Infinitesimal reasoning in information retrieval and trust-based recommendation systems




Chowdhury, Maria

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We propose preferential and trust-based frameworks for Information Retrieval and Recommender Systems, which utilize the power of Hyperreal Numbers. In the first part of our research, we propose a preferential framework for Information Retrieval which enables expressing preference annotations on search keywords and document elements, respectively. Our framework is flexible and allows expressing preferences such as “A is infinitely more preferred than B,” which we capture by using hyperreal numbers. Due to widespread use of XML as a standard for representing documents, we consider XML documents in this research and propose a consistent preferential weighting scheme for nested document elements. We show how to naturally incorporate preferences on search keywords and document elements into an IR ranking process using the well-known TF-IDF (Term Frequency - Inverse Document Frequency) ranking measure. In the second part of our research we propose a novel recommender system which enhances user-based collaborative filtering by using a trust-based social network. Again, we use hyperreal numbers and polynomials for capturing natural preferences in aggregating opinions of trusted users. We use these opinions to “help” users who are similar to an active user to come up with recommendations for items for which they might not have an opinion themselves. We argue that the method we propose reflects better the real life behaviour of the people. Our method is justified by the experimental results; we are the first to break a stated “barrier” of 0.73 for the mean absolute error (MAE) of the predicted ratings. Our results are based on a large, real life dataset from, for which, we also achieve a prediction coverage that is significantly better than that of the state-of-the-art methods.



Information Retrieval, Recommendation Systems, Search Engine, Trust-based network, hyperreal numbers, infinitesimal