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Aggregation Functions for Recommender Systems

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Recommender Systems Handbook

Abstract

This chapter gives an overview of aggregation functions and their use in recommender systems. The classical weighted average lies at the heart of various recommendation mechanisms, often being employed to combine item feature scores or predict ratings from similar users. Some improvements to accuracy and robustness can be achieved by aggregating different measures of similarity or using an average of recommendations obtained through different techniques. Advances made in the theory of aggregation functions therefore have the potential to deliver increased performance to many recommender systems. We provide definitions of some important families and properties, sophisticated methods of construction, and various examples of aggregation functions in the domain of recommender systems.

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Notes

  1. 1.

    We note here also that such rules could be used in any RS to decide when to recommend items, e.g. “IF user is inactive THEN recommend something”.

  2. 2.

    Idempotency and averaging behavior are equivalent for aggregation functions due to the monotonicity requirement. This property is sometimes referred to as unanimity since the output agrees with each input when the inputs are unanimous.

  3. 3.

    The Lipschitz property for quasi-arithmetic means and other generated aggregation functions is explored in [13].

  4. 4.

    A set function is a function whose domain consists of all possible subsets of \(\mathcal{N}\). For example, for n = 3, a set function is specified by 23 = 8 values at v(∅), v({1}), v({2}), v({3}), v({1, 2}), v({1, 3}), v({2, 3}), v({1, 2, 3}).

  5. 5.

    All examples in this section utilize the software packages aotool and fmtools [9]. Versions have also been created in the R programming language, available at http://aggregationfunctions.wordpress.com/r-code and http://www.tulip.org.au/resources/rfmtool.

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Authors and Affiliations

  1. School of Information Technology, Deakin University, 221 Burwood Hwy, Burwood, VIC, 3125, Australia

    Gleb Beliakov & Simon James

  2. Departamento de Ciencias de la Computación, Universidad de Alcalá, 28871 Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

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  1. Gleb Beliakov
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  2. Tomasa Calvo
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  3. Simon James
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Correspondence to Simon James .

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Editors and Affiliations

  1. Faculty of Computer Science, Free University of Bozen-Bolzano, Bolzano - Bozen, Italy

    Francesco Ricci

  2. Information Systems Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Lior Rokach

  3. Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Bracha Shapira

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Beliakov, G., Calvo, T., James, S. (2015). Aggregation Functions for Recommender Systems. In: Ricci, F., Rokach, L., Shapira, B. (eds) Recommender Systems Handbook. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7637-6_23

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  • DOI: https://doi.org/10.1007/978-1-4899-7637-6_23

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