Paradox-free Formal Foundation of Vector Space Model

In the Vector Space Model (VSM) of Information Retrieval (IR), the documents and queries are conceived as vectors of weights belonging to the same linear space, and retrieval is based on similarity measures. This view yields paradoxes and problems as regards concepts of fundamental importance to IR (similarity, term independence, preference, linearity). In the present paper, a different view is proposed: the VSM of IR may be conceived as a probability space that decreases the amount of the Shannon information associated to the selection of documents as answers to queries. This view can serve as another formal foundation of the VSM that is paradox-free and, at the same time, preserves the computational practice developed thus far. Experiments are also reported to reflect this view in practice.