An FCA-based Boolean Matrix Factorisation for Collaborative Filtering

We propose a new approach for Collaborative Filtering which is based on Boolean Matrix Factorisation (BMF) and Formal Concept Analysis. In a series of experiments on real data (Movielens dataset) we compare the approach with the SVD- and NMF-based algorithms in terms of Mean Average Error (MAE). One of the experimental consequences is that it is enough to have a binary-scaled rating data to obtain almost the same quality in terms of MAE by BMF than for the SVD-based algorithm in case of non-scaled data.

[1]  Radim Belohlávek,et al.  Triadic concept lattices of data with graded attributes , 2012, Int. J. Gen. Syst..

[2]  Jonas Poelmans,et al.  Concept-Based Biclustering for Internet Advertisement , 2012, 2012 IEEE 12th International Conference on Data Mining Workshops.

[3]  Andrzej Cichocki,et al.  Fast Nonnegative Matrix/Tensor Factorization Based on Low-Rank Approximation , 2012, IEEE Transactions on Signal Processing.

[4]  Ito Wasito,et al.  Nearest neighbours in least-squares data imputation algorithms with different missing patterns , 2006, Comput. Stat. Data Anal..

[5]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[6]  Radim Belohlávek,et al.  Optimal decompositions of matrices with entries from residuated lattices , 2012, J. Log. Comput..

[7]  Boris G. Mirkin,et al.  Core Concepts in Data Analysis: Summarization, Correlation and Visualization , 2011, Undergraduate Topics in Computer Science.

[8]  Jonas Poelmans,et al.  A New Cross-Validation Technique to Evaluate Quality of Recommender Systems , 2012, PerMIn.

[9]  Lars Elden,et al.  Matrix methods in data mining and pattern recognition , 2007, Fundamentals of algorithms.

[10]  Chih-Jen Lin,et al.  Projected Gradient Methods for Nonnegative Matrix Factorization , 2007, Neural Computation.

[11]  Sergei O. Kuznetsov,et al.  Concept-based Recommendations for Internet Advertisement , 2009, ArXiv.

[12]  Éric Gaussier,et al.  Relation between PLSA and NMF and implications , 2005, SIGIR '05.

[13]  Vilém Vychodil,et al.  Discovery of optimal factors in binary data via a novel method of matrix decomposition , 2010, J. Comput. Syst. Sci..

[14]  L. Trefethen,et al.  Numerical linear algebra , 1997 .

[15]  Gediminas Adomavicius,et al.  Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions , 2005, IEEE Transactions on Knowledge and Data Engineering.

[16]  Derek G. Bridge,et al.  Collaborative Recommending using Formal Concept Analysis , 2006, Knowl. Based Syst..

[17]  Bernhard Ganter,et al.  Formal Concept Analysis , 2013 .