Dimensionality reduction

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129 we work with the ratio In the latter case we do not see the retrieval problem as one of discriminating between relevant and non relevant documents,instead we merely wish to compute the P relevance x for each document x and present the user with documents in decreasing order of this probability ...The decision rules derived above are couched in terms of P x wi ...I will now proceed to discuss ways of using this probabilistic model of retrieval and at the same time discuss some of the practical problems that arise ...The curse of dimensionality In deriving the decision rules I assumed that a document is represented by an n dimensional vector where n is the size of the index term vocabulary ...
163 normalising the ESL by a factor proportional to the expected number of non relevant documents collected for each relevant one ...which has been called the expected search length reduction factor by Cooper ...where 1 R is the total number of documents in the collection relevant to q;2 I is the total number of documents in the collection non relevant to q;3 S is the total desired number of documents relevant to q ...The explicit form for ESL was given before ...which is known as the mean expected search length reduction factor ...Within the framework as stated at the head of this section this final measure meets the bill admirably ...For a further defence of its subjective nature see Cooper [1]...