What metric is used to measure the similarity of two documents regardless of their size?

Cosine Similarity is the appropriate metric for measuring the similarity of two documents regardless of their size, particularly in the context of text and vector space models. This metric assesses the cosine of the angle between two non-zero vectors. By focusing on the direction rather than the magnitude of the vectors, Cosine Similarity effectively captures the similarity in content between two documents, making it particularly useful in situations where document length may vary significantly.

In practical terms, this means that even if one document is much longer than another, Cosine Similarity can still judge their content similarity based on how closely the vectors align in the multi-dimensional space defined by the terms or features involved. This is particularly beneficial in natural language processing and information retrieval, where the relevance of documents needs to be determined without being skewed by their length.

Other metrics, like Jaccard Similarity and Hamming Distance, are less effective for this purpose. Jaccard Similarity measures the size of the intersection divided by the size of the union of two sets, which may not be optimal for continuous data like text vectors. Hamming Distance applies well to fixed-length strings and does not account for the directionality of the vectors, while Euclidean Distance measures the straight-line distance between two points in