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between the algorithms of Rocchio,Rieber and Marathe,Bonner see below and his own
...One further algorithm that should be mentioned here is that due to Litofsky [28]...Finally,the Bonner [45]algorithm should be mentioned
...The major advantage of the algorithmically defined cluster methods is their speed:order n log n where n is the number of objects to be clustered compared with order n 2 for the methods based on association measures
...One obvious omission from the list of cluster methods is the group of mathematically or statistically based methods such as Factor Analysis and Latest Class Analysis
...The method of single link avoids the disadvantages just mentioned
...Single link The dissimilarity coefficient is the basic input to a single link clustering algorithm
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In general the dependence can be arbitrarily complex as the following identity illustrates,P x P x 1 P x 2 x 1 P x 3 x 1,x 2
...Therefore,to capture all dependence data we would need to condition each variable in turn on a steadily increasing set of other variables
...where m 1,m 2,...Pt x P x 1 P x 2 x 1 P x 3 x 2 P x 4 x 2 P x 5 x 2 P x 6 x 5 Notice how similar the A 2 assumption is to the independence assumption A 1,the only difference being that in A 2 each factor has a conditioning variable associated with it
...The permutation and the function j
...write the function Pt x the way I did with xi as the unconditioned variable,and hence the root of the tree,and all others consistently conditioned each on its parent node,in fact any one of the nodes of the tree could be singled out as the root as long as the conditioning is done consistently with respect to the new root node
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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
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probability function P x,and of course a better approximation than the one afforded by making assumption A 1
...The goodness of the approximation is measured by a well known function see,for example,Kullback [12];if P x and Pa x are two discrete probability distributions then That this is indeed the case is shown by Ku and Kullback [11]...is a measure of the extent to which P a x approximates P x
...If the extent to which two index terms i and j deviate from independence is measured by the expected mutual information measure EMIM see Chapter 3,p 41
...then the best approximation Pt x,in the sense of minimising I P,Pt,is given by the maximum spanning tree MST see Chapter 3,p
...is a maximum
...One way of looking at the MST is that it incorporates the most significant of the dependences between the variables subject to the global constraint that the sum of them should be a maximum
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