A systematic approach to normalization in probabilistic models.

Every information retrieval (IR) model embeds in its scoring function a form of term frequency (TF) quantification. The contribution of the term frequency is determined by the properties of the function of the chosen TF quantification, and by its TF normalization. The first defines how independent the occurrences of multiple terms are, while the second acts on mitigating the a priori probability of having a high term frequency in a document (estimation usually based on the document length). New test collections, coming from different domains (e.g. medical, legal), give evidence that not only document length, but in addition, verboseness of documents should be explicitly considered. Therefore we propose and investigate a systematic combination of document verboseness and length. To theoretically justify the combination, we show the duality between document verboseness and length. In addition, we investigate the duality between verboseness and other components of IR models. We test these new TF normalizations on four suitable test collections. We do this on a well defined spectrum of TF quantifications. Finally, based on the theoretical and experimental observations, we show how the two components of this new normalization, document verboseness and length, interact with each other. Our experiments demonstrate that the new models never underperform existing models, while sometimes introducing statistically significantly better results, at no additional computational cost.