Jaccard similarity is computed using the following formula:

The library contains both procedures and functions to calculate similarity between sets of data. The function is best used when calculating the similarity between small numbers of sets. The procedures parallelize the computation, and are therefore more appropriate for computing similarities on bigger datasets.

We can use the Jaccard Similarity algorithm to work out the similarity between two things. We might then use the computed similarity as part of a recommendation query. For example, you can use the Jaccard Similarity algorithm to show the products that were purchased by similar customers, in terms of previous products purchased.

The Jaccard similarity function computes the similarity of two lists of numbers.

We can use it to compute the similarity of two hardcoded lists.

The following will return the Jaccard similarity of two lists of numbers: 

RETURN algo.similarity.jaccard([1,2,3], [1,2,4,5]) AS similarity

These two lists of numbers have a Jaccard similarity of 0.4. We can see how this result is derived by breaking down the formula:

J(A,B) = ∣A ∩ B∣ / ∣A∣ + ∣B∣ - ∣A ∩ B|
J(A,B) = 2 / 3 + 4 - 2
       = 2 / 5
       = 0.4

We can also use it to compute the similarity of nodes based on lists computed by a Cypher query.

The following will create a sample graph: 

MERGE (french:Cuisine {name:'French'})
MERGE (italian:Cuisine {name:'Italian'})
MERGE (indian:Cuisine {name:'Indian'})
MERGE (lebanese:Cuisine {name:'Lebanese'})
MERGE (portuguese:Cuisine {name:'Portuguese'})

MERGE (zhen:Person {name: "Zhen"})
MERGE (praveena:Person {name: "Praveena"})
MERGE (michael:Person {name: "Michael"})
MERGE (arya:Person {name: "Arya"})
MERGE (karin:Person {name: "Karin"})

MERGE (praveena)-[:LIKES]->(indian)
MERGE (praveena)-[:LIKES]->(portuguese)

MERGE (zhen)-[:LIKES]->(french)
MERGE (zhen)-[:LIKES]->(indian)

MERGE (michael)-[:LIKES]->(french)
MERGE (michael)-[:LIKES]->(italian)
MERGE (michael)-[:LIKES]->(indian)

MERGE (arya)-[:LIKES]->(lebanese)
MERGE (arya)-[:LIKES]->(italian)
MERGE (arya)-[:LIKES]->(portuguese)

MERGE (karin)-[:LIKES]->(lebanese)
MERGE (karin)-[:LIKES]->(italian)

The following will return the Jaccard similarity of Karin and Arya: 

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

The following will return the Jaccard similarity of Karin and the other people that have a cuisine in common: 

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

The Jaccard Similarity procedure computes similarity between all pairs of items. It is a symmetrical algorithm, which means that the result from computing the similarity of Item A to Item B is the same as computing the similarity of Item B to Item A. We can therefore compute the score for each pair of nodes once. We don’t compute the similarity of items to themselves.

The number of computations is ((# items)^2 / 2) - # items, which can be very computationally expensive if we have a lot of items.

The following will create a sample graph: 

MERGE (french:Cuisine {name:'French'})
MERGE (italian:Cuisine {name:'Italian'})
MERGE (indian:Cuisine {name:'Indian'})
MERGE (lebanese:Cuisine {name:'Lebanese'})
MERGE (portuguese:Cuisine {name:'Portuguese'})

MERGE (zhen:Person {name: "Zhen"})
MERGE (praveena:Person {name: "Praveena"})
MERGE (michael:Person {name: "Michael"})
MERGE (arya:Person {name: "Arya"})
MERGE (karin:Person {name: "Karin"})

MERGE (shrimp:Recipe {title: "Shrimp Bolognese"})
MERGE (saltimbocca:Recipe {title: "Saltimbocca alla roman"})
MERGE (periperi:Recipe {title: "Peri Peri Naan"})

MERGE (praveena)-[:LIKES]->(indian)
MERGE (praveena)-[:LIKES]->(portuguese)

MERGE (zhen)-[:LIKES]->(french)
MERGE (zhen)-[:LIKES]->(indian)

MERGE (michael)-[:LIKES]->(french)
MERGE (michael)-[:LIKES]->(italian)
MERGE (michael)-[:LIKES]->(indian)

MERGE (arya)-[:LIKES]->(lebanese)
MERGE (arya)-[:LIKES]->(italian)
MERGE (arya)-[:LIKES]->(portuguese)

MERGE (karin)-[:LIKES]->(lebanese)
MERGE (karin)-[:LIKES]->(italian)

MERGE (shrimp)-[:TYPE]->(italian)
MERGE (shrimp)-[:TYPE]->(indian)

MERGE (saltimbocca)-[:TYPE]->(italian)
MERGE (saltimbocca)-[:TYPE]->(french)

MERGE (periperi)-[:TYPE]->(portuguese)
MERGE (periperi)-[:TYPE]->(indian)

The following will return a stream of node pairs along with their intersection and Jaccard similarities: 

MATCH (p:Person)-[:LIKES]->(cuisine)
WITH {item:id(p), categories: collect(id(cuisine))} as userData
WITH collect(userData) as data
CALL algo.similarity.jaccard.stream(data)
YIELD item1, item2, count1, count2, intersection, similarity
RETURN algo.asNode(item1).name AS from, algo.asNode(item2).name AS to, intersection, similarity
ORDER BY similarity DESC

Arya and Karin, and Zhen and Michael have the most similar food preferences, with two overlapping cuisines for a similarity of 0.66. We also have 3 pairs of users who are not similar at all. We’d probably want to filter those out, which we can do by passing in the similarityCutoff parameter.

The following will return a stream of node pairs that have a similarity of at least 0.1, along with their intersection and Jaccard similarities: 

MATCH (p:Person)-[:LIKES]->(cuisine)
WITH {item:id(p), categories: collect(id(cuisine))} as userData
WITH collect(userData) as data
CALL algo.similarity.jaccard.stream(data, {similarityCutoff: 0.0})
YIELD item1, item2, count1, count2, intersection, similarity
RETURN algo.asNode(item1).name AS from, algo.asNode(item2).name AS to, intersection, similarity
ORDER BY similarity DESC

We can see that those users with no similarity have been filtered out. If we’re implementing a k-Nearest Neighbors type query we might instead want to find the most similar k users for a given user. We can do that by passing in the topK parameter.

The following will return a stream of users along with the most similar user to them (i.e. k=1): 

MATCH (p:Person)-[:LIKES]->(cuisine)
WITH {item:id(p), categories: collect(id(cuisine))} as userData
WITH collect(userData) as data
CALL algo.similarity.jaccard.stream(data, {topK: 1, similarityCutoff: 0.0})
YIELD item1, item2, count1, count2, intersection, similarity
RETURN algo.asNode(item1).name AS from, algo.asNode(item2).name AS to, similarity
ORDER BY from

These results will not be symmetrical. For example, the person most similar to Praveena is Zhen, but the person most similar to Zhen is actually Michael.

The following will find the most similar user for each user, and store a relationship between those users: 

MATCH (p:Person)-[:LIKES]->(cuisine)
WITH {item:id(p), categories: collect(id(cuisine))} as userData
WITH collect(userData) as data
CALL algo.similarity.jaccard(data, {topK: 1, similarityCutoff: 0.1, write:true})
YIELD nodes, similarityPairs, write, writeRelationshipType, writeProperty, min, max, mean, stdDev, p25, p50, p75, p90, p95, p99, p999, p100
RETURN nodes, similarityPairs, write, writeRelationshipType, writeProperty, min, max, mean, p95

We then could write a query to find out what types of cuisine that other people similar to us might like.

The following will find the most similar user to Praveena, and return their favorite cuisines that Praveena doesn’t (yet!) like: 

MATCH (p:Person {name: "Praveena"})-[:SIMILAR]->(other),
      (other)-[:LIKES]->(cuisine)
WHERE not((p)-[:LIKES]->(cuisine))
RETURN cuisine.name AS cuisine

Sometimes, we don’t want to compute all pairs similarity, but would rather specify subsets of items to compare to each other. We do this using the sourceIds and targetIds keys in the config.

We might want to use this technique when comparing nodes with different labels that intersect on a common label. In our sample dataset, recipes and people both have relationships to cuisines, which means we have a way of computing similarities between recipes and people.

The following will find similarities between recipes and people, based on the cuisines that they have in common: 

// compute categories for recipes
MATCH (recipe:Recipe)-[:TYPE]->(cuisine)
WITH {item:id(recipe), categories: collect(id(cuisine))} as data
WITH collect(data) AS recipeCuisines

// compute categories for people
MATCH (person:Person)-[:LIKES]->(cuisine)
WITH recipeCuisines, {item:id(person), categories: collect(id(cuisine))} as data
WITH recipeCuisines, collect(data) AS personCuisines

// create sourceIds and targetIds lists
WITH recipeCuisines, personCuisines,
     [value in recipeCuisines | value.item] AS sourceIds,
     [value in personCuisines | value.item] AS targetIds

CALL algo.similarity.jaccard.stream(recipeCuisines + personCuisines, {sourceIds: sourceIds, targetIds: targetIds})
YIELD item1, item2, similarity
WITH algo.getNodeById(item1) AS from, algo.getNodeById(item2) AS to, similarity
RETURN from.title AS from, to.name AS to, similarity
ORDER BY similarity DESC
LIMIT 10

The Peri Peri Naan and Praveena have a perfect score of 1.0 because they overlap via Portuguese and Indian cuisines. Michael likes French, Indian, and Italian food, and two of the fusion recipes combine two of those cuisines, giving us a score of 0.66.

We could also use this technique to compute the similarity of a subset of items to all other items.

The following will find the most similar person (i.e. k=1) to Arya and Praveena: 

MATCH (person:Person)-[:LIKES]->(cuisine)
WITH {item:id(person), name: person.name, categories: collect(id(cuisine))} as data
WITH collect(data) AS personCuisines

// create sourceIds list containing ids for Praveena and Arya
WITH personCuisines,
     [value in personCuisines WHERE value.name IN ["Praveena", "Arya"] | value.item ] AS sourceIds

CALL algo.similarity.jaccard.stream(personCuisines, {sourceIds: sourceIds, topK: 1})
YIELD item1, item2, similarity
WITH algo.getNodeById(item1) AS from, algo.getNodeById(item2) AS to, similarity
RETURN from.name AS from, to.name AS to, similarity
ORDER BY similarity DESC

The following will run the algorithm and write back results: 

CALL algo.similarity.jaccard(userData:List<Map>, {
    topK: 1, similarityCutoff: 0.1, write:true, writeProperty: "jaccardSimilarity"
})
YIELD nodes, similarityPairs, write, writeRelationshipType, writeProperty, min, max, mean, stdDev, p25, p50, p75, p90, p95, p99, p999, p100

The following will run the algorithm and stream results: 

CALL algo.similarity.jaccard.stream(userData:List<Map>, {
    degreeCutoff: 10, similarityCutoff: 0.1, concurrency:4
})
YIELD item1, item2, count1, count2, intersection, similarity