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EigenRec: generalizing PureSVD for effective and efficient top-N recommendations

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Abstract

We introduce EigenRec, a versatile and efficient latent factor framework for top-N recommendations that includes the well-known PureSVD algorithm as a special case. EigenRec builds a low-dimensional model of an inter-item proximity matrix that combines a similarity component, with a scaling operator, designed to control the influence of the prior item popularity on the final model. Seeing PureSVD within our framework provides intuition about its inner workings, exposes its inherent limitations, and also, paves the path toward painlessly improving its recommendation performance. A comprehensive set of experiments on the MovieLens and the Yahoo datasets based on widely applied performance metrics, indicate that EigenRec outperforms several state-of-the-art algorithms, in terms of Standard and Long-Tail recommendation accuracy, exhibiting low susceptibility to sparsity, even in its most extreme manifestations—the Cold-Start problems. At the same time, EigenRec has an attractive computational profile and it can apply readily in large-scale recommendation settings.

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Notes

  1. Note that even though the actual values of the reconstructed matrix do not have a meaning in terms of ratings, they induce an ordering of the items which is sufficient for recommending top-N lists.

  2. A preliminary version of this work has been presented in [28].

  3. High-level and MPI implementations of EigenRec can be found here: https://github.com/nikolakopoulos/EigenRec.

  4. Remember that these “scores” are by definition the elements that replace the previously zero-valued entries of the original ratings matrix \({\mathbf {R}}\), after its reconstruction using only the f largest singular dimensions.

  5. For which, if we assume scaling parameter d, matrix W equals \({\mathbf {R}}\,{\mathrm{diag}}\{\Vert {\mathbf {r}}_{{\mathbf {1}}}\Vert ,\Vert {\mathbf {r}}_{{\mathbf {2}}}\Vert ,\dots ,\Vert {\mathbf {r}}_{{\mathbf {m}}}\Vert \}^{d-1}.\)

  6. Note that to alleviate this, one can use sophisticated parallel schemes that try to overlap communication with computations; however, their analysis goes deep into high-performance computing and lies outside the scope of this paper.

  7. Different approaches to compute partial singular value decompositions of sparse matrices can be found in [38, 39].

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Acknowledgements

Vassilis Kalantzis was partially supported by a Gerondelis Foundation Fellowship. The authors acknowledge the Minnesota Supercomputing Institute (http://www.msi.umn.edu) at the University of Minnesota for providing resources that contributed to the research results reported within this paper.

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Authors and Affiliations

  1. Digital Technology Center, University of Minnesota, Minneapolis, MN, USA

    Athanasios N. Nikolakopoulos

  2. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA

    Vassilis Kalantzis

  3. Department of Computer Engineering and Informatics, University of Patras, Patras, Greece

    Efstratios Gallopoulos & John D. Garofalakis

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  1. Athanasios N. Nikolakopoulos
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Correspondence to Athanasios N. Nikolakopoulos.

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Nikolakopoulos, A.N., Kalantzis, V., Gallopoulos, E. et al. EigenRec: generalizing PureSVD for effective and efficient top-N recommendations. Knowl Inf Syst 58, 59–81 (2019). https://doi.org/10.1007/s10115-018-1197-7

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