cosinesimilarityA

Cosine similarity is a measure of similarity between two non-zero vectors of an inner product space that measures the cosine of the angle between them. The cosine of the angle, when non-zero vectors are the comparison, is the dot product of the vectors divided by the product of their norms.

Mathematically, the cosine similarity between two vectors A and B is defined as:

similarity = cos(θ) = (A · B) / (||A|| ||B||)

where A · B is the dot product of vectors A and B, ||A|| is the norm (or magnitude) of vector A, and ||B|| is the norm of vector B.

The value of cosine similarity ranges from -1 to 1.

A similarity of 1 means that the vectors are identical in orientation (the angle between them is 0 degrees).

A similarity of 0 means that the vectors are orthogonal (the angle between them is 90 degrees), indicating no similarity.

A similarity of -1 means that the vectors are diametrically opposed in orientation (the angle between them is 180 degrees).

Cosine similarity is commonly used in data analysis and machine learning, particularly in text mining and information retrieval, to measure the similarity between documents. In this context, documents are often represented as vectors in a high-dimensional space, where each dimension corresponds to a word or term. The value of each dimension can be based on the frequency of the term in the document or other weighting schemes. By calculating the cosine similarity between document vectors, one can determine how similar the content of the documents is. It is also used in recommendation systems and clustering algorithms.