Ähnlichkeitsabfragen ausführen

Welcome! In this lesson, we'll dive into one of the most powerful features of vector databases: similarity queries.

You'll learn how to ask your database to find items that are 'similar' to a given item, based on their vector embeddings.

Similarity queries are at the heart of many AI applications:

• Recommendation Systems: Find products similar to what a user liked.
• Semantic Search: Retrieve documents with similar meaning, not just keyword matches.
• Anomaly Detection: Identify data points that are unusually 'far' from others.

They help us make sense of high-dimensional data.

How do we define 'similarity' for vectors? We use distance metrics.

Imagine vectors as points in space. The 'closer' two points are, the more similar their underlying data is. Different metrics measure this distance in different ways.

Euclidean distance, also known as L2 distance, is the most intuitive metric. It's the straight-line distance between two points in a Euclidean space.

In pgvector, you use the <-> operator to calculate Euclidean distance. A smaller value means higher similarity.

Cosine similarity measures the cosine of the angle between two vectors. It tells you if vectors are pointing in roughly the same direction, regardless of their magnitude (length).

pgvector uses the <#> operator for cosine distance. Cosine distance is 1 - cosine_similarity. A smaller cosine distance (closer to 0) means the vectors are more aligned and similar.

To demonstrate queries, let's set up a simple table with some 3-dimensional vectors. This ensures our code snippets are runnable.

Now, let's find the 3 items whose embeddings are closest to [1,2,3] using Euclidean distance.

Notice the <-> operator in action!

When you run the query, you'll see a euclidean_distance column. The items with the smallest distance values are the most similar to your query vector [1,2,3].

For example, [1.1,2.1,3.1] should have a very small Euclidean distance, indicating high similarity.

Next, let's perform a similarity search using cosine distance. We'll again query for items similar to [1,2,3].

Observe the <#> operator. Remember, it returns cosine distance, where lower values mean higher similarity.

The cosine_distance column shows how aligned the vectors are. A value close to 0 means the vectors point in almost the same direction (very similar).

A value close to 2 means they point in opposite directions (very dissimilar). Values near 1 mean they are orthogonal.

Which metric should you use?

• Euclidean distance is great when the magnitude (length) of the vector is important.
• Cosine similarity/distance is preferred when only the direction of the vector matters, not its length. This is common for text embeddings where vector length might vary but direction captures semantic meaning.

You've learned about two key pgvector operators for similarity queries. Let's test your knowledge!

Great job! You've learned how to perform similarity queries with pgvector.

• We use distance metrics to quantify similarity.
• Euclidean distance (<->) measures straight-line distance.
• Cosine distance (<#>) measures the angle between vectors.
• Choosing the right metric depends on whether vector magnitude or direction is more relevant for your data.