Page 121 Concepts and similar pages

Concepts

Similarity Concept
First order tree dependence
Dependence tree
Dependence stochastic
Generality
Information content
Information structure
Information measure
Similarity matrix generation
Function word
Data independence

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123 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 ...
122 an edge ...IMG SRC P ...Applying this to the link between the root node x 1 and its immediate descendant x 2 in the example will shift the root to x 2 and change the expansion to Pt x 1,x 2,...Of course,to satisfy the rule about relabelling we would exchange the names 1 and 2 ...In what follows I shall assume that the relabelling has been done and that xmi xi ...Selecting the best dependence trees Our problem now is to find a probability function of the form Pt x on a set of documents which is the bestapproximation to the true joint