Methods that I know of
- Bag of words + weighting: tf-idf, bm25
- Topic models: LSA, LDA
- Word/sentence/document embedding
Are there other commonly used methods to represent a document by a vector?
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Aside from unsupervised methods like doc2vec, there are couple of supervised methods:
All of them aims to create vector representations for documents, so dot product of vectors would represent semantically similar of documents.
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In the topic models category there is also NMF (Non-negative matrix factorization)