What is Approximate Near Neibour Search

Approximate Nearest Neighbors (ANN) algorithms are a class of algorithms designed to find the approximate nearest neighbors to a query point in a high-dimensional space.  They don't guarantee finding the absolute nearest neighbors (hence "approximate"), but they do so much faster than exact nearest neighbor search, which becomes computationally very expensive in high dimensions.  This speedup is crucial for many applications, including:   

Information Retrieval: Finding similar documents, images, or other data points.   

Recommendation Systems: Recommending items similar to those a user has interacted with.   

Clustering: Preprocessing step for some clustering algorithms.

Anomaly Detection: Identifying data points that are significantly different from others.

Why Approximate?

The curse of dimensionality makes exact nearest neighbor search computationally prohibitive in high-dimensional spaces.  The number of possible neighbors grows exponentially with the number of dimensions, making exhaustive search impractical. ANN algorithms trade off a small amount of accuracy (by finding approximate neighbors) for a massive gain in speed.   

HNSW (Hierarchical Navigable Small World):

HNSW is a graph-based ANN algorithm. It constructs a hierarchical graph structure where each node represents a data point.  The graph is designed so that you can efficiently navigate from any node to its nearest neighbors. The hierarchy allows for faster searching by starting at a higher level and progressively moving down to the lower levels.   

How it works (simplified):

Graph Construction: Data points are connected to their nearest neighbors at multiple levels of the hierarchy. Connections at higher levels are longer-range, while connections at lower levels are shorter-range.   

Search: Given a query point, the search starts at the top level of the graph. It navigates to the nearest neighbor at that level. Then, it proceeds to the next level and repeats the process until it reaches the lowest level. The nodes visited at the lowest level are considered the approximate nearest neighbors.   

Advantages:  Excellent performance, relatively low memory usage, good for various distance metrics.

Used in: Milvus (a vector database), and other vector search libraries.   

FAISS (Facebook AI Similarity Search):

FAISS is a library developed by Facebook AI for efficient similarity search and clustering of dense vectors. It provides implementations of many ANN algorithms, including several variations of Locality Sensitive Hashing (LSH), Product Quantization (PQ), and IVF (Inverted File Index).  It is highly optimized for performance and can handle very large datasets.   

Key Techniques used in FAISS:

Quantization: Reduces the size of vectors by mapping them to a smaller set of representative vectors.

Locality Sensitive Hashing (LSH): Uses hash functions to map similar vectors to the same buckets, increasing the probability of finding neighbors.   

Inverted File Index (IVF): Partitions the data into clusters and builds an index on these clusters, enabling faster search by only considering relevant clusters.   

Advantages:  Highly optimized for performance, supports various ANN algorithms, handles large datasets.

Used in: Many large-scale similarity search applications.