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# Cosine Similarity

✓ File Writeback ✕ Property Writeback ✓ Direct Return ✓ Stream Return ✕ Stats

## Overview

In cosine similarity, data objects in a dataset are treated as vectors, and it uses the cosine value of the angle between two vectors to indicate the similarity between them. In the graph, specifying N numeric properties (features) of nodes to form N-dimensional vectors, two nodes are considered similar if their vectors are similar.

Cosine similarity ranges from -1 to 1; 1 means that the two vectors have the same direction, -1 means that the two vectors have the opposite direction.

In 2-dimensional space, the cosine similarity between vectors A(a1, a2) and B(b1, b2) is computed as:

In 3-dimensional space, the cosine similarity between vectors A(a1, a2, a3) and B(b1, b2, b3) is computed as:

The following diagram shows the relationship between vectors A and B in 2D and 3D spaces, as well as the angle θ between them:

Generalize to N-dimensional space, the cosine similarity is computed as:

## Considerations

• Theoretically, the calculation of cosine similarity between two nodes does not depend on their connectivity.
• The value of cosine similarity is independent of the length of the vectors, but only the direction of the vectors.

## Syntax

• Command: `algo(similarity)`
• Parameters:
Name
Type
Spec
Default
Optional
Description
ids / uuids []`_id` / []`_uuid` / / No ID/UUID of the first group of nodes to calculate
ids2 / uuids2 []`_id` / []`_uuid` / / Yes ID/UUID of the second group of nodes to calculate
type string `cosine` `cosine` Yes Type of similarity; for Cosine Similarity, keep it as `cosine`
node_schema_property []`@<schema>?.<property>` Numeric type, must LTE / No Specify two or more node properties to form the vectors, all properties must belong to the same (one) schema
limit int ≥-1 `-1` Yes Number of results to return, `-1` to return all results
top_limit int ≥-1 `-1` Yes In the selection mode, limit the maximum number of results returned for each node specified in `ids`/`uuids`, `-1` to return all results with similarity > 0; in the pairing mode, this parameter is invalid

The algorithm has two calculation modes:

1. Pairing: when both `ids`/`uuids` and `ids2`/`uuids2` are configured, pairing each node in `ids`/`uuids` with each node in `ids2`/`uuids2` (ignore the same node) and computing pair-wise similarities.
2. Selection: when only `ids`/`uuids` is configured, for each target node in it, computing pair-wise similarities between it and all other nodes in the graph. The returned results include all or limited number of nodes that have similarity > 0 with the target node and is ordered by the descending similarity.

## Examples

The example graph has 4 products (edges are ignored), each product has properties price, weight, weight and height:

### File Writeback

Spec Content
filename `node1`,`node2`,`similarity`
``````algo(similarity).params({
uuids: [1],
uuids2: [2,3,4],
node_schema_property: ['price', 'weight', 'width', 'height']
}).write({
file:{
filename: 'cs_result'
}
})
``````

Results: File cs_result

``````product1,product2,0.986529
product1,product3,0.878858
product1,product4,0.816876
``````
``````algo(similarity).params({
uuids: [1,2,3,4],
node_schema_property: ['price', 'weight', 'width', 'height'],
type: 'cosine'
}).write({
file:{
filename: 'list'
}
})
``````

Results: File list

``````product1,product2,0.986529
product1,product3,0.878858
product1,product4,0.816876
product2,product1,0.986529
product2,product3,0.934217
product2,product4,0.881988
product3,product2,0.934217
product3,product4,0.930153
product3,product1,0.878858
product4,product3,0.930153
product4,product2,0.881988
product4,product1,0.816876
``````

### Direct Return

Alias Ordinal
Type
Description Columns
0 []perNodePair Node pair and its similarity `node1`, `node2`, `similarity`
``````algo(similarity).params({
uuids: [1,2],
uuids2: [2,3,4],
node_schema_property: ['price', 'weight', 'width', 'height'],
type: 'cosine'
}) as cs
return cs
``````

Results: cs

node1 node2 similarity
1 2 0.986529413529119
1 3 0.878858407519654
1 4 0.816876150267203
2 3 0.934216530725663
2 4 0.88198819302226
``````algo(similarity).params({
uuids: [1,2],
type: 'cosine',
node_schema_property: ['price', 'weight', 'width', 'height'],
top_limit: 1
}) as top
``````

Results: top

node1 node2 similarity
1 2 0.986529413529119
2 1 0.986529413529119

### Stream Return

Alias Ordinal
Type
Description Columns
0 []perNodePair Node pair and its similarity `node1`, `node2`, `similarity`
``````algo(similarity).params({
uuids: [3],
uuids2: [1,2,4],
node_schema_property: ['@product.price', '@product.weight', '@product.width'],
type: 'cosine'
}).stream() as cs
where cs.similarity > 0.8
return cs
``````

Results: cs

node1 node2 similarity
3 2 0.883292081301959
3 4 0.877834381494613
``````algo(similarity).params({
uuids: [1,3],
node_schema_property: ['price', 'weight', 'width', 'height'],
type: 'cosine',
top_limit: 1
}).stream() as top