Geometric representations for multiple documents

Combining multiple documents to represent an information object is well-known as an effective approach for many Information Retrieval tasks. For example, passages can be combined to represent a document for retrieval, document clusters are represented using combinations of the documents they contain, and feedback documents can be combined to represent a query model. Various techniques for combination have been introduced, and among them, representation techniques based on concatenation and the arithmetic mean are frequently used. Some recent work has shown the potential of a new representation technique using the geometric mean. However, these studies lack a theoretical foundation explaining why the geometric mean should have advantages for representing multiple documents. In this paper, we show that the arithmetic mean and the geometric mean are approximations to the center of mass in certain geometries, and show empirically that the geometric mean is closer to the center. Through experiments with two IR tasks, we show the potential benefits for geometric representations, including a geometry-based pseudo-relevance feedback method that outperforms state-of-the-art techniques.