What is vector similarity search (VSS)?
Vector similarity search (VSS) refers to the process of finding vectors in a dataset that are similar to a given query vector based on a similarity metric or distance measure. VSS is commonly used in various fields, including information retrieval, machine learning, data mining, and computer vision. In the vast landscape of data exploration and information retrieval, VSS is a powerful methodology that reshapes how we analyze and understand complex datasets.
Let’s start with identifying the components of VSS in the following section.
Components of VSS
Vectors embeddings: Items in the dataset are represented as vectors in a high-dimensional space. Each vector value represents a feature or attribute of the data item. For example, in natural language processing, documents can be represented as vectors, where each dimension represents the frequency of a specific word. The item for which similarity is being searched, also called query vector, is also represented as a vector.
Similarity metrics or distance: A similarity metric or distance measure is defined to quantify the similarity between vectors. Common measures include Euclidean distance, cosine similarity, and Jaccard similarity. The choice of metric depends on the data's nature and the application’s requirements. Cosine similarity is frequently used for text-based applications, Euclidean distance may be used for numerical data, and Jaccard similarity is used for imagery data.
Indexing structures or search algorithm: Indexing structures are often used to efficiently search for similar vectors. These structures organize the vectors to reduce the search space, making the search process faster. Examples of indexing structures include k-d trees, ball trees, and locality-sensitive hashing (LSH). These structures are designed to quickly eliminate portions of the dataset that are unlikely to contain similar vectors.
Working of VSS
The working of VSS is demonstrated using the following Python code:
from sklearn.neighbors import NearestNeighborsimport numpy as np# Generate 10 random vectors of dimension 5sample_size=10dimensions=5# Maintain a random staterand_seed=50np.random.seed(rand_seed)# Generate random vectorsvectors=np.random.rand(sample_size, dimensions)#Define the query vectorq_vector = np.array([0.5, 0.85, 0.37, 0.8, 0.65])# Nearest neighbours to retrievek = 3# Generate a NearestNeighbors model with cosine similaritymodel = NearestNeighbors(n_neighbors=k, algorithm='brute', metric='cosine')model.fit(vectors)# Find k-nearest neighbors for the query vectordistances, indices = model.kneighbors([q_vector])# Print the resultsprint(f"Query Vector: {q_vector}")print(f"Indices of k-nearest neighbors: {indices}")print(f"Distances to k-nearest neighbors: {distances}")print("Nearest Neighbors:")for i, index in enumerate(indices.flatten()):print(f"Neighbor {i + 1}: Index {index}, Vector {vectors[index]}")
Code explanation
Line 1–2: Essential libraries are imported. The
NearestNeighborsis an unsupervised learner to perform neighbor searches. Similarly, thenumpylibrary is used for performing various matrix operations.Line 5–11: Generate a random dataset of vectors. The random seed is added to maintain the same state each time.
Line 14: A query vector is defined for which we need to find similar vectors in the dataset.
Line 17: The
kvalue is set to3, meaning we must find at most 3 similar vectors from the dataset.Line 20–21: We create a
NearestNeighborsmodel withcosinesimilarity to measure the distance between vectors. The parameteralgorithm='brute'shows that the brute-force approach is used to find nearest neighbors. In other words, it computes distances between all pairs of points in the dataset.Line 24: The query vector is passed to the model to find similar vectors in the dataset. The
model.kneighborsreturns the distances and indexes ofksimilar vectors.Line 27–32: Print the query vector, the distances and indexes of
ksimilar vectors, and the similar vectors as well.
Let’s look at some of the applications of VSS in different fields.
Applications of VSS in different fields
Information retrieval: Vector similarity search facilitates efficient document retrieval by identifying documents similar to a given query.
Recommendation systems: E-commerce platforms use vector similarity to recommend products based on user preferences, enhancing user experience.
Image and video analysis: Image and video analysis applications benefit from vector similarity search, assisting tasks such as image retrieval and object recognition.
Genomic data analysis: In bioinformatics, vector similarity search helps analyze genomic data, identifying sequences with shared characteristics.
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