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Advanced package for recommender systems
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Advanced Package for Recommender Systems


  • Incorporate user and item covariate information, including item category preferences.

  • Parallel computation.

  • Novel variations on common models, e.g. a hybrid of NMF and k-Nearest Neighbor.

  • Plotting.

  • Focus group finder.

  • NMF, ANOVA, cosine models all in one package.

  • Some functions new, others enhancements of existing libraries.

Overview and Examples

Random effects ANOVA model:

A simple random effects latent factor model is

E(Y) = μ + αi + βj

where Yij is the rating, with αi and βj being specific latent effects for user i and item j, e.g. movie reviewer i and movie j.

Though typically Maximum Likelihood Estimation is used for latent factor models, this is computationally infeasible on large data sets. Instead, we use the Method of Moments, estimating αi by Yi. - Y.., where the first term is the mean of all observed ratings by user i and the second is the overall mean of all ratings. We estimate βj similarly, and estimate μ by the overall mean Y.. The predicted value of Yij is then

Yi. + Y.j - Y..

Computation is simple, with estimation conducted by our function findYdotsMM(); prediction is done on the output by our function predict.ydotsMM().

A novel enhancement in the package is to allow for different weights to be given to the αi and βj components in the MM version. (With MLE it wouldn't matter, just changing the variances.)

We do make MLE available. Here αi and βj are assumed to have independent normal distributions with different variances. (The error term εij = Yij - EYij is assumed independent of αi and βj, with variance constant across i and j.) We piggyback R's lme4 package, forming a wrapper for our application, and adding our function predict.ydotsMLE() for prediction, also an lme4 wrapper suited for our context. Since MLE computation can be voluminous, our package offers a parallel version.

Covariates are allowed for both the MM and MLE versions.

Let's try it:

(Some output has been omitted for clarity.)

> # Try lme4 data set, needs some prep first.
> data(InstEval)
> ivl <- InstEval
> # Convert factors to numeric:
> ivl$s <- as.numeric(ivl$s)
> ivl$d <- as.numeric(ivl$d)
> ivl$studage <- as.numeric(ivl$studage)
> ivl$lectage <- as.numeric(ivl$lectage)
> ivl$service <- as.numeric(ivl$service)
> # Make correct format (user ID, item ID, rating), choose covs:
> ivl <- ivl[,c(1,2,7,3:6)]
> # Create dummy variables in place of dept:
> library(dummies)
> dms <- dummy(ivl$dept)
> dms <-
> dms$dept2 <- NULL
> ivl$dept <- NULL
> ivl <- cbind(ivl,dms)
# Run the training data, no covariates:
> ydout <- trainMLE(ivl[,1:3]) 
# Form a test set to illustrate prediction:
> testSet <- ivl[c(3,8),]  # these happen to be students 1, 3
# Say want to predict how well students 1 and 3 would like instructor 12
> testSet[1,2] <- 12
> testSet[2,2] <- 12
> # Predict:
> predict(ydout,testSet[,1:2])  
[1] 4.272660 4.410612
> # Try using the covariates:
> ydout <- findYdotsMLE(ivl)
> predict(ydout,testSet[,-3])  
3 3.286828
8 3.551587

Matrix factorization model:

Let A denote the matrix of ratings, with Yij in row i, column j. Most of A is unknown, and we wish to predict the unknown values. Nonnegative Matrix Factorization (NMF) does this as follows:

We find nonnegative matrices W and H, each of rank k, such that A is approximately equal to the product WH. Here k is a user-defined tuning parameter, typically much smaller than the number of rows and columns of A. It is kept small to avoid overfitting but large enough to capture most of the structure of the data. Default value is k = 10.

Here we piggyback on the R package recosystem, adding convenient wrappers and adding a parallel computation capability. See the functions trainReco(), predictReco() and so on.

Cosine model:

(EXPERIMENTAL, likely to be replaced or modified.)

The basic idea here is as follows. The predict the rating user i would give to item j, find some users who are similar to user i and who have rated item j, and average their ratings of that item. The CRAN package recommderlab is one implementation of this idea, but our rectools package uses its own implementation, including novel enhancements.

One such enhancement is to do item category matching, an example of categories being movie genres. For each user, our code calculates the proportion of items in each category rated by this user, and incorporates this into the calculation of similarity between any pair of users. See the functions cosDist(), formUserData() and predictUsrData().

Cross validation:

The MM, MLE, NMF and cosine methods all have wrappers to do cross-validation, reporting the accuracy measures exact prediction; mean absolute deviation; and l2. In our experiments so far, MM seems to give the best accuracy (and the greatest speed).


Some plotting capability is provided, currently in the functions plot.ydotsMM() and plot.xvalb(). The former, for instance, can be used to assess the normality and independence assumptions of the MLE model, and to identify a possible need to consider separate analyses for subpopulations.


K. Gao and A. Owen, Efficient Moment Calculations for Variance Components in Large Unbalanced Crossed Random Effects Models, 2016.

M. Hahsler, recommderlab, CRAN vignette.

Y. Koren et al, Matrix Factorization Techniques for Recommender Systems, IEEE Computer, 2009.

N. Matloff, Collaborative Filtering in Recommender Systems: a Short Introduction, 2016.

P. Perry, Fast Moment-Based Estimation for Hierarchical Models, 2015.

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