HDC
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, N numeric node properties (features) are specified to form N-dimensional vectors; two nodes are considered similar if their vectors are similar.
Cosine similarity ranges from -1 to 1, where 1 indicates that the two vectors point in the same direction, and -1 indicates they point in opposite directions.
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:
Generalized to N-dimensional space, cosine similarity is computed as:
Considerations
- Theoretically, the calculation of cosine similarity between two nodes is independent of their connectivity in the graph.
- The value of cosine similarity is independent of the length of the vectors, but only the direction of the vectors.
Example Graph
Run the following statements on an empty graph to define its structure and insert data:
ALTER GRAPH CURRENT_GRAPH ADD NODE {
product ({price int32, weight int32, width int32, height int32})
};
INSERT (:product {_id:"product1", price:50, weight:160, width:20, height:152}),
(:product {_id:"product2", price:42, weight:90, width:30, height:90}),
(:product {_id:"product3", price:24, weight:50, width:55, height:70}),
(:product {_id:"product4", price:38, weight:20, width:32, height:66});
create().node_schema("product");
create().node_property(@product, "price", int32).node_property(@product, "weight", int32).node_property(@product, "width", int32).node_property(@product, "height", int32);
insert().into(@product).nodes([{_id:"product1", price:50, weight:160, width:20, height:152}, {_id:"product2", price:42, weight:90, width:30, height:90}, {_id:"product3", price:24, weight:50, width:55, height:70}, {_id:"product4", price:38, weight:20, width:32, height:66}]);
Creating HDC Graph
To load the entire graph to the HDC server hdc-server-1 as my_hdc_graph:
CREATE HDC GRAPH my_hdc_graph ON "hdc-server-1" OPTIONS {
nodes: {"*": ["*"]},
edges: {"*": ["*"]},
direction: "undirected",
load_id: true,
update: "static"
}
hdc.graph.create("my_hdc_graph", {
nodes: {"*": ["*"]},
edges: {"*": ["*"]},
direction: "undirected",
load_id: true,
update: "static"
}).to("hdc-server-1")
Parameters
Algorithm name: similarity
| Name | Type | Spec | Default | Optional | Description | |
|---|---|---|---|---|---|---|
ids/uuids |
_id/_uuid |
Yes | Specifies the first group of nodes by their _id or _uuid. If unset, all nodes in the graph are used as the first group of nodes. |
The algorithm supports two calculation modes:
|
||
ids2/uuids2 |
_id/_uuid |
Yes | Specifies the second group of nodes for pairwise similarity by their _id or _uuid. If only ids2/uuids2 is set (and ids/uuids is not), the algorithm returns no result. |
|||
type |
String | cosine |
cosine |
No | Specifies the type of similarity to compute; for Cosine Similarity, keep it as cosine. |
|
node_schema_property |
[]"<@schema.?><property>" |
No | Specifies numeric node properties to form a vector for each node; all specified properties must belong to the same label (schema). | |||
return_id_uuid |
String | uuid,id,both |
uuid |
Yes | Includes _uuid, _id, or both to represent nodes in the results. |
|
order |
String | asc,desc |
Yes | Sorts the results by similarity. |
||
limit |
Integer | ≥-1 | -1 |
Yes | Limits the number of results returned. Set to -1 to include all results. |
|
top_limit |
Integer | ≥-1 | -1 |
Yes | Limits the number of results returned for each node specified with ids/uuids in selection mode. Set to -1 to include all results with a similarity greater than 0. This parameter is invalid in pairing mode. |
|
File Writeback
CALL algo.similarity.write("my_hdc_graph", {
return_id_uuid: "id",
ids: "product1",
ids2: ["product2", "product3", "product4"],
node_schema_property: ["price", "weight", "width", "height"],
type: "cosine"
}, {
file: {
filename: "cosine"
}
})
algo(similarity).params({
projection: "my_hdc_graph",
return_id_uuid: "id",
ids: "product1",
ids2: ["product2", "product3", "product4"],
node_schema_property: ["price", "weight", "width", "height"],
type: "cosine"
}).write({
file: {
filename: "cosine"
}
})
Result:
_id1,_id2,similarity
product1,product2,0.986529
product1,product3,0.878858
product1,product4,0.816876
Full Return
CALL algo.similarity.run("my_hdc_graph", {
return_id_uuid: "id",
ids: ["product1","product2"],
ids2: ["product2","product3","product4"],
node_schema_property: ["price", "weight", "width", "height"],
type: "cosine"
}) YIELD cs
RETURN cs
exec{
algo(similarity).params({
return_id_uuid: "id",
ids: ["product1","product2"],
ids2: ["product2","product3","product4"],
node_schema_property: ["price", "weight", "width", "height"],
type: "cosine"
}) as cs
return cs
} on my_hdc_graph
Result:
| _id1 | _id2 | similarity |
|---|---|---|
| product1 | product2 | 0.986529 |
| product1 | product3 | 0.878858 |
| product1 | product4 | 0.816876 |
| product2 | product3 | 0.934217 |
| product2 | product4 | 0.881988 |
Stream Return
CALL algo.similarity.stream("my_hdc_graph", {
return_id_uuid: "id",
ids: ["product1", "product3"],
node_schema_property: ["price", "weight", "width", "height"],
type: "cosine",
top_limit: 1
}) YIELD top
RETURN top
exec{
algo(similarity).params({
return_id_uuid: "id",
ids: ["product1", "product3"],
node_schema_property: ["price", "weight", "width", "height"],
type: "cosine",
top_limit: 1
}).stream() as cs
return cs
} on my_hdc_graph
Result:
| _id1 | _id2 | similarity |
|---|---|---|
| product1 | product2 | 0.986529 |
| product3 | product2 | 0.934217 |