Dense Vector

Dense vectors are numerical data representations widely used in machine learning and data analysis. They consist of arrays with real numbers, where most or all elements are non-zero. Compared to sparse vectors, dense vectors contain more information at the same dimensional level, as each dimension holds meaningful values. This representation can effectively capture complex patterns and relationships, making data easier to analyze and process in high-dimensional spaces. Dense vectors typically have a fixed number of dimensions, ranging from a few dozen to several hundred or even thousands, depending on the specific application and requirements.

Dense vectors are mainly used in scenarios that require understanding the semantics of data, such as semantic search and recommendation systems. In semantic search, dense vectors help capture the underlying connections between queries and documents, improving the relevance of search results. In recommendation systems, they aid in identifying similarities between users and items, offering more personalized suggestions.

Overview

Dense vectors are typically represented as arrays of floating-point numbers with a fixed length, such as [0.2, 0.7, 0.1, 0.8, 0.3, ..., 0.5]. The dimensionality of these vectors usually ranges from hundreds to thousands, such as 128, 256, 768, or 1024. Each dimension captures specific semantic features of an object, making it applicable to various scenarios through similarity calculations.

Dense vectors in 2D space

The image above illustrates the representation of dense vectors in a 2D space. Although dense vectors in real-world applications often have much higher dimensions, this 2D illustration effectively conveys several key concepts:

• Multidimensional Representation: Each point represents a conceptual object (like Milvus, vector database, retrieval system, etc.), with its position determined by the values of its dimensions.

• Semantic Relationships: The distances between points reflect the semantic similarity between concepts. Closer points indicate concepts that are more semantically related.

• Clustering Effect: Related concepts (such as Milvus, vector database, and retrieval system) are positioned close to each other in space, forming a semantic cluster.

Below is an example of a real dense vector representing the text "Milvus is an efficient vector database":

[
    -0.013052909,
    0.020387933,
    -0.007869,
    -0.11111383,
    -0.030188112,
    -0.0053388323,
    0.0010654867,
    0.072027855,
    // ... more dimensions
]

Dense vectors can be generated using various embedding models, such as CNN models (like ResNet, VGG) for images and language models (like BERT, Word2Vec) for text. These models transform raw data into points in high-dimensional space, capturing the semantic features of the data. Additionally, Milvus offers convenient methods to help users generate and process dense vectors, as detailed in Embeddings.

Once data is vectorized, it can be stored in Milvus for management and vector retrieval. The diagram below shows the basic process.

Use dense vecctors in Milvus

Use dense vectors in Milvus

Add vector field

To use dense vectors in Milvus, first define a vector field for storing dense vectors when creating a collection. This process includes:

1. Setting datatype to a supported dense vector data type. For supported dense vector data types, see Data Types.

2. Specifying the dimensions of the dense vector using the dim parameter.

In the example below, we add a vector field named dense_vector to store dense vectors. The field’s data type is FLOAT_VECTOR, with a dimension of 4.

from pymilvus import MilvusClient, DataType

client = MilvusClient(uri="http://localhost:19530")

schema = client.create_schema(
    auto_id=True,
    enable_dynamic_fields=True,
)

schema.add_field(field_name="pk", datatype=DataType.VARCHAR, is_primary=True, max_length=100)
schema.add_field(field_name="dense_vector", datatype=DataType.FLOAT_VECTOR, dim=4)

import io.milvus.v2.client.ConnectConfig;
import io.milvus.v2.client.MilvusClientV2;

import io.milvus.v2.common.DataType;
import io.milvus.v2.service.collection.request.AddFieldReq;
import io.milvus.v2.service.collection.request.CreateCollectionReq;

MilvusClientV2 client = new MilvusClientV2(ConnectConfig.builder()
        .uri("http://localhost:19530")
        .build());

CreateCollectionReq.CollectionSchema schema = client.createSchema();
schema.setEnableDynamicField(true);
schema.addField(AddFieldReq.builder()
        .fieldName("pk")
        .dataType(DataType.VarChar)
        .isPrimaryKey(true)
        .autoID(true)
        .maxLength(100)
        .build());

schema.addField(AddFieldReq.builder()
        .fieldName("dense_vector")
        .dataType(DataType.FloatVector)
        .dimension(4)
        .build());

import { DataType } from "@zilliz/milvus2-sdk-node";

schema.push({
  name: "dense_vector",
  data_type: DataType.FloatVector,
  dim: 128,
});

export primaryField='{
    "fieldName": "pk",
    "dataType": "VarChar",
    "isPrimary": true,
    "elementTypeParams": {
        "max_length": 100
    }
}'

export vectorField='{
    "fieldName": "dense_vector",
    "dataType": "FloatVector",
    "elementTypeParams": {
        "dim": 4
    }
}'

export schema="{
    \"autoID\": true,
    \"fields\": [
        $primaryField,
        $vectorField
    ]
}"

Supported data types for dense vector fields:

Type	Description
FLOAT_VECTOR	Stores 32-bit floating-point numbers, commonly used for representing real numbers in scientific computations and machine learning. Ideal for scenarios requiring high precision, such as distinguishing similar vectors.
FLOAT16_VECTOR	Stores 16-bit half-precision floating-point numbers, used for deep learning and GPU computations. It saves storage space in scenarios where precision is less critical, such as in the low-precision recall phase of recommendation systems.
BFLOAT16_VECTOR	Stores 16-bit Brain Floating Point (bfloat16) numbers, offering the same range of exponents as Float32 but with reduced precision. Suitable for scenarios that need to process large volumes of vectors quickly, such as large-scale image retrieval.

Set index params for vector field

To accelerate semantic searches, an index must be created for the vector field. Indexing can significantly improve the retrieval efficiency of large-scale vector data.

index_params = client.prepare_index_params()

index_params.add_index(
    field_name="dense_vector",
    index_name="dense_vector_index",
    index_type="IVF_FLAT",
    metric_type="IP",
    params={"nlist": 128}
)

import io.milvus.v2.common.IndexParam;
import java.util.*;

List<IndexParam> indexes = new ArrayList<>();
Map<String,Object> extraParams = new HashMap<>();
extraParams.put("nlist",128);
indexes.add(IndexParam.builder()
        .fieldName("dense_vector")
        .indexType(IndexParam.IndexType.IVF_FLAT)
        .metricType(IndexParam.MetricType.IP)
        .extraParams(extraParams)
        .build());

import { MetricType, IndexType } from "@zilliz/milvus2-sdk-node";

const indexParams = {
    index_name: 'dense_vector_index',
    field_name: 'dense_vector',
    metric_type: MetricType.IP,
    index_type: IndexType.IVF_FLAT,
    params: {
      nlist: 128
    },
};

export indexParams='[
        {
            "fieldName": "dense_vector",
            "metricType": "IP",
            "indexName": "dense_vector_index",
            "indexType": "IVF_FLAT",
            "params":{"nlist": 128}
        }
    ]'

In the example above, an index named dense_vector_index is created for the dense_vector field using the IVF_FLAT index type. The metric_type is set to IP, indicating that inner product will be used as the distance metric.

Milvus supports other index types as well. For more details, refer to Floating Vector Indexes. Additionally, Milvus supports other metric types. For more information, refer to Metric Types.

Create collection

Once the dense vector and index param settings are complete, you can create a collection containing dense vectors. The example below uses the create_collection method to create a collection named my_dense_collection.

client.create_collection(
    collection_name="my_dense_collection",
    schema=schema,
    index_params=index_params
)

import io.milvus.v2.client.ConnectConfig;
import io.milvus.v2.client.MilvusClientV2;

MilvusClientV2 client = new MilvusClientV2(ConnectConfig.builder()
        .uri("http://localhost:19530")
        .build());

CreateCollectionReq requestCreate = CreateCollectionReq.builder()
        .collectionName("my_dense_collection")
        .collectionSchema(schema)
        .indexParams(indexes)
        .build();
client.createCollection(requestCreate);

import { MilvusClient } from "@zilliz/milvus2-sdk-node";

const client = new MilvusClient({
    address: 'http://localhost:19530'
});

await client.createCollection({
    collection_name: 'my_dense_collection',
    schema: schema,
    index_params: indexParams
});

curl --request POST \
--url "${CLUSTER_ENDPOINT}/v2/vectordb/collections/create" \
--header "Authorization: Bearer ${TOKEN}" \
--header "Content-Type: application/json" \
-d "{
    \"collectionName\": \"my_dense_collection\",
    \"schema\": $schema,
    \"indexParams\": $indexParams
}"

Insert data

After creating the collection, use the insert method to add data containing dense vectors. Ensure that the dimensionality of the dense vectors being inserted matches the dim value defined when adding the dense vector field.

data = [
    {"dense_vector": [0.1, 0.2, 0.3, 0.7]},
    {"dense_vector": [0.2, 0.3, 0.4, 0.8]},
]

client.insert(
    collection_name="my_dense_collection",
    data=data
)

import com.google.gson.Gson;
import com.google.gson.JsonObject;
import io.milvus.v2.service.vector.request.InsertReq;
import io.milvus.v2.service.vector.response.InsertResp;

List<JsonObject> rows = new ArrayList<>();
Gson gson = new Gson();
rows.add(gson.fromJson("{\"dense_vector\": [0.1, 0.2, 0.3, 0.4]}", JsonObject.class));
rows.add(gson.fromJson("{\"dense_vector\": [0.2, 0.3, 0.4, 0.5]}", JsonObject.class));

InsertResp insertR = client.insert(InsertReq.builder()
        .collectionName("my_dense_collection")
        .data(rows)
        .build());

const data = [
  { dense_vector: [0.1, 0.2, 0.3, 0.7] },
  { dense_vector: [0.2, 0.3, 0.4, 0.8] },
];

client.insert({
  collection_name: "my_dense_collection",
  data: data,
});

curl --request POST \
--url "${CLUSTER_ENDPOINT}/v2/vectordb/entities/insert" \
--header "Authorization: Bearer ${TOKEN}" \
--header "Content-Type: application/json" \
-d '{
    "data": [
        {"dense_vector": [0.1, 0.2, 0.3, 0.4]},
        {"dense_vector": [0.2, 0.3, 0.4, 0.5]}        
    ],
    "collectionName": "my_dense_collection"
}'

## {"code":0,"cost":0,"data":{"insertCount":2,"insertIds":["453577185629572531","453577185629572532"]}}

Perform similarity search

Semantic search based on dense vectors is one of the core features of Milvus, allowing you to quickly find data that is most similar to a query vector based on the distance between vectors. To perform a similarity search, prepare the query vector and search parameters, then call the search method.

search_params = {
    "params": {"nprobe": 10}
}

query_vector = [0.1, 0.2, 0.3, 0.7]

res = client.search(
    collection_name="my_dense_collection",
    data=[query_vector],
    anns_field="dense_vector",
    search_params=search_params,
    limit=5,
    output_fields=["pk"]
)

print(res)

# Output
# data: ["[{'id': '453718927992172271', 'distance': 0.7599999904632568, 'entity': {'pk': '453718927992172271'}}, {'id': '453718927992172270', 'distance': 0.6299999952316284, 'entity': {'pk': '453718927992172270'}}]"]

import io.milvus.v2.service.vector.request.data.FloatVec;

Map<String,Object> searchParams = new HashMap<>();
searchParams.put("nprobe",10);

FloatVec queryVector = new FloatVec(new float[]{0.1f, 0.3f, 0.3f, 0.4f});

SearchResp searchR = client.search(SearchReq.builder()
        .collectionName("my_dense_collection")
        .data(Collections.singletonList(queryVector))
        .annsField("dense_vector")
        .searchParams(searchParams)
        .topK(5)
        .outputFields(Collections.singletonList("pk"))
        .build());
        
System.out.println(searchR.getSearchResults());

// Output
//
// [[SearchResp.SearchResult(entity={pk=453444327741536779}, score=0.65, id=453444327741536779), SearchResp.SearchResult(entity={pk=453444327741536778}, score=0.65, id=453444327741536778)]]

query_vector = [0.1, 0.2, 0.3, 0.7];

client.search({
    collection_name: my_dense_collection,
    data: query_vector,
    limit: 5,
    output_fields: ['pk'],
    params: {
        nprobe: 10
    }
});

curl --request POST \
--url "${CLUSTER_ENDPOINT}/v2/vectordb/entities/search" \
--header "Authorization: Bearer ${TOKEN}" \
--header "Content-Type: application/json" \
-d '{
    "collectionName": "my_dense_collection",
    "data": [
        [0.1, 0.2, 0.3, 0.7]
    ],
    "annsField": "dense_vector",
    "limit": 5,
    "searchParams":{
        "params":{"nprobe":10}
    },
    "outputFields": ["pk"]
}'

## {"code":0,"cost":0,"data":[{"distance":0.55,"id":"453577185629572532","pk":"453577185629572532"},{"distance":0.42,"id":"453577185629572531","pk":"453577185629572531"}]}

For more information on similarity search parameters, refer to Basic ANN Search.