## What is approximate nearest neighbor search (ANNS)?

Approximate nearest neighbor search is a powerful technique in machine learning (ML) and data science pipelines that allows for efficient semantic similarity search in large datasets often found in vector databases like Zilliz. ANNS is a method of finding the nearest neighbor of a given query point in a large dataset of points. ANNS aims to find an approximate nearest neighbor with high probability while minimizing the computational cost.

The standard **nearest neighbor** search (NN search) algorithm is an exhaustive search that checks the distance between the query point and every other point in the dataset. However, this can be computationally expensive and infeasible for large datasets. ANNS is a solution to this problem using a data structure or algorithm to reduce the distance calculations required.

## Differences between NN, ANN, and KNN

The following will clarify the differences between Nearest Neighbor (NN), Approximate Nearest Neighbor (ANN), and K-Nearest Neighbors (KNN):

Nearest Neighbor (NN):

NN is a basic algorithm used for classification and regression tasks.

It works by finding the single closest data point (neighbor) to a given query point based on a distance metric (e.g., Euclidean distance).

The class or value of the query point is determined by the class or value of its nearest neighbor.

NN is a simple and intuitive algorithm but can be computationally expensive for large datasets.

Approximate Nearest Neighbor (ANN):

ANN is a variant of the nearest neighbor algorithm that aims to find approximate nearest neighbors instead of exact ones.

It is used when the dataset is very large, and finding the exact nearest neighbors is computationally expensive or infeasible.

ANN algorithms trade-off some accuracy for improved speed and efficiency.

They use techniques like locality-sensitive hashing (LSH) or tree-based structures to quickly find approximate nearest neighbors.

ANN is useful in scenarios where an approximate result is sufficient and the dataset is too large for exact nearest neighbor search.

K-Nearest Neighbors (KNN):

KNN is an extension of the nearest neighbor algorithm that considers the K nearest neighbors instead of just one.

It works by identifying the K most similar data points in the feature space, where similarity is measured using a chosen distance function.

The class or value of the query point is determined by the majority class or average value of its K nearest neighbors.

KNN is a non-parametric algorithm and can be used for both classification and regression tasks.

The choice of K is important and can impact the performance and generalization of the algorithm.

The main differences between these algorithms are:

NN considers only the single nearest neighbor, while KNN considers K nearest neighbors.

ANN focuses on finding approximate nearest neighbors efficiently, sacrificing some accuracy for speed.

KNN is a more general algorithm that can be used for both classification and regression, while NN and ANN are primarily used for nearest neighbor search.

Basically, NN finds the single nearest neighbor, ANN finds approximate nearest neighbors efficiently, and KNN considers K nearest neighbors for classification or regression tasks.

## When to use approximate nearest neighbor search?

Approximate nearest neighbor search techniques find application in various fields, including recommendation systems, image and audio recognition, natural language processing (NLP), and Retrieval Augmented Generation (RAG). ANNS methods can provide approximate solutions that are still accurate enough for many applications, even when dealing with large datasets.

## Common ANNS algorithms

ANNS algorithms use a variety of data structures and algorithms that are designed to optimize the search process. Some popular ANNS algorithms include KD-trees, locality-sensitive hashing (LSH), and product quantization. KD-trees are commonly used in low-dimensional spaces, while LSH is preferred for high-dimensional spaces. Product quantization is a technique that divides the feature space into subspaces and compresses each subspace into a small codebook.

The dataset is divided into a tree-like structure in KD-trees, where each node represents a region of points. The algorithm traverses the tree during the search process, checking the areas closest to the query point. In contrast, LSH groups similar points into the same bucket, allowing quick retrieval of approximate nearest neighbors. Product quantization checks the codes of each subspace to find the approximate nearest neighbor.

The efficiency with which ANNS algorithms can find the approximate nearest neighbor makes them popular in various applications. In recommendation systems, ANNS algorithms can be used to find similar items or users efficiently. ANNS algorithms can help find matching images and sound in image and audio recognition. In natural language processing, ANNS algorithms can find similar documents or sentences.

## When to use approximate nearest neighbor search?

When dealing with high-dimensional data, finding the exact nearest neighbor can become computationally expensive and not necessary. In such cases, the approximate nearest neighbor search significantly reduces the search time while providing a reasonably accurate result. Approximate nearest neighbor search is commonly used in applications such as image and speech recognition, recommendation systems, and natural language processing.

## Approximate Nearest Neighbor Search Summary

In conclusion, approximate nearest neighbor search is a valuable tool in data science and machine learning pipelines. Using clever data structures and algorithms, ANNS can provide computationally feasible solutions that are still accurate enough for many applications. Moreover, ANNS techniques are widely applicable and allow for efficient nearest-neighbor search in large datasets.