Abstract
On internet today, an overabundance of information can be accessed, making it difficult for users to process and evaluate options and make appropriate choices. This phenomenon is known as information overload. Over time, various methods of information filtering have been introduced in order to assist users in choosing what may be of their interest. Recommender Systems (RS) [14] are techniques for information filtering which play an important role in e-commerce, advertising, e-mail filtering, etc. Therefore, RS are an answer, though partial, to the problem of information overload. Recommendation algorithms need to be continuously updated because of a constant increase in both the quantity of information and ways of access to that information, which define the different contexts of information use. The research of more effective and more efficient methods than those currently known in literature is also stimulated by the interests of industrial research in this field, as demonstrated by the Netflix Prize Contest, the open competition for the best algorithm to predict user ratings for films, based on previous ratings. The contest showed the superiority of mathematical methods that discover latent factors which drives user-item similarity, with respect to classical collaborative filtering algorithms. With the ever-increasing information available in digital archives and textual databases, the challenge of implementing personalized filters has become the challenge of designing algorithms able to manage huge amounts of data for the elicitation of user needs and preferences. In recent years, matrix factorization techniques have proved to be a quite promising solution to the problem of designing efficient filtering algorithms in the Big Data Era. The main contribution of this paper is an analysis of these methods, which focuses on tensor factorization techniques, as well as the definition of a method for tensor factorization suitable for recommender systems.
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References
Acar, E., Dunlavy, D.M., Kolda, T.G., Mørup, M.: Scalable tensor factorizations with missing data. In: SDM 2010: Proceedings of the 2010 SIAM International Conference on Data Mining, Philadelphia, pp. 701–712. SIAM (April 2010)
Adomavicius, G., Sankaranarayanan, R., Sen, S., Tuzhilin, A.: Incorporating contextual information in recommender systems using a multidimensional approach. ACM Trans. Inf. Syst. 23(1), 103–145 (2005)
Bennett, J., Lanning, S.: The netflix prize. In: Proceedings of the KDD Cup Workshop 2007, pp. 3–6. ACM, New York (2007)
Carroll, J., Chang, J.-J.: Analysis of individual differences in multidimensional scaling via an n-way generalization of ”eckart-young” decomposition. Psychometrika 35(3), 283–319 (1970)
Funk, S.: Netflix update: Try this at home (2006), http://sifter.org/~simon/journal/20061211.html
Harshman, R.A.: Foundations of the PARAFAC Procedure: Models and Conditions for an ”explanatory” Multi-modal Factor Analysis. In: Working papers in phonetics, vol. 1(16), University of California at Los Angeles (1970)
Karatzoglou, A., Amatriain, X., Baltrunas, L., Oliver, N.: Multiverse recommendation: n-dimensional tensor factorization for context-aware collaborative filtering. In: Proceedings of the fourth ACM Conference on Recommender Systems, RecSys 2010, pp. 79–86. ACM, New York (2010)
Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2009)
Koren, Y.: Factorization meets the neighborhood: a multifaceted collaborative filtering model. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2008, pp. 426–434. ACM, New York (2008)
Koren, Y., Bell, R., Volinsky, C.: Matrix factorization techniques for recommender systems. IEEE Computer 42(8), 30–37 (2009)
Kurucz, M., Benczúr, A.A., Torma, B.: Methods for large scale svd with missing values. In: KDDCup 2007 (2007)
De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21, 1253–1278 (2000)
Rendle, S., Marinho, L.B., Nanopoulos, A., Schmidt-Thieme, L.: Learning optimal ranking with tensor factorization for tag recommendation. In: KDD, pp. 727–736 (2009)
Ricci, F., Rokach, L., Shapira, B., Kantor, P.B. (eds.): Recommender Systems Handbook. Springer (2011)
Sarwar, B., Karypis, G., Konstan, J., Riedl, J.: Incremental singular value decomposition algorithms for highly scalable recommender systems. In: Fifth International Conference on Computer and Information Science, pp. 27–28 (2002)
Shi, Y., Karatzoglou, A., Baltrunas, L., Larson, M., Hanjalic, A., Oliver, N.: Tfmap: optimizing map for top-n context-aware recommendation. In: Proceedings of the 35th International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR 2012, pp. 155–164. ACM, New York (2012)
Sun, J.-T., Zeng, H.-J., Liu, H., Lu, Y., Chen, Z.: Cubesvd: a novel approach to personalized web search. In: Proceedings of the 14th International Conference on World Wide Web, WWW 2005, pp. 382–390. ACM, New York (2005)
Tomasi, G., Bro, R.: Parafac and missing values. Chemometrics and Intelligent Laboratory Systems 75(2), 163 (2005)
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Ricci, G., de Gemmis, M., Semeraro, G. (2014). Mathematical Methods of Tensor Factorization Applied to Recommender Systems. In: Catania, B., et al. New Trends in Databases and Information Systems. Advances in Intelligent Systems and Computing, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-319-01863-8_40
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DOI: https://doi.org/10.1007/978-3-319-01863-8_40
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