Pages with this concept

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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 ...
	133	3 ...It must be emphasised that in the non linear case the estimation of the parameters for g x will ideally involve a different MST for each of P x w 1 and P x w 2 ...There is a choice of how one would implement the model for g x depending on whether one is interested in setting the cut off a prior or a posteriori ...If one assumes that the cut off is set a posteriori then we can rank the documents according to P w 1 x and leave the user to decide when he has seen enough ...to calculate estimate the probability of relevance for each document x ...
	128	objected to on the same grounds that one might object to the probability of Newton s Second Law of Motion being the case ...To approach the problem in this way would be useless unless one believed that for many index terms the distribution over the relevant documents is different from that over the non relevant documents ...The elaboration in terms of ranking rather than just discrimination is trivial:the cut off set by the constant in g x is gradually relaxed thereby increasing the number of documents retrieved or assigned to the relevant category ...If one is prepared to let the user set the cut off after retrieval has taken place then the need for a theory about cut off disappears ...
	119	and The importance of writing it this way,apart from its simplicity,is that for each document x to calculate g x we simply add the coefficients ci for those index terms that are present,i ...The constant C which has been assumed the same for all documents x will of course vary from query to query,but it can be interpreted as the cut off applied to the retrieval function ...Let us now turn to the other part of g x,namely ci and let us try and interpret it in terms of the conventional contingency table ...There will be one such table for each index term;I have shown it for the index term i although the subscript i has not been used in the cells ...This is in fact the weighting formula F 4 used by Robertson and Sparck Jones 1 in their so called retrospective experiments ...
	117	D 1 and D 2 can be shown to be equivalent under certain conditions ...[P x w 1 P w 1 >P x w 2 P w 2 >x is relevant,x is non relevant]D 3 Notice that P x has disappeared from the equation since it does not affect the outcome of the decision ...[R w 1 x <R w 2 x][[equivalence]][l 21 l 11 P x w 1 P w 1 >l 12 l 22 P x w 2 P w 2]When a special loss function is chosen,namely,which implies that no loss is assigned to a correct decision quite reasonable and unit loss to any error not so reasonable,then we have [R w 1 x <R w 2 x [[equivalence]]P x w 1 P w 1 >P x w 2 P w 2]which shows the equivalence of D 2 and D 3,and hence of D 1 and D 2 under a binary loss function ...This completes the derivation of the decision rule to be used to decide relevance or non relevance,or to put it differently to retrieve or not to retrieve ...Form of retrieval function The previous section was rather abstract and left the connection of the various probabilities with IR rather open ...