Modelling documents with multiple poisson distributions

Abstract

This paper is the initial report of a study attempting to find a useful statistical model of large collections of full text documents. We investigate the validity of the Multiple Poisson ( nP) model of word distribution in document collections. An nP distribution is a mixture of n Poisson distributions with different means. We describe a practical algorithm for determining if a certain word is distributed according to an nP distribution. The algorithm is applied to every term (reduced word) in three different document collections. It was found that over 70% of frequently occurring terms indeed behave according to the nP distributions. The results indicate that the proportion of nP terms is even higher (over 80%) for the collections in which documents have similar length. Most of the nP terms recognised are distributed according to the mixture of relatively few single Poisson distributions (two, three, or four). There is an indication that the number of single Poisson components in the mixture depends on the collection frequency of terms.