Today, finding the most valuable information to your search is more complicated than finding a needle in a haystack. Traditional search engines match keywords and favor SEO-optimized content, but what if there was a way for search engines to truly understand the meaning behind our queries? Enter vector search – a powerful technology that is transforming how we navigate information, not just for users, but also for applications performing background searches. In this article, we will discuss what vector search is and how it works.

What is a vector search and why should you care?

Example Results with a traditional search for “Simple Fruit Cake”.

Vector search, which is also known as semantic search, is a technology that improves search accuracy by understanding the meaning (semantics) of the data and relations between its parts. Unlike traditional search, vector search efficiently handles synonyms, typos, ambiguous language, and broad or fuzzy queries. This is because it focuses on meaning, not just keywords.

Imagine that you are searching for a dessert to cook during the weekend. In a traditional search engine, the “simple fruit cake” query will reveal only websites that include these keywords. However, a vector search engine is able to provide results like “apple pie in 20 minutes” or “easy summer desserts”, which capture the essence of the query and align with your desire for a straightforward dessert option, providing more valuable results to you. 

At its core, vector search uses Large Language models (LLMs), like GPT, to transform data into mathematical vectors, also known as vector embeddings

What is a vector embedding?

2D Vector Space Representation. “Easy apple pie” is close to “simple fruit cake” as they are both simple and have fruit as an ingredient. “Easy chocolate mousse” shares simplicity but does not contain fruit. “Fancy plum cake” has fruit but is not simple to make. And “extravagant chocolate mousse” does not share either simplicity or fruit as an ingredient. Thus, it is the farthest from “simple fruit cake”.

A vector or vector embedding is a numerical representation of any kind of unstructured data (e.g. texts, images, videos, audio). It captures its meaning while being easy and efficient to compute with. Think of it like this: imagine you have a collection of cake recipes. You can convert each recipe into a vector embedding, which is like a unique numerical code that represents the recipe’s characteristics (ingredients, cooking methods, flavors, etc.).

Once all the recipes are encoded into embeddings, we can perform a similarity search. This means we can compare the vectors to see how similar the recipes are. For example, the vector for an easy apple pie recipe would be close to the vector for a simple fruit cake recipe because they share similar characteristics (e.g. simplicity, fruitiness). On the other hand, the vector for an extravagant chocolate mousse cake would be farther away because it involves different ingredients and methods.

How to compare vectors?

Vector similarity is a measure of how similar two vectors are (see ep. 4 of ObjectBox Bites). There are three ways to compare vectors: Jaccard Similarity, Cosine Similarity, and L2 Distance (also known as Euclidean distance). Jaccard Similarity calculates the ratio of elements that are common to both vectors divided by the total number of elements in both vectors. Cosine Similarity calculates the cosine of the angle between two vectors. The last method is the L2 distance. It calculates the straight-line distance between two points in space represented by the vectors. This is the most frequently used method in AI applications. It is important to note that the choice of vector comparison method does not affect the mechanics of similarity search.

What is a vector database and how is it related to vector search?

A vector database is a specialized database designed to store, manage, and search vectors efficiently. This efficiency is crucial for handling large datasets and performing fast vector similarity searches. Also, with a vector database, the knowledge of AI models can be improved, adapted, and updated. Therefore, today, most AI apps use a vector database.

Imagine having an AI that knows your habits, your preferences, your health data, maybe even what’s in your fridge, and can use this knowledge to suggest recipes that fit your lifestyle and individual preferences. A standard AI model doesn’t have that data and wouldn’t learn that way, but with a vector database it can. Now, when you search for a “fruit cake recipe”, using this data, it can suggest a “simple fruit cake” without sugar if you usually prefer quick, easy, and healthy recipes, or a “fancy plum cake” if you enjoy more challenging baking projects and don’t like apples. Or, a vegan option, if you have neither milk nor eggs left in the fridge.

This technique is called Retrieval-Augmented Generation (RAG). It enhances the capabilities of LLMs with additional data (e.g. personal data, company data, fresh data) stored in a vector database.

When you query a vector database, it uses the query’s vector representation to find the nearest neighbors in the database.

Nearest Neighbor Search

How do we find the nearest neighbor to our query vector? The most straightforward approach is a brute-force search. It calculates the distance between our query vector and all other vectors in the database, one by one. Any metrics discussed in “How to compare vectors” can be used. However, this brute-force approach has a time complexity of O(N*d), where N is the number of vectors and d is the dimensionality. This becomes computationally expensive for large datasets.

Since exact nearest neighbor search can be slow for massive datasets, we often turn to approximate nearest neighbor (ANN) algorithms. These algorithms prioritize efficiency by finding neighbors that are very close (but not necessarily the absolute closest) to the query vector, significantly reducing search time. 

Continuing with the cooking assistant app example, imagine you’re searching for a “fruit cake recipe”. Assume that in our database, the real closest recipe is “simple apple pie”. With a massive database, an exact nearest neighbor search might take a long time to find the perfect match. However, an ANN algorithm can quickly find a recipe that is very similar to what you’re looking for, such as a “simple fruit cake” or a “basic apple pie”, even if it might not be the exact closest match. This efficiency ensures you get relevant and useful recipe suggestions promptly, enhancing your overall experience without a noticeable compromise in quality.

Approximate Nearest Neighbour Search

Now, let’s delve into the world of Approximate Nearest Neighbor (ANN) algorithms. The way you search for nearest neighbors depends on how the data is stored in the vector database. One of the earliest ANN algorithms, established in 1975, is called k-d trees. These trees work by recursively splitting the data space using hyperplanes, making the search process more efficient (see ep. 5 of ObjectBox Bites). However, k-d trees, like many exact nearest neighbor algorithms, suffer from the dimensionality curse. This means that as the number of dimensions (features) in your data increases, the distance between points becomes less meaningful, making searching very slow in high-dimensional spaces like those used in vector databases. 

For instance, consider simple fruit recipes. With a few features, such as cooking time and number of ingredients, finding similar recipes would be relatively straightforward. However, if we also include many other features like sweetness level, calorie count, fruit type, all specific ingredients, preparation complexity, and user ratings, the number of dimensions increases significantly. In such high-dimensional spaces, the traditional k-d tree method becomes inefficient because the distances between points (recipes) become less distinct and meaningful.

To overcome this challenge, ANN algorithms leverage two main approaches: indexing methods and sketching methods. Indexing methods work by creating a hierarchical data structure that allows for faster exploration of the search space. Imagine a well-organized library with categorized sections instead of just randomly placed books.  Sketching methods, on the other hand,  don’t search the entire dataset directly.  Instead, they create compressed versions (sketches) of the data that are faster to compare with the query vector. This reduces the search time significantly. Often, these two approaches are combined for optimal performance.

A popular example of an ANN search implementation for high-dimensional data is the Hierarchical Navigable Small World (HNSW) algorithm (e.g. implemented in Azure AI). HNSW relies on graph-based indexing to efficiently navigate the data space and find nearest neighbors. For more details watch episodes 6, 7, and 8 of ObjectBox Bites miniseries, where we describe the fundamentals of HNSW.

Take-away notes

To sum up, vector search offers a significant leap forward in how we search for information. By understanding the meaning and relationships behind data, it delivers more relevant and accurate results, even for unstructured data and complex queries. This technology has the potential to revolutionize various fields, from enhancing search engines to empowering AI applications. As vector search continues to evolve, we can expect even more exciting possibilities for navigating the ever-growing ocean of information and unlocking its full potential. This includes operating with data directly on the devices it was created on, reducing cloud costs, eliminating the reliance on an internet connection, and opening up using your private data without it ever being shared (100% private). If you’re interested in other AI and vector database-related topics, check out the ObjectBox mini-series. Stay tuned for more articles in the future.