# Overlap Similarity

This section describes the Overlap Similarity algorithm in the Neo4j Graph Data Science library.

Overlap similarity measures overlap between two sets. It is defined as the size of the intersection of two sets, divided by the size of the smaller of the two sets.

This algorithm is in the alpha tier. For more information on algorithm tiers, see Algorithms.

## 1. History and explanation

Overlap 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.

## 2. Use-cases - when to use the Overlap Similarity algorithm

We can use the Overlap Similarity algorithm to work out which things are subsets of others. We might then use these computed subsets to learn a taxonomy from tagged data, as described by Jesús Barrasa.

## 3. Overlap Similarity algorithm function sample

The following will return the Overlap similarity of two lists of numbers:
``RETURN gds.alpha.similarity.overlap([1,2,3], [1,2,4,5]) AS similarity``
Table 1. Results
`similarity`

0.6666666666666666

These two lists of numbers have an overlap similarity of 0.66. We can see how this result is derived by breaking down the formula:

```O(A,B) = (∣A ∩ B∣) / (min(∣A|,|B|))
O(A,B) = 2 / min(3,4)
= 2 / 3
= 0.66```

## 4. Overlap Similarity algorithm procedures sample

The following will create a sample graph:
``````CREATE
(fahrenheit451:Book {title:'Fahrenheit 451'}),
(dune:Book {title:'Dune'}),
(hungerGames:Book {title:'The Hunger Games'}),
(nineteen84:Book {title:'1984'}),
(gatsby:Book {title:'The Great Gatsby'}),

(scienceFiction:Genre {name: "Science Fiction"}),
(fantasy:Genre {name: "Fantasy"}),
(dystopia:Genre {name: "Dystopia"}),
(classics:Genre {name: "Classics"}),

(fahrenheit451)-[:HAS_GENRE]->(dystopia),
(fahrenheit451)-[:HAS_GENRE]->(scienceFiction),
(fahrenheit451)-[:HAS_GENRE]->(fantasy),
(fahrenheit451)-[:HAS_GENRE]->(classics),

(hungerGames)-[:HAS_GENRE]->(scienceFiction),
(hungerGames)-[:HAS_GENRE]->(fantasy),

(nineteen84)-[:HAS_GENRE]->(scienceFiction),
(nineteen84)-[:HAS_GENRE]->(dystopia),
(nineteen84)-[:HAS_GENRE]->(classics),

(dune)-[:HAS_GENRE]->(scienceFiction),
(dune)-[:HAS_GENRE]->(fantasy),
(dune)-[:HAS_GENRE]->(classics),

(gatsby)-[:HAS_GENRE]->(classics)``````

### 4.1. Stream

The following will return a stream of node pairs, along with their intersection and overlap similarities:
``````MATCH (book:Book)-[:HAS_GENRE]->(genre)
WITH {item:id(genre), categories: collect(id(book))} AS userData
WITH collect(userData) AS data
CALL gds.alpha.similarity.overlap.stream({data: data})
YIELD item1, item2, count1, count2, intersection, similarity
RETURN gds.util.asNode(item1).name AS from, gds.util.asNode(item2).name AS to,
count1, count2, intersection, similarity
ORDER BY similarity DESC``````
Table 2. Results
`from` `to` `count1` `count2` `intersection` `similarity`

Fantasy

Science Fiction

3

4

3

1.0

Dystopia

Science Fiction

2

4

2

1.0

Dystopia

Classics

2

4

2

1.0

Science Fiction

Classics

4

4

3

0.75

Fantasy

Classics

3

4

2

0.66

Dystopia

Fantasy

2

3

1

0.5

Fantasy and Dystopia are both clear subgenres of Science Fiction - 100% of the books that list those as genres also list Science Fiction as a genre. Dystopia is also a subgenre of Classics. The others are less obvious; Dystopia probably isn’t a subgenre of Fantasy, but the other two pairs could be subgenres.

The following will return a stream of node pairs that have a similarity of at least 0.75, along with their intersection and overlap similarities:
``````MATCH (book:Book)-[:HAS_GENRE]->(genre)
WITH {item:id(genre), categories: collect(id(book))} AS userData
WITH collect(userData) AS data
CALL gds.alpha.similarity.overlap.stream({
data: data,
similarityCutoff: 0.75
})
YIELD item1, item2, count1, count2, intersection, similarity
RETURN gds.util.asNode(item1).name AS from, gds.util.asNode(item2).name AS to,
count1, count2, intersection, similarity
ORDER BY similarity DESC``````
Table 3. Results
`from` `to` `count1` `count2` `intersection` `similarity`

Fantasy

Science Fiction

3

4

3

1.0

Dystopia

Classics

2

4

2

1.0

Dystopia

Science Fiction

2

4

2

1.0

Science Fiction

Classics

4

4

3

0.75

We can see that those genres with lower 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` super genres for a given genre. We can do that by passing in the `topK` parameter.

The following will return a stream of genres, along with the two most similar super genres to them (i.e. `k=2`):
``````MATCH (book:Book)-[:HAS_GENRE]->(genre)
WITH {item:id(genre), categories: collect(id(book))} AS userData
WITH collect(userData) AS data
CALL gds.alpha.similarity.overlap.stream({
data: data,
topK: 2
})
YIELD item1, item2, count1, count2, intersection, similarity
RETURN gds.util.asNode(item1).name AS from, gds.util.asNode(item2).name AS to,
count1, count2, intersection, similarity
ORDER BY from``````
Table 4. Results
`from` `to` `count1` `count2` `intersection` `similarity`

Dystopia

Classics

2

4

2

1.0

Dystopia

Science Fiction

2

4

2

1.0

Fantasy

Science Fiction

3

4

3

1.0

Fantasy

Classics

3

4

2

0.6666666666666666

Science Fiction

Classics

4

4

3

0.75

### 4.2. Write

The following will find the most similar genre for each genre, and store a relationship between those genres:
``````MATCH (book:Book)-[:HAS_GENRE]->(genre)
WITH {item:id(genre), categories: collect(id(book))} AS userData
WITH collect(userData) AS data
CALL gds.alpha.similarity.overlap.write({
data: data,
topK: 2,
similarityCutoff: 0.5
})
YIELD nodes, similarityPairs, writeRelationshipType, writeProperty, min, max, mean, stdDev, p25, p50, p75, p90, p95, p99, p999, p100
RETURN nodes, similarityPairs, writeRelationshipType, writeProperty, min, max, mean, p95``````
Table 5. Results
`nodes` `similarityPairs` `writeRelationshipType` `writeProperty` `min` `max` `mean` `p95`

4

5

NARROWER_THAN

score

0.6666641235351562

1.0000038146972656

0.8833351135253906

1.0000038146972656

We then could write a query to find out the genre hierarchy for a specific genre.

The following will find the genre hierarchy for the Fantasy genre
``````MATCH path = (fantasy:Genre {name: "Fantasy"})-[:NARROWER_THAN*]->(genre)
RETURN [node in nodes(path) | node.name] AS hierarchy
ORDER BY length(path)``````
Table 6. Results
`hierarchy`

["Fantasy", "Science Fiction"]

["Fantasy", "Classics"]

["Fantasy", "Science Fiction", "Classics"]

### 4.3. Stats

The following will run the algorithm and returns the result in form of statistical and measurement values
``````MATCH (book:Book)-[:HAS_GENRE]->(genre)
WITH {item:id(genre), categories: collect(id(book))} AS userData
WITH collect(userData) AS data
CALL gds.alpha.similarity.overlap.stats({
data: data,
topK: 2,
similarityCutoff: 0.5
})
YIELD nodes, similarityPairs, writeRelationshipType, writeProperty, min, max, mean, p95
RETURN nodes, similarityPairs, writeRelationshipType, writeProperty, min, max, mean, p95``````

## 5. Specifying source and target ids

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

The following will return the super genres for the `Fantasy` and `Classics` genres:
``````MATCH (book:Book)-[:HAS_GENRE]->(genre)
WITH {item:id(genre), name: genre.name, categories: collect(id(book))} AS userData
WITH collect(userData) AS data
WITH data,
[value in data WHERE value.name IN ["Fantasy", "Classics"] | value.item ] AS sourceIds
CALL gds.alpha.similarity.overlap.stream({
data: data,
sourceIds: sourceIds
})
YIELD item1, item2, count1, count2, intersection, similarity
RETURN gds.util.asNode(item1).name AS from, gds.util.asNode(item2).name AS to, similarity
ORDER BY similarity DESC``````
Table 7. Results
`from` `to` `similarity`

Fantasy

Science Fiction

1.0

Classics

Science Fiction

0.75

Fantasy

Classics

0.6666666666666666

## 6. Syntax

The following will run the algorithm and write back results:
``````CALL gds.alpha.similarity.overlap.write(configuration: Map)
YIELD nodes, similarityPairs, writeRelationshipType, writeProperty, min, max, mean, stdDev, p25, p50, p75, p90, p95, p99, p999, p100``````
Table 8. Parameters
Name Type Default Optional Description

configuration

Map

n/a

no

Algorithm-specific configuration.

Table 9. Configuration
Name Type Default Optional Description

data

List or String

null

no

A list of maps of the following structure: `{item: nodeId, weights: [double, double, double]}` or a Cypher query.

top

Integer

0

yes

The number of similar pairs to return. If `0`, it will return as many as it finds.

topK

Integer

3

yes

The number of similar values to return per node. If `0`, it will return as many as it finds.

similarityCutoff

Integer

-1

yes

The threshold for similarity. Values below this will not be returned.

degreeCutoff

Integer

0

yes

The threshold for the number of items in the `targets` list. If the list contains less than this amount, that node will be excluded from the calculation.

skipValue

Float

gds.util.NaN()

yes

Value to skip when executing similarity computation. A value of `null` means that skipping is disabled.

concurrency

Integer

4

yes

The number of concurrent threads used for running the algorithm. Also provides the default value for 'writeConcurrency'.

writeConcurrency

Integer

value of 'concurrency'

yes

The number of concurrent threads used for writing the result.

graph

String

dense

yes

The graph name ('dense' or 'cypher').

writeBatchSize

Integer

10000

yes

The batch size to use when storing results.

writeRelationshipType

String

SIMILAR

yes

The relationship type to use when storing results.

writeProperty

String

score

yes

The property to use when storing results.

sourceIds

List of String

null

yes

The ids of items from which we need to compute similarities. Defaults to all the items provided in the `data` parameter.

targetIds

List of String

null

yes

The ids of items to which we need to compute similarities. Defaults to all the items provided in the `data` parameter.

Table 10. Results
Name Type Description

nodes

Integer

The number of nodes passed in.

similarityPairs

Integer

The number of pairs of similar nodes computed.

writeRelationshipType

String

The relationship type used when storing results.

writeProperty

String

The property used when storing results.

min

Float

The minimum similarity score computed.

max

Float

The maximum similarity score computed.

mean

Float

The mean of similarities scores computed.

stdDev

Float

The standard deviation of similarities scores computed.

p25

Float

The 25 percentile of similarities scores computed.

p50

Float

The 50 percentile of similarities scores computed.

p75

Float

The 75 percentile of similarities scores computed.

p90

Float

The 90 percentile of similarities scores computed.

p95

Float

The 95 percentile of similarities scores computed.

p99

Float

The 99 percentile of similarities scores computed.

p999

Float

The 99.9 percentile of similarities scores computed.

p100

Float

The 100 percentile of similarities scores computed.

The following will run the algorithm and stream results:
``````CALL gds.alpha.similarity.overlap.stream(configuration: Map)
YIELD item1, item2, count1, count2, similarity``````
Table 11. Parameters
Name Type Default Optional Description

configuration

Map

n/a

no

Algorithm-specific configuration.

Table 12. Configuration
Name Type Default Optional Description

data

List or String

null

no

A list of maps of the following structure: `{item: nodeId, weights: [double, double, double]}` or a Cypher query.

top

Integer

0

yes

The number of similar pairs to return. If `0`, it will return as many as it finds.

topK

Integer

3

yes

The number of similar values to return per node. If `0`, it will return as many as it finds.

similarityCutoff

Integer

-1

yes

The threshold for similarity. Values below this will not be returned.

degreeCutoff

Integer

0

yes

The threshold for the number of items in the `targets` list. If the list contains less than this amount, that node will be excluded from the calculation.

skipValue

Float

gds.util.NaN()

yes

Value to skip when executing similarity computation. A value of `null` means that skipping is disabled.

concurrency

Integer

4

yes

The number of concurrent threads used for running the algorithm.

graph

String

dense

yes

The graph name ('dense' or 'cypher').

sourceIds

List of Integer

null

yes

The ids of items from which we need to compute similarities. Defaults to all the items provided in the `data` parameter.

targetIds

List of Integer

null

yes

The ids of items to which we need to compute similarities. Defaults to all the items provided in the `data` parameter.

Table 13. Results
Name Type Description

item1

Integer

The ID of one node in the similarity pair.

item2

Integer

The ID of other node in the similarity pair.

count1

Integer

The size of the `targets` list of one node.

count2

Integer

The size of the `targets` list of other node.

intersection

Integer

The number of intersecting values in the two nodes `targets` lists.

similarity

Integer

The overlap similarity of the two nodes.