Cosine similarity is a metric that measures the similarity of two non-zero vectors, focusing on their direction rather than magnitude. It determines how closely two vectors point in the same direction by calculating the cosine of the angle between them. Linear Algebra, the mathematical foundation of cosine similarity, deals with linear functions, vectors, and matrices.
To calculate cosine similarity, you need to follow these steps:
- Calculate the dot product of the vectors
- Calculate the magnitude of each vector
- Combine the results using the cosine similarity formula
Example Calculation:
Consider two vectors A = [1, 2, 3] and B = [4, 5, 6]. By calculating the dot product and magnitude of each vector, you can determine their cosine similarity.
Interpretation:
The cosine similarity ranges from -1 to 1: 1 indicates identical direction, 0 indicates orthogonality, and -1 indicates diametric opposition.
Applications:
Cosine similarity is used in recommender systems like YouTube and Spotify to suggest music based on user preferences. It is also utilized in natural language processing for tasks such as text prediction, similarity analysis, and plagiarism detection.