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| 98 |
is another example of a matching function
...A popular one used by the SMART project,which they call cosine correlation,assumes that the document and query are represented as numerical vectors in t space,that is Q q 1,q 2,...or,in the notation for a vector space with a Euclidean norm,where [[theta]]is the angle between vectors Q and D
...Serial search Although serial searches are acknowledge to be slow,they are frequently still used as parts of larger systems
...Suppose there are N documents Di in the system,then the serial search proceeds by calculating N values M Q,Di the set of documents to be retrieved is determined
...1 the matching function is given a suitable threshold,retrieving the documents above the threshold and discarding the ones below
...2 the documents are ranked in increasing order of matching function value
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keyword is indicated by a zero or one in the i th position respectively
...where summation is over the total number of different keywords in the document collection
...Salton considered document representatives as binary vectors embedded in an n dimensional Euclidean space,where n is the total number of index terms
...can then be interpreted as the cosine of the angular separation of the two binary vectors X and Y
...where X,Y is the inner product and
...X x 1,...we get Some authors have attempted to base a measure of association on a probabilistic model [18]...When xi and xj are independent P xi P xj P xi,xj and so I xi,xj 0
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| 106 |
account of past performance
...Consider now a retrieval strategy that has been implemented by means of a matching function M
...It is the aim of every retrieval strategy to retrieve the relevant documents A and withhold the non relevant documents A
...the decision procedure M Q,D T >0 corresponds to a linear discriminant function used to linearly separate two sets A and A in R [t]...M Q 0,D >T whenever D [[propersubset]]A and M Q 0,D <T whenever D [[propersubset]][[Alpha]]The interesting thing is that starting with any Q we can adjust it iteratively using feedback information so that it will converge to Q 0
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| 107 |
exists there is an iterative procedure which will ensure that Q will converge to Q 0 in a finite number of steps
...The iterative procedure is called the fixed increment error correction procedure
...It goes as follows:Qi Qi 1 cD if M Qi 1,D T <0 and D [[propersubset]]A Qi Qi 1 cD if M Qi 1,D T >0 and D [[propersubset]]A and no change made to Qi 1 if it diagnoses correctly
...The situation in actual retrieval is not as simple
...Once again this is not the whole story
...If M is taken to be the cosine function Q,D Q D then it is easy to show that [[Phi]]is maximised by where c is an arbitrary proportionality constant
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