Similarity Function Examples

doc/asciidoc/scripts/similarity-cosine.cypher

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

doc/asciidoc/scripts/similarity-euclidean.cypher

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

doc/asciidoc/scripts/similarity-jaccard.cypher

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

doc/asciidoc/scripts/similarity-pearson.cypher

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

doc/asciidoc/similarity-cosine.adoc

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

doc/asciidoc/similarity-euclidean.adoc

@@ -73,6 +73,39 @@ These two lists of numbers have a euclidean distance of 8.42.
 include::scripts/similarity-euclidean.cypher[tag=create-sample-graph]
 ----
 
+.The following will return the Euclidean distance of Zhen and Praveena:
+[source, cypher]
+----
+include::scripts/similarity-euclidean.cypher[tag=function-cypher]
+----
+
+// tag::function-cypher[]
+.Results
+[opts="header"]
+|===
+| `from`       | `to`         | `similarity`
+| "Zhen" | "Praveena" | 6.708203932499369
+
+|===
+// end::function-cypher[]
+
+.The following will return the Euclidean distance  of Zhen and the other people that have a cuisine in common:
+[source, cypher]
+----
+include::scripts/similarity-euclidean.cypher[tag=function-cypher-all]
+----
+
+// tag::function-cypher--all[]
+.Results
+[opts="header"]
+|===
+| `from`       | `to`         | `similarity`
+| "Zhen" | "Praveena" | 6.708203932499369
+| "Zhen" | "Michael"  | 3.605551275463989
+
+|===
+// end::function-cypher-all[]
+
 .The following will return a stream of node pairs, along with their intersection and euclidean similarities:
 [source, cypher]
 ----

doc/asciidoc/similarity-jaccard.adoc

@@ -79,6 +79,41 @@ J(A,B) = 2 / 3 + 4 - 2
 include::scripts/similarity-jaccard.cypher[tag=create-sample-graph]
 ----
 
+.The following will return the Jaccard similarity of Karin and Arya:
+[source, cypher]
+----
+include::scripts/similarity-jaccard.cypher[tag=function-cypher]
+----
+
+// tag::function-cypher[]
+.Results
+[opts="header"]
+|===
+| `from`       | `to`         | `similarity`
+| "Karin" | "Arya" | 0.66
+
+|===
+// end::function-cypher[]
+
+.The following will return the Jaccard similarity of Karin and the other people that have a cuisine in common:
+[source, cypher]
+----
+include::scripts/similarity-jaccard.cypher[tag=function-cypher-all]
+----
+
+// tag::function-cypher--all[]
+.Results
+[opts="header"]
+|===
+| `from`       | `to`         | `similarity`
+| "Karin" | "Arya"     | 0.66
+| "Karin" | "Michael"  | 0.25
+| "Karin" | "Praveena" | 0.0
+| "Karin" | "Zhen"     | 0.0
+
+|===
+// end::function-cypher-all[]
+
 .The following will return a stream of node pairs along with their intersection and Jaccard similarities:
 [source, cypher]
 ----

doc/asciidoc/similarity-pearson.adoc

@@ -66,6 +66,47 @@ include::scripts/similarity-pearson.cypher[tag=function]
 include::scripts/similarity-pearson.cypher[tag=create-sample-graph]
 ----
 
+.The following will return the Pearson similarity of Arya and Karin:
+[source, cypher]
+----
+include::scripts/similarity-pearson.cypher[tag=function-cypher]
+----
+
+// tag::function-cypher[]
+.Results
+[opts="header"]
+|===
+| `from`       | `to`         | `similarity`
+|"Arya" |	"Karin"	 | 0.8194651785206903
+
+|===
+// end::function-cypher[]
+
+
+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.
+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.
+We can't therefore just pass in collections of the ratings of movies that have been reviewed by both people.
+
+.The following will return the Pearson similarity of Arya and other people that have rated at least one movie:
+[source, cypher]
+----
+include::scripts/similarity-pearson.cypher[tag=function-cypher-all]
+----
+
+// tag::function-cypher--all[]
+.Results
+[opts="header"]
+|===
+| `from`       | `to`         | `similarity`
+| "Arya" | "Karin"    | 0.8194651785206903
+| "Arya" | "Zhen"     | 0.4839533792540704
+| "Arya" | "Praveena" | 0.09262336892949784
+| "Arya" | "Michael"  | -0.9551953674747637
+
+|===
+// end::function-cypher-all[]
+
+
 .The following will return a stream of node pairs along with their Pearson similarities:
 [source, cypher]
 ----