Collective Matrix Factorization for Recommender Systems
Collective matrix factorization (a.k.a. multi-view or multi-way factorization,
Singh, Gordon, (2008) <10.1145>) tries to approximate a matrix 'X' as the
product of two low-dimensional matrices, optionally aided with secondary information matrices about rows
and/or columns of 'X' which are also factorized using the same latent components.
The intended usage is for recommender systems, dimensionality reduction, and missing value imputation.
Implements extensions of the original model (Cortes, (2018) <1809.00366>) and can produce
different factorizations such as the weighted 'implicit-feedback' model (Hu, Koren, Volinsky,
(2008) <10.1109>), the 'weighted-lambda-regularization' model,
(Zhou, Wilkinson, Schreiber, Pan, (2008) <10.1007>),
or the enhanced model with 'implicit features' (Rendle, Zhang,
Koren, (2019) <1905.01395>), with or without side information. Can use gradient-based
procedures or alternating-least squares procedures (Koren, Bell, Volinsky, (2009)
<10.1109>), with either a Cholesky solver, a faster conjugate gradient solver
(Takacs, Pilaszy, Tikk, (2011) <10.1145>), or a non-negative
coordinate descent solver (Franc, Hlavac, Navara, (2005) <10.1007>),
providing efficient methods for sparse and dense data, and mixtures thereof.
Supports L1 and L2 regularization in the main models,
offers alternative most-popular and content-based models, and implements functionality
for cold-start recommendations and imputation of 2D data.10.1007>10.1145>10.1109>1905.01395>10.1007>10.1109>1809.00366>10.1145>