I am working on a project for collaborative filtering (CF), i.e. completing a partially observed matrix or more generally tensor. I am a newbie to the field, and for this project eventually I have to compare our method to other well-known ones that nowadays, proposed methods are compared against them, namely state-of-the-art in CF.

My search revealed the following methods. Indeed I came across them by looking at some of these papers and their references, or by looking at experiments section when they do comparisons. I would be happy to know for a new proposed method and to do a comparison with SoTA, which of the following would be a good pick to do so? If not among them, I would be happy to know a good representative.

Based on Matrix Factorization:

  1. Weighted Low Rank Approximation (ICML 2003)
  2. Modeling User Rating Profiles For Collaborative Filtering (NIPS 2003)
  3. The Multiple Multiplicative Factor Model For Collaborative Filtering (ICML 2004)
  4. Fast Maximum Margin Matrix Factorization for Collaborative Prediction (ICML 2005)
  5. Probabilistic Matrix Factorization (NIPS 2007)
  6. Bayesian Probabilistic Matrix Factorization (ICML 2008)
  7. Regression-based Latent Factor Models (KDD 2009)
  8. Non-linear Matrix Factorization with Gaussian Processes (ICML 2009)
  9. Dynamic Poission Factorization (ACM Conference on Recommender Systems 2015)

Based on Tensor Factorization:

  1. Incorporating Contextual Information in Recommender Systems Using a Multidimensional Approach (ACM Transactions on Information Systems (TOIS) 2005)
  2. Bayesian Probabilistic Tensor Factorization (SIAM Data Mining 2010)
  3. Low-rank tensor completion by Riemannian optimization (BIT Numerical Mathematics 54.2 (2014))
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    $\begingroup$ A tensor for continuous data? Mixed data? Categorical data? Since you don't say, maybe we can assume continuous. David Dunson's Bayesian Tensor Regression is an approach for tensor contingency tables that might provide some insight or guidance -- but it's not an RS approach. researchgate.net/publication/… Also, check out the papers on his website at Duke U. $\endgroup$ Oct 24, 2015 at 20:12
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    $\begingroup$ You may also consider nonnegative matrix factorization (NMF). $\endgroup$
    – diadochos
    Jan 24, 2018 at 0:44
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    $\begingroup$ Your list seems reasonable, I also would add methods based on neural networks. There's a survey paper that is a good place to start: arxiv.org/pdf/1707.07435.pdf $\endgroup$
    – sebp
    Aug 15, 2018 at 11:26

1 Answer 1


You can also take a look on the Gravity Recommendation System (GRS) paper, which is also about Matrix Factorization. The authors competed using this algorithm in the well known Netflix Prize.


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