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Matrix factorization is a common machine learning technique for recommender systems, like books for Amazon or movies for Netflix.
.. figure:: https://raw.githubusercontent.com/ExaScience/smurff/master/docs/_static/matrix_factorization.svg?sanitize=true :alt: Matrix Factorizaion
The idea of these methods is to approximate the user-movie rating matrix R as a product of two low-rank matrices U and V such that R ≈ U × V . In this way U and V are constructed from the known ratings in R, which is usually very sparsely filled. The recommendations can be made from the approximation U × V which is dense. If M × N is the dimension of R then U and V will have dimensions M × K and N × K.
Bayesian probabilistic matrix factorization (BPMF) has been proven to be more robust to data-overfitting compared to non-Bayesian matrix factorization.
SMURFF is a highly optimized and parallelized framework for Bayesian Matrix and Tensors Factorization. SMURFF supports multiple matrix factorization methods:
BPMF <https://www.cs.toronto.edu/~amnih/papers/bpmf.pdf>__, the basic
version;Macau <https://arxiv.org/abs/1509.04610>__, adding support
for high-dimensional side information to the factorization;GFA <https://arxiv.org/pdf/1411.5799.pdf>__, doing Group Factor
Anaysis.Macau and BPMF can also perform tensor factorization.
Documentation is generated from Jupyter Notebooks. You can find the
notebooks in docs/notebooks <docs/notebooks> and the resulting
documentation on
smurff.readthedocs.io <http://smurff.readthedocs.io>
Using conda <http://anaconda.org>__:
.. code:: bash
conda install -c vanderaa smurffCompile from source code: see INSTALL.rst <docs/INSTALL.rst>__
If you are using SMURFF in a scientific publication, please cite the following preprint plus the paper describing the corresponding algorithm:
SMURFF: a High-Performance Framework for Matrix Factorization arXiv preprint arXiv:1904:02514 <https://arxiv.org/abs/1904.02514>_
When using pure Bayesian Probabilistic Matrix Factorization, please also cite:
Salakhutdinov R, Mnih A. Bayesian probabilistic matrix factorization using Markov chain Monte Carlo. In Proceedings of the 25th international conference on Machine learning (ICML '08), 2008. ACM, New York, NY, USA, 880-887.
When using Bayesian Factorization with Side Information, please also cite:
Simm J, Arany Á, Zakeri P, Haber T, Wegner JK, Chupakhin V, Ceulemans H, Moreau Y. Macau: Scalable Bayesian Factorization with High-Dimensional Side Information Using MCMC Proc. of the Machine Learning for Signal Processing (MLSP), 2017 IEEE 27th International Workshop on MLSP; 2017; Vol. 2017-September; pp. 1 - 6. Tokyo, Japan.
When using Group Factor Analysis, please also cite:
Klami A, Virtanen S, Leppäaho E, Kaski S., "Group Factor Analysis," in IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 9, pp. 2136-2147, Sept. 2015.
Over the course of the last 5 years, this work has been supported by the EU H2020 FET-HPC projects EPEEC (contract #801051), ExCAPE (contract #671555) and EXA2CT (contract #610741), and the Flemish Exaptation project.
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