Koszinuszhasonlóság

Koszinuszhasonlóság is a Hungarian term that translates to "cosine similarity" in English. It 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 similarity is a measure of orientation, not magnitude. It is widely used in data mining and information retrieval for tasks such as document similarity and text analysis.

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

cos(θ) = (A ⋅ B) / (||A|| ||B||)

where A ⋅ B is the dot product of vectors A and B, and ||A|| and ||B|| are the magnitudes (or Euclidean norms) of vectors A and B, respectively.

The value of cosine similarity ranges from -1 to 1. A value of 1 indicates that the vectors are identical in direction, while a value of -1 indicates that they are diametrically opposed. A value of 0 means that the vectors are orthogonal, or that there is no correlation between them.

In the context of text analysis, documents are often represented as vectors, where each dimension corresponds to a word and the value in that dimension represents the frequency or importance of that word in the document. Cosine similarity is then used to determine how similar two documents are based on their shared vocabulary and word frequencies. This is particularly useful in search engines and recommendation systems for finding relevant content.