Computational geometry: an introduction
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This paper analyzes the properties, structures and limitations of vector-based models for information retrieval from the computational geometry point of view. It is shown that both the pseudo-cosine and the standard vector space models can be viewed as special cases of a generalized linear model. More importantly, both the necessary and sufficient conditions have been identified, under which ranking functions such as the inner-product, cosine, pseudo-cosine, Dice, covariance and product-moment correlation measures can be used to rank the documents. The structure of the solution region for acceptable ranking is analyzed and an algorithm for finding all the solution vectors is suggested.