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Is paragraph2vec the same as Doc2vec or is every approach different?

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There may be differing implementations, but these two terms refer to the same thing.

Both convert a generic block of text into a vector similarly to how word2vec converts a word to vector. Paragraph vectors don't need to refer to paragraphs as they are traditionally laid out in text. They can theoretically be applied to phrases, sentences, paragraphs, or even larger blocks of text.

Here's one definition of a paragraph vector:

An unsupervised algorithm that learns fixed-length feature representations from variable-length pieces of texts, such as sentences, paragraphs, and documents.

And the full paper if you are interested:

https://cs.stanford.edu/~quocle/paragraph_vector.pdf

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