Similarity Search

Introduction to Similarity Search

In many real-life applications, no two situations are exactly alike. The same object looks different in different lighting. The same person’s voice changes day to day. Two fraudulent transactions have somewhat different details, even though they were committed by the same team following the same plan. To classify data and make predictions, you would waste your time looking for exact matches. The answer is to measure how similar objects are to one another and to be able to do so efficiently, when data sets are large and complex.

Whether powering product recommendations, detecting fraud patterns, or enabling semantic search, similarity search is about understanding closeness in a way that reflects meaning, not just matching.

What People Misunderstand About Similarity Search

A common misconception is that there is one standard way or one best way to define similarity. The truth is, there are many approaches, each with its pros and cons. The best method is the one that highlights the factors that are important for the application at hand. 

Similarity search is sometimes confused with keyword search or synonym search. Similarity search goes deeper. It works even when the items have no overlapping terms or identifiers, capturing nuance and context. Similarity search is not limited to text.

Data Vectors

In the past, a data scientist might manually record a number of numerical characteristics of each data object, such as size, weight, location, and influence. Each characteristic would be normalized, e.g., scaled from -1 to 1. The characteristics would be listed in a standard sequence, so each object would be described by a normalized vector.  Then functions like cosine similarity or Euclidean distance, or even approximate nearest neighbor (ANN) methods, could be used to measure how similar two objects are, long before automated embedding models made vector creation easier.

The problem with this method is that some characteristics don’t fit on a linear scale. How do you scale “emotion”?  And if you are trying to recognize everyday objects, there’s no linear scale for that.

The recent development of embedding, a form of machine learning, makes it possible to “teach” a computer program to describe very complex objects with numeric vectors, sometimes very long vectors. The trick is that the meaning of individual vector dimensions is lost; each vector can only be treated as a whole. The big win, however, is that we get our similarity property.  If two vectors are numerically similar, then the objects they describe are similar. Moreover, each embedding model is customized for a particular type of data and for our intuition about similarity. AI always deals with complex data such as human language, such embedding vectors are the standard approach for modeling data. This approach enables far more flexible, semantic, and insightful retrieval.

What is Similarity Search?

Similarity search is the process of retrieving data items that are most alike a given input, based on a mathematical measure of closeness rather than strict equality. It plays a foundational role in modern AI systems, where identifying near matches is more useful, and often more challenging than finding exact duplicates.

Rather than relying on shared keywords or IDs, similarity search works by translating complex data into vector embeddings—multi-dimensional numeric representations that capture the underlying semantics or behavior of the item. These vectors can represent anything from product descriptions and user behavior to text, images, or graph structures.

Once embedded into a vector space, items are compared using similarity metrics that quantify how closely two items relate. These include:

• Cosine similarity: Measures the angle between two vectors to assess alignment. If two vectors point in nearly the same direction, their cosine similarity approaches 1, meaning they are semantically very similar. This metric is scale-invariant, making it ideal for applications like document and sentence similarity in natural language processing (NLP). That is, a long document can have high cosine similarity to a short document, if they are expressing very similar ideas.
• Euclidean distance (L2): Calculates the straight-line distance between two vectors in space. The smaller the distance, the more similar the items. Euclidean distance works well when absolute magnitude is important, such as comparing user behavior patterns or physical measurements.
• Inner product (dot product): Computes the sum of the products of corresponding vector components, reflecting how aligned and proportionally similar two vectors are. It’s frequently used in recommendation systems to score and rank content by relevance, especially when vectors are normalized.

Each metric offers different strengths depending on the context. Cosine similarity captures orientation and ignores scale differences. Euclidean distance captures magnitude-based difference. Inner product emphasizes directional similarity and is efficient for ranking.

In large-scale applications, datasets can include millions or billions of vectors. To search efficiently at that scale, Approximate Nearest Neighbor (ANN) algorithms are used. These methods speed up search dramatically by intelligently pruning the search space, returning results that are close to optimal with far less computational cost.

Similarity search is particularly valuable in environments where data is high-dimensional, unstructured, or noisy, and where “close enough” is essential for relevance.

The Core Concepts of Similarity Search

How It Works

1. Vectorization: The first step in similarity search is to convert input items—whether text, images, graph nodes, or user behaviors—into numerical representations called vector embeddings. These embeddings can be generated using large language models (like BERT, OpenAI embeddings) or through custom training. Each vector captures semantic or structural meaning, mapping complex data into a shared high-dimensional space.
2. Indexing: As the vectors are being stored in a vector database, the database builds an index to make searches more efficient. Most indexing schemes implement some form of Appropriate Nearest Neighbor (ANN) search. The index pre-groups vectors that are somewhat close to one another. Closeness can mean angular alignment (cosine similarity), physical distance (Euclidean), or magnitude of projection (inner product). The choice of metric depends on the type of data and the relevance criteria for the use case.
3. Nearest Neighbor Search: When the database is asked to find vectors that are similar to a query vector, it uses the index to perform a fast approximate search. Rather than scanning every vector individually (which would be computationally expensive), specialized search algorithms retrieve the top-k most similar items efficiently. Approximate Nearest Neighbor (ANN) methods speed this up by strategically narrowing the search, allowing near-real-time results even at massive scale.

The Key Components of Similarity Search

• Vector Embeddings: Dense numerical arrays that represent high-dimensional data in a format suitable for mathematical comparison. For example:
  • A customer’s shopping history may be embedded as a vector summarizing preferences.
  • A document may be embedded based on topic and tone.
  • A node in a graph may be embedded based on its structure and context.
• Similarity Metrics:
  • Cosine Similarity: Measures the angle between two vectors, effective when vector magnitude doesn’t matter (e.g., in NLP or behavioral comparisons).
  • Euclidean Distance (L2): Captures absolute difference between vectors; commonly used when actual proximity is meaningful (e.g., user activity levels).
  • Inner Product (Dot Product): Emphasizes direction and magnitude; useful in ranking scenarios like personalized recommendations.
• Index Structures:
  • HNSW (Hierarchical Navigable Small World): A multi-layered proximity graph that supports fast, scalable search by reducing the number of comparisons required.
  • IVF (Inverted File Index): Partitions the vector space into clusters and limits search to likely candidates, balancing speed and precision.
  • Annoy (Approximate Nearest Neighbors Oh Yeah): A tree-based method designed for memory-efficient, fast similarity lookups, particularly for recommendation systems and mobile apps. Spotify originally used it for recommending music tracks based on audio features and user preferences.

The Associated Methods of Similarity Search

LLM-Generated Embeddings:

Large Language Models (LLMs) like BERT, OpenAI embeddings, and SentenceTransformers convert unstructured inputs (like text) into dense vector representations. 

These vectors capture nuanced meaning, context, and intent, not just keywords. For instance, “physician” and “doctor” may be semantically similar even if the words are different, and their vectors will be close together.

These embeddings power applications like semantic search, question answering, chatbots, and recommendation engines by enabling systems to understand the conceptual intent behind queries and content. They’re especially effective in high-dimensional text analysis where synonymy, paraphrasing, and contextual shifts matter. Embeddings can be fine-tuned on specific domains (e.g., legal, healthcare) for improved precision.

Graph Embeddings:

Unlike LLM embeddings, graph embeddings focus on relational structure—how nodes are connected within a network. These methods (e.g., node2vec, GraphSAGE, GAT) learn vector representations of graph nodes based on the paths, neighbors, and communities they participate in.

This is crucial when similarity is defined by structure. Two users might appear unrelated by features, but graph embeddings could reveal they belong to the same fraud ring or influence cluster. 

In recommendation systems, for example, graph embeddings help uncover latent connections across users and products. They’re also used in fraud detection, biological pathway modeling, and supply chain risk analysis, where relationships carry more signal than standalone features.

How Similarity Search is different from Other Types of Search

• Similarity Search vs. Exact Match:

Exact match looks for results that match the query exactly, such as an email address or product ID. It’s fast and precise, but brittle: if the input varies slightly (e.g., typos, synonyms, paraphrasing), it fails.

Similarity search, by contrast, thrives in ambiguity. It uses distance metrics in embedding space to find nearby items—those that are conceptually or behaviorally similar, even if not textually identical. For example, a user searching for “best hiking backpack” might be shown results like “top-rated trail gear” or “ultralight trekking packs,” because their embeddings are semantically close. This flexibility is essential in modern AI-driven applications.

• Similarity Search vs. Graph Search

These two approaches differ fundamentally in how they model and retrieve information:

Similarity search operates in the embedding space. It ranks items based on how “close” they are in terms of learned meaning or behavior. It’s great for retrieval tasks where relationships are implicit, like image or document search, recommendation, or customer matching.

Graph search, on the other hand, walks through explicit connections in a graph (e.g., from person A to friend B to transaction C) to find things that are connected. It’s ideal for tracing paths, dependencies, or influence chains, especially in use cases like fraud detection, cybersecurity, or supply chain modeling.
In hybrid systems, the two methods work together: vector search retrieves relevant candidates, and graph search analyzes how those items are interconnected, surfacing deeper insights like shared ownership, network reach, or multi-hop influence paths.

Real-World Applications of Similarity Search

Product Recommendations: Suggest similar items based on prior purchases, co-viewed products, product descriptions, or behavioral embeddings. For example, a user who buys a noise-canceling headset may be shown high-fidelity earbuds—even if the brand or category differs—because their usage patterns and appeal overlap.

Semantic Search: Power natural language queries that return conceptually relevant documents. For example, a query like “natural ways to sleep better” might surface articles on melatonin or nighttime yoga, even if those terms aren’t in the query.

Anomaly Detection: Spot data points that are significantly distant from clusters of similar activity. For example, a login event from an unusual location or device may not match any known pattern and gets flagged for review.

Fraud Detection: Find accounts or transactions that behave like known fraudulent entities. Even when account numbers or IP addresses differ, vector similarity can highlight behavioral resemblance, while graph traversal confirms suspicious relationships.

Document De-duplication and Clustering: Group documents, resumes, legal filings, or emails that vary in wording but carry the same intent or structure. This reduces redundancy and streamlines discovery in enterprise search, legal tech, and HR platforms.

Customer 360 and Identity Matching: Connect fragmented customer records across systems by comparing embeddings derived from names, emails, IPs, addresses, or interactions. This helps create a unified view even when conventional fields don’t match precisely.