Kosinietäisyys

Kosinietäisyys, also known as cosine similarity, is a measure of similarity between two non-zero vectors of an inner product space. It is defined as the cosine of the angle between the two vectors. The formula for cosine similarity is:

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

where A and B are two vectors, A ⋅ B is their dot product, and ||A|| and ||B|| are their respective magnitudes (or Euclidean norms).

The value of cosine similarity ranges from -1 to 1. A similarity score of 1 means the vectors are identical in direction. A score of 0 means the vectors are orthogonal (perpendicular), indicating no similarity. A score of -1 means the vectors are diametrically opposed.

In practice, cosine similarity is often used in natural language processing (NLP) and information retrieval. Documents or text fragments are represented as vectors, typically using techniques like TF-IDF (Term Frequency-Inverse Document Frequency) or word embeddings. Cosine similarity is then used to measure how similar these documents are to each other, which can be useful for tasks like document clustering, duplicate detection, and recommendation systems. It is particularly effective for high-dimensional data where the magnitude of the vectors might not be as important as their orientation.