Cosineavstanden

Cosineavstanden is a measure of similarity between two non-zero vectors of an inner product space that measures the cosine of the angle between them. It is often used in natural language processing and information retrieval to determine the similarity of documents. The cosine distance is defined as 1 minus the cosine similarity. Cosine similarity ranges from -1 to 1, where 1 means the vectors are identical, 0 means they are orthogonal, and -1 means they are diametrically opposed. Cosine distance, therefore, ranges from 0 to 2, where 0 means the vectors are identical, 1 means they are orthogonal, and 2 means they are diametrically opposed.

The formula for cosine similarity between two vectors A and B is:

similarity = (A . B) / (||A|| * ||B||)

where '.' denotes the dot product and '|| ||' denotes the Euclidean norm (or L2 norm).

The formula for cosine distance is:

distance = 1 - similarity

Cosineavstanden is particularly useful when the magnitude of the vectors is not important, such as when comparing documents of different lengths. For example, two documents that discuss the same topic but have different numbers of words can still be considered similar if their word vectors have a high cosine similarity. This is because the cosine similarity only considers the direction of the vectors, not their length.

---