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Before any of this involved learning, it involved geometry. Salton, Wong, and Yang proposed representing each document as a vector of weighted index terms and ranking documents by the similarity of their vectors to a query vector, arguing that a well-separated document space — one where unrelated documents sit far apart — should correspond to better retrieval performance than a densely packed one [ 1 ] . Their paper is worth reading in the original rather than through summary, because the term-weighting scheme it specifies is exactly the ancestor of what every later retriever, sparse or dense, still does: score a term by how often it occurs locally and how rare it is globally. They define the inverse document frequency of a term k , for a collection of n documents in which k appears in $d_k$ of them, as $(\mathrm{IDF})_k = \lceil \log_2 n \rceil - \lceil \log_2 d_k \rceil + 1$. and combine it multiplicatively with raw term frequency so that a term scores highest when it occurs often in one document but rarely across the collection. Evaluated on three test collections in aerodynamics, medicine, and world affairs, replacing raw term-frequency weighting with this scheme, together with a term-discrimination-value model for phrase and thesaurus construction, improved average recall-precision by 17 to 50 percent depending on the collection [ 1 ] .