Cosine Similarity and Cosine Distance for Comparing Vectors

Summary

The document introduces cosine similarity as a way to compare two vectors by the angle between them. It also describes the equivalent calculation as their dot product divided by the product of their magnitudes. Cosine distance is presented as one minus cosine similarity, making the two measures directly related.

These definitions are useful when representing observations as vectors, including in quantitative research workflows that compare feature profiles or signals. The post offers a simple conceptual explanation and mentions an accompanying example, but the example itself is not included in the supplied text. It also flags that the cited explanation contains an incorrect cosine value for a 45-degree angle. No trading application, empirical evidence, or guidance on normalization, zero-length vectors, or interpreting the measures in a specific dataset is provided.

Key ideas

• Cosine similarity compares two vectors using the cosine of the angle between them.
• It can be computed from the dot product divided by the vectors’ magnitudes.
• Cosine distance is defined here as one minus cosine similarity.
• The referenced simple example is not included, and the post notes an error in its cosine value.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.