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The representation of documents as vectors is fundamentally lossy: the relative order of terms in a document is lost in the encoding of a document as a vector. Even if we were to try and somehow treat every biword as a term (and thus an axis in the vector space), the weights on different axes not independent: for instance the phrase German shepherd gets encoded in the axis german shepherd, but immediately has a non-zero weight on the axes german and shepherd. Further, notions such as idf would have to be extended to such biwords. Thus an index built for vector space retrieval cannot, in general, be used for phrase queries. Moreover, there is no way of demanding a vector space score for a phrase query -- we only know the relative weights of each term in a document.
On the query german shepherd, we could use vector space retrieval to identify documents heavy in these two terms, with no way of prescribing that they occur consecutively. Phrase retrieval, on the other hand, tells us of the existence of the phrase german shepherd in a document, without any indication of the relative frequency or weight of this phrase. While these two retrieval paradigms (phrase and vector space) consequently have different implementations in terms of indexes and retrieval algorithms, they can in some cases be combined usefully, as in the three-step example of query parsing in Section 7.2.3 .
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2009-04-07