| cmfrec {cmfrec} | R Documentation |
cmfrec package
Description
This is a library for approximate low-rank matrix factorizations, mainly oriented towards recommender systems but being also usable for other domains such as dimensionality reduction or imputation of missing data.
In short, the main goal behind the models in this library is to produce an approximate factorization
of a matrix \mathbf{X} (which might potentially be sparse or very large) as the product of two
lower-dimensional matrices:
\mathbf{X} \approx \mathbf{A} \mathbf{B}^T
For recommender systems, it is assumed that \mathbf{X} is a matrix encoding user-item
interactions, with rows representing users, columns representing items, and values representing
some interaction or rating (e.g. numer of times each user listened to different songs), where higher
numbers mean better affinity for a given item. Under this setting, the items for which a user might have
higher affinity should have larger values in the approximate factorization, and thus items with larger
values for a given user can be considered as better candidates to recommend - the idea being to recommend
new items to users that have not yet been seen/consumed/bought/etc.
This matrix factorization might optionally be enhanced by incorporating side information about users/items
in the 'X' matrix being factorized, which is assumed to come in the form of additional matrices
\mathbf{U} (for users) and/or \mathbf{I} (for items), which might also get factorized along
the way sharing some of the same low-dimensional components.
The main function in the library is CMF, which can fit many variations of the model described above under different settings (e.g. whether entries missing in a sparse matrix are to be taken as zeros or ignored in the objective function, whether to apply centering, to including row/column intercepts, which kind of regularization to apply, etc.).
A specialized function for implicit-feedback models is also available under CMF_implicit, which provides more appropriate defaults for such data.
Nomenclature used throughout the library
The documentation and function namings use the following naming conventions:
About data:
'X' -> data about interactions between users/rows and items/columns (e.g. ratings given by users to items).
'U' -> data about user/row attributes (e.g. user's age).
'I' -> data about item/column attributes (e.g. a movie's genre).
About functionalities:
'warm' -> predictions based on new, unseen 'X' data, and potentially including new 'U' data along.
'cold' -> predictions based on new user attributes data 'U', without 'X'.
'new' -> predictions about new items based on attributes data 'I'.
About function descriptions:
'existing' -> the user/item was present in the training data to which the model was fit.
'new' -> the user/items was not present in the training data that was passed to 'fit'.
Be aware that the package's functions are user-centric (e.g. it will recommend items for users, but not users for items). If predictions about new items are desired, it's recommended to use the method swap.users.and.items, as the item-based functions which are provided for convenience might run a lot slower than their user equivalents.
Implicit and explicit feedback
In recommender systems, data might come in the form of explicit user judgements about items (e.g. movie ratings) or in the form of logged user activity (e.g. number of times that a user listened to each song in a catalogue). The former is typically referred to as "explicit feedback", while the latter is referred to as "implicit feedback".
Historically, driven by the Netflix competition, formulations of this problem have geared towards predicting the rating that users would give to items under explicit-feedback datasets, determining the components in the low-rank factorization in a way that minimizes the deviation between predicted and observed numbers on the observed data only (i.e. predictions about items that a user did not rate do not play any role in the optimization problem for determining the low-rank factorization as they are simply ignored), but this approach has turned out to oftentimes result in very low-quality recommendations, particularly for users with few data, and is usually not suitable for implicit feedback as the data in such case does not contain any examples of dislikes and might even come in just binary (yes/no) form.
As such, research has mostly shifted towards the implicit-feedback setting, in which items that are not consumed by users do play a role in the optimization objective for determining the low-rank components - that is, the goal is more to predict which items would users have consumed than to predict the exact rating that they'd give to them - and the evaluation of recommendation quality has shifted towards looking at how items that were consumed by users would be ranked compared to unconsumed items (evaluation metrics for implicit-feedback for this library can be calculated through the package recometrics).
Other problem domains
The documentation and naming conventions in this library are all oriented towards recommender systems, with the assumption that users are rows in a matrix, items are columns, and values denote interactions between them, with the idea that values under different columns are comparable (e.g. the rating scale is the same for all items).
The concept of approximate low-rank matrix factorizations is however still useful for other problem domains, such as general dimensionality reduction for large sparse data (e.g. TF-IDF matrices) or imputation of high-dimensional tabular data, in which assumptions like values being comparable between different columns would not hold.
Be aware that functions like CMF come with some defaults that might not be reasonable in other applications, but which can be changed by passing non-default arguments to functions - for example:
Global centering - the "explicit-feedback" models here will by default calculate a global mean for all entries in 'X' and center the matrix by substracting this value from all entries. This is a reasonable thing to do when dealing with movie ratings as all ratings follow the same scale, but if columns of the 'X' matrix represent different things that might have different ranges or different distributions, global mean centering is probably not going to be desirable or useful.
User/row biases: models might also have one bias/intercept parameter per row, which in the approximation, would get added to every column for that user/row. This is again a reasonable thing to do for movie ratings, but if the columns of 'X' contain different types of information, it might not be a sensible thing to add.
Regularization for item/column biases: since the models perform global mean centering beforehand, the item/column-specific bias/intercept parameters will get a regularization penalty ("shrinkage") applied to them, which might not be desirable if global mean centering is removed.
Improving performance
This library will run faster when compiled from source with non-default compiler arguments, particularly '-march=native' (replace with '-mcpu=native' for ARM/PPC); and when using an optimized BLAS library for R. See this guide for details: installing optimized libraries.
Author(s)
Maintainer: David Cortes david.cortes.rivera@gmail.com [copyright holder]
Other contributors:
Jorge Nocedal (Copyright holder of included LBFGS library) [copyright holder]
Naoaki Okazaki (Copyright holder of included LBFGS library) [copyright holder]
David Blackman (Copyright holder of original Xoshiro code) [copyright holder]
Sebastiano Vigna (Copyright holder of original Xoshiro code) [copyright holder]
NumPy Developers (Copyright holder of formatted ziggurat tables) [copyright holder]