Cosine Similarity measures the cosine of the angle between two non-zero vectors in a multi-dimensional space. It is widely used in text analysis and data science to measure document similarity.

The value ranges from -1 (exactly opposite) to 1 (exactly the same), with 0 indicating orthogonality (uncorrelated).

The Formula:

$$ \text{Similarity} = \cos(\theta) = \frac{A \cdot B}{\|A\| \|B\|} = \frac{\sum_{i=1}^{n} A_i B_i}{\sqrt{\sum_{i=1}^{n} A_i^2} \sqrt{\sum_{i=1}^{n} B_i^2}} $$

Where:

• $A \cdot B$ is the dot product of vectors A and B.
• $\|A\|$ and $\|B\|$ are the magnitudes (or Euclidean norms) of vectors A and B.