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Cosine similarity and Jaccard similarity are two widely used metrics in data science and big data for measuring the similarity between data objects, especially in text analytics, recommendation systems, and clustering tasks. Cosine similarity measures the cosine of the angle between two non-zero vectors in a multi-dimensional space. It focuses on the orientation rather than magnitude, which makes it suitable for comparing documents with different lengths. Mathematically, for two vectors A and B, cosine similarity is calculated as the dot product of A and B divided by the product of their magnitudes: Cosine Similarity = (A · B) / (||A|| \* ||B||). For example, consider two text documents represented as term frequency vectors: Document 1 = \[1, 2, 0, 3] and Document 2 = \[2, ______ ______ ______ ___ __________ ___ ____ ________ __________ _________ _________ __________.
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