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| 171 |
In other words we are ensuring that the equation R,P R,P is soluble for R provided that there exist R,R such that R,P >R,P >R,P
...The fifth condition is not limiting in any way but needs to be stated
...Definition 5
...Thus we require that variation in one while leaving the other constant gives a variation in effectiveness
...Finally we need a technical condition which will not be explained here,that is the Archimedean property for each component
...We now have six conditions on the relational structure <R x P,>>which in the theory of measurement are necessary and sufficient conditions for it to be an additive conjoint structure
...In our case we can therefore expect to find real valued functions [[Phi]]1 on R and [[Phi]]2 on P and a function F from Re x Re into Re,1:1 in each variable,such that,for all R,R [[propersubset]]R and P,P [[propersubset]]P we have:R,P >R,P <>F [[[Phi]]1 R,[[Phi]]2 P]>F [[[Phi]]1 R,[[Phi]]2 P]Note that although the same symbol >is used,the first is a binary relation on R x P,the second is the usual one on Re,the set of reals
...In other words there are numerical scales [[Phi]]i on the two components and a rule F for combining them such that the resultant measure preserves the qualitative ordering of effectiveness
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| 172 |
structures are decomposable
...A further simplification of the measurement function may be achieved by requiring a special kind of non interaction of the components which has become known as additive independence
...R,P >R,P <>[[Phi]]1 R [[Phi]]2 P >[[Phi]]1 R [[Phi]]2 P where F is simply the addition function
...R,P >R,P <>[[Phi]]1 R [[Phi]]2 P [[Phi]]1 R [[Phi]]2 P >[[Phi]]1 R [[Phi]]2 P [[Phi]]1 R [[Phi]]2 P It can be shown that starting at the other end given an additively independent representation the properties defined in 1 and 3,and the Archimedean property are necessary
...Here the term [[Phi]]1 [[Phi]]2 is referred to as the interaction term,its absence accounts for the non interaction in the previous condition
...We are now in a position to state the main representation theorem
...Theorem Suppose <R x P,>>is an additive conjoint structure,then there exist functions,[[Phi]]1 from R,and [[Phi]]2 from P into the real numbers such that,for all R,R [[propersubset]]R and P,P [[propersubset]]P:R,P >R,P <>[[Phi]]1 R [[Phi]]2 P >[[Phi]]1 R [[Phi]]2 P If [[Phi]]i []are two other functions with the same property,then there exist constants [[Theta]]>0,[[gamma]]1,and [[gamma]]2 such that [[Phi]]1 [][[Theta]][[Phi]]1 [[gamma]]1 [[Phi]]2 [][[Theta]][[Phi]]2 [[gamma]]2 The proof of this theorem may be found in Krantz et al
...Let us stop and take stock of this situation
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| 185 |
approaching this problem of speeding up clustering is to look for what one might call almost classifications
...A big question,that has not yet received much attention,concerns the extent to which retrieval effectiveness is limited by the type of document description used
...Document classification is a special case of a more general process which would also attempt to exploit relationships between documents
...An argument parallel to the one in the last paragraph could be given for automatic keyword classification,which in the more general context might be called automatic content unit classification
...H
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DAMERAU,F
...DAMERAU,F
...DATE,C
...DATTOLA,R
...DATTOLA,R
...DE FINETTI,B
...DENNIS,S
...DISISS,Design of information systems in the social sciences
...DODD,G
...DOROFEYUK,A
...DOYLE,L
...DOYLE,L
...DOYLE,L
...DOYLE,L
...DOYLE,L
...DOYLE,L
...DUDA,R
...EDMUNDSON,H
...EFRON,B
...EIN DOR,P
...ELLIS,B
...ETZWEILER,L
...EVERITT,B
...FAIRTHORNE,R
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have been clustered as clustered files
...Some of the work that has been largely ignored in this chapter,but which is nevertheless of importance when considering the implementation of a file structure,is concerned directly with the physical organisation of a storage device in terms of block sizes,etc
...References 1
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