (praveena)-[:LIKES {score: 9}]->(indian)
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MERGE (praveena)-[:LIKES {score: 7}]->(portuguese)
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MERGE (praveena)-[:LIKES {score: 8}]->(british)
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MERGE (praveena)-[:LIKES {score: 1}]->(mauritian)
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MERGE (zhen)-[:LIKES {score: 10}]->(french)
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MERGE (zhen)-[:LIKES {score: 6}]->(indian)
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MERGE (zhen)-[:LIKES {score: 2}]->(british)
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MERGE (michael)-[:LIKES {score: 8}]->(french)
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MERGE (michael)-[:LIKES {score: 7}]->(italian)
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MERGE (michael)-[:LIKES {score: 9}]->(indian)
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MERGE (michael)-[:LIKES {score: 3}]->(portuguese)
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MERGE (arya)-[:LIKES {score: 10}]->(lebanese)
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MERGE (arya)-[:LIKES {score: 10}]->(italian)
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MERGE (arya)-[:LIKES {score: 7}]->(portuguese)
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MERGE (arya)-[:LIKES {score: 9}]->(mauritian)
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MERGE (karin)-[:LIKES {score: 9}]->(lebanese)
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MERGE (karin)-[:LIKES {score: 7}]->(italian)
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MERGE (karin)-[:LIKES {score: 10}]->(portuguese)
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// end::create-sample-graph[]
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// tag::function-cypher[]
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MATCH (p1:Person {name: 'Zhen'})-[likes1:LIKES]->(cuisine)
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MATCH (p2:Person {name: "Praveena"})-[likes2:LIKES]->(cuisine)
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.euclideanDistance(collect(likes1.score), collect(likes2.score)) AS similarity
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// end::function-cypher[]
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// tag::function-cypher-all[]
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MATCH (p1:Person {name: 'Zhen'})-[likes1:LIKES]->(cuisine)
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MATCH (p2:Person)-[likes2:LIKES]->(cuisine) WHERE p2 <> p1
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.euclideanDistance(collect(likes1.score), collect(likes2.score)) AS similarity
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ORDER BY similarity DESC
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// end::function-cypher-all[]
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// tag::stream[]
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MATCH (p:Person), (c:Cuisine)
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OPTIONAL MATCH (p)-[likes:LIKES]->(c)

‎doc/asciidoc/scripts/similarity-jaccard.cypher‎

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@@ -35,6 +35,28 @@ MERGE (karin)-[:LIKES]->(italian)
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// end::create-sample-graph[]
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// tag::function-cypher[]
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MATCH (p1:Person {name: 'Karin'})-[:LIKES]->(cuisine1)
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WITH p1, collect(id(cuisine1)) AS p1Cuisine
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MATCH (p2:Person {name: "Arya"})-[:LIKES]->(cuisine2)
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WITH p1, p1Cuisine, p2, collect(id(cuisine2)) AS p2Cuisine
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.jaccard(p1Cuisine, p2Cuisine) AS similarity
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// end::function-cypher[]
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// tag::function-cypher-all[]
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MATCH (p1:Person {name: 'Karin'})-[:LIKES]->(cuisine1)
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WITH p1, collect(id(cuisine1)) AS p1Cuisine
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MATCH (p2:Person)-[:LIKES]->(cuisine2) WHERE p1 <> p2
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WITH p1, p1Cuisine, p2, collect(id(cuisine2)) AS p2Cuisine
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.jaccard(p1Cuisine, p2Cuisine) AS similarity
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ORDER BY similarity DESC
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// end::function-cypher-all[]
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// tag::stream[]
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MATCH (p:Person)-[:LIKES]->(cuisine)
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WITH {item:id(p), categories: collect(id(cuisine))} as userData

‎doc/asciidoc/scripts/similarity-pearson.cypher‎

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@@ -45,6 +45,28 @@ MERGE (karin)-[:RATED {score: 9}]->(gruffalo)
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// end::create-sample-graph[]
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// tag::function-cypher[]
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MATCH (p1:Person {name: 'Arya'})-[rated:RATED]->(movie)
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WITH p1, algo.similarity.asVector(movie, rated.score) AS p1Vector
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MATCH (p2:Person {name: 'Karin'})-[rated:RATED]->(movie)
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WITH p1, p2, p1Vector, algo.similarity.asVector(movie, rated.score) AS p2Vector
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.pearson(p1Vector, p2Vector, {vectorType: "maps"}) AS similarity
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// end::function-cypher[]
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// tag::function-cypher-all[]
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MATCH (p1:Person {name: 'Arya'})-[rated:RATED]->(movie)
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WITH p1, algo.similarity.asVector(movie, rated.score) AS p1Vector
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MATCH (p2:Person)-[rated:RATED]->(movie) WHERE p2 <> p1
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WITH p1, p2, p1Vector, algo.similarity.asVector(movie, rated.score) AS p2Vector
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RETURN p1.name AS from,
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p2.name AS to,
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algo.similarity.pearson(p1Vector, p2Vector, {vectorType: "maps"}) AS similarity
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ORDER BY similarity DESC
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// end::function-cypher-all[]
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// tag::stream[]
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MATCH (p:Person), (m:Movie)
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OPTIONAL MATCH (p)-[rated:RATED]->(m)

‎doc/asciidoc/similarity-cosine.adoc‎

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@@ -79,6 +79,41 @@ image::cosine-similarity2.png[role="middle"]
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include::scripts/similarity-cosine.cypher[tag=create-sample-graph]
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----
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.The following will return the Cosine similarity of Michael and Arya:
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[source, cypher]
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----
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include::scripts/similarity-cosine.cypher[tag=function-cypher]
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----
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// tag::function-cypher[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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| "Michael" | "Arya" | 0.9788908326303921
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|===
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// end::function-cypher[]
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.The following will return the Cosine similarity of Michael and the other people that have a cuisine in common:
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[source, cypher]
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----
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include::scripts/similarity-cosine.cypher[tag=function-cypher-all]
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----
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// tag::function-cypher--all[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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| "Michael" | "Arya" | 0.9788908326303921
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| "Michael" | "Zhen" | 0.9542262139256075
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| "Michael" | "Praveena" | 0.9429903335828894
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| "Michael" | "Karin" | 0.8498063272285821
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|===
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// end::function-cypher-all[]
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.The following will return a stream of node pairs along with their Cosine similarities:
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[source, cypher]
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----

‎doc/asciidoc/similarity-euclidean.adoc‎

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include::scripts/similarity-euclidean.cypher[tag=create-sample-graph]
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----
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.The following will return the Euclidean distance of Zhen and Praveena:
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[source, cypher]
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----
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include::scripts/similarity-euclidean.cypher[tag=function-cypher]
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----
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// tag::function-cypher[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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| "Zhen" | "Praveena" | 6.708203932499369
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|===
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// end::function-cypher[]
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.The following will return the Euclidean distance of Zhen and the other people that have a cuisine in common:
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[source, cypher]
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----
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include::scripts/similarity-euclidean.cypher[tag=function-cypher-all]
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----
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// tag::function-cypher--all[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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| "Zhen" | "Praveena" | 6.708203932499369
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| "Zhen" | "Michael" | 3.605551275463989
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|===
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// end::function-cypher-all[]
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.The following will return a stream of node pairs, along with their intersection and euclidean similarities:
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[source, cypher]
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----

‎doc/asciidoc/similarity-jaccard.adoc‎

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include::scripts/similarity-jaccard.cypher[tag=create-sample-graph]
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----
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.The following will return the Jaccard similarity of Karin and Arya:
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[source, cypher]
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----
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include::scripts/similarity-jaccard.cypher[tag=function-cypher]
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----
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// tag::function-cypher[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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| "Karin" | "Arya" | 0.66
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|===
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// end::function-cypher[]
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.The following will return the Jaccard similarity of Karin and the other people that have a cuisine in common:
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[source, cypher]
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----
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include::scripts/similarity-jaccard.cypher[tag=function-cypher-all]
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----
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// tag::function-cypher--all[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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| "Karin" | "Arya" | 0.66
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| "Karin" | "Michael" | 0.25
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| "Karin" | "Praveena" | 0.0
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| "Karin" | "Zhen" | 0.0
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|===
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// end::function-cypher-all[]
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.The following will return a stream of node pairs along with their intersection and Jaccard similarities:
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[source, cypher]
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----

‎doc/asciidoc/similarity-pearson.adoc‎

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include::scripts/similarity-pearson.cypher[tag=create-sample-graph]
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.The following will return the Pearson similarity of Arya and Karin:
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[source, cypher]
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----
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include::scripts/similarity-pearson.cypher[tag=function-cypher]
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----
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// tag::function-cypher[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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|"Arya" | "Karin" | 0.8194651785206903
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|===
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// end::function-cypher[]
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In this example, we pass in `vectorType: "maps"` as an extra parameter, as well as using the `algo.similarity.asVector` function to construct a vector of maps containing each movie and the corresponding rating.
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We do this because the Pearson Similarity algorithm needs to compute the average of *all* the movies that a user has reviewed, not just the ones that they have in common with the user we're comparing them to.
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We can't therefore just pass in collections of the ratings of movies that have been reviewed by both people.
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.The following will return the Pearson similarity of Arya and other people that have rated at least one movie:
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[source, cypher]
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----
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include::scripts/similarity-pearson.cypher[tag=function-cypher-all]
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----
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// tag::function-cypher--all[]
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.Results
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[opts="header"]
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|===
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| `from` | `to` | `similarity`
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| "Arya" | "Karin" | 0.8194651785206903
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| "Arya" | "Zhen" | 0.4839533792540704
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| "Arya" | "Praveena" | 0.09262336892949784
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| "Arya" | "Michael" | -0.9551953674747637
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|===
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// end::function-cypher-all[]
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.The following will return a stream of node pairs along with their Pearson similarities:
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[source, cypher]
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----

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