recommenderlab (version 1.0.6)

funkSVD: Funk SVD for Matrices with Missing Data

Description

Implements matrix decomposition by the stochastic gradient descent optimization popularized by Simon Funk to minimize the error on the known values. This function is used by the recommender method "SVDF" (see Recommender).

Usage

funkSVD(x, k = 10, gamma = 0.015, lambda = 0.001,
  min_improvement = 1e-06, min_epochs = 50, max_epochs = 200,
  verbose = FALSE)

Value

An object of class "funkSVD" with components

U

the \(U\) matrix.

V

the \(V\) matrix.

parameters

a list with parameter values.

Arguments

x

a matrix, potentially containing NAs.

k

number of features (i.e, rank of the approximation).

gamma

regularization term.

lambda

learning rate.

min_improvement

required minimum improvement per iteration.

min_epochs

minimum number of iterations per feature.

max_epochs

maximum number of iterations per feature.

verbose

show progress.

Details

Funk SVD decomposes a matrix (with missing values) into two components \(U\) and \(V\). The singular values are folded into these matrices. The approximation for the original matrix can be obtained by \(R = UV'\).

This function predict in this implementation folds in new data rows by estimating the \(u\) vectors using gradient descend and then calculating the reconstructed complete matrix r for these users via \(r = uV'\).

References

Y. Koren, R. Bell, and C. Volinsky. Matrix Factorization Techniques for Recommender Systems, IEEE Computer, pp. 42-49, August 2009.

Examples

# this takes a while to run!
if (FALSE) {
data("Jester5k")

# helper to calculate root mean squared error
rmse <- function(pred, truth) sqrt(sum((truth-pred)^2, na.rm = TRUE))

train <- as(Jester5k[1:100], "matrix")
fsvd <- funkSVD(train, verbose = TRUE)

# reconstruct the original rating matrix as R = UV'
r <- tcrossprod(fsvd$U, fsvd$V)
rmse(train, r)

# fold in new users for matrix completion
test <- as(Jester5k[101:105], "matrix")
p <- predict(fsvd, test, verbose = TRUE)
rmse(test, p)
}