What is a common way to calculate similarity in an embedding space?

Cosine similarity is a widely used measure to calculate the similarity between two vectors in an embedding space. This method evaluates the cosine of the angle between the vectors, which can effectively capture how similar the two vectors are in terms of direction, irrespective of their magnitude. When vectors represent data points in a high-dimensional space, cosine similarity provides a normalized measure that is particularly useful, especially in contexts such as natural language processing or when dealing with various types of embeddings.

The strength of cosine similarity lies in its ability to focus on the orientation of the vectors rather than their absolute lengths. This makes it especially effective in scenarios where the scale of the embedding may vary, and where the direction of the vector is more important than its magnitude.

In contrast, other methods like Euclidean distance quantify similarity by measuring the straight-line distance between two points in a space, which can be sensitive to the scale of the data, potentially leading to misleading results if the vectors are not normalized. Logistic regression is primarily a classification algorithm rather than a similarity measure, and feature elimination is a strategy used in feature selection, focusing on improving model performance rather than calculating similarity between data points.