murnmf {rnnmf} | R Documentation |
Multiplicative update Non-negative matrix factorization with regularization.
murnmf(
Y,
L,
R,
W_0R = NULL,
W_0C = NULL,
lambda_1L = 0,
lambda_1R = 0,
lambda_2L = 0,
lambda_2R = 0,
gamma_2L = 0,
gamma_2R = 0,
epsilon = 1e-07,
max_iterations = 1000L,
min_xstep = 1e-09,
on_iteration_end = NULL,
verbosity = 0
)
Y |
an |
L |
an |
R |
an |
W_0R |
the row space weighting matrix.
This should be a positive definite non-negative symmetric |
W_0C |
the column space weighting matrix.
This should be a positive definite non-negative symmetric |
lambda_1L |
the scalar |
lambda_1R |
the scalar |
lambda_2L |
the scalar |
lambda_2R |
the scalar |
gamma_2L |
the scalar |
gamma_2R |
the scalar |
epsilon |
the numerator clipping value. |
max_iterations |
the maximum number of iterations to perform. |
min_xstep |
the minimum L-infinity norm of the step taken. Once the step falls under this value, we terminate. |
on_iteration_end |
an optional function that is called at the end of
each iteration. The function is called as
|
verbosity |
controls whether we print information to the console. |
This function uses multiplicative updates only, and may not optimize the nominal objective. It is also unlikely to achieve optimality. This code is for reference purposes and is not suited for usage other than research and experimentation.
a list with the elements
The final estimate of L.
The final estimate of R.
The infinity norm of the final step in L.
The infinity norm of the final step in R.
The number of iterations taken.
Whether convergence was detected.
This package provides proof of concept code which is unlikely to be fast or robust, and may not solve the optimization problem at hand. User assumes all risk.
Steven E. Pav shabbychef@gmail.com
Merritt, Michael, and Zhang, Yin. "Interior-point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems." Journal of Optimization Theory and Applications 126, no 1 (2005): 191–202. https://scholarship.rice.edu/bitstream/handle/1911/102020/TR04-08.pdf
Pav, S. E. "An Iterative Algorithm for Regularized Non-negative Matrix Factorizations." Forthcoming. (2024)
Lee, Daniel D. and Seung, H. Sebastian. "Algorithms for Non-negative Matrix Factorization." Advances in Neural Information Processing Systems 13 (2001): 556–562. http://papers.nips.cc/paper/1861-algorithms-for-non-negative-matrix-factorization.pdf
nr <- 100
nc <- 20
dm <- 4
randmat <- function(nr,nc,...) { matrix(pmax(0,runif(nr*nc,...)),nrow=nr) }
set.seed(1234)
real_L <- randmat(nr,dm)
real_R <- randmat(dm,nc)
Y <- real_L %*% real_R
# without regularization
objective <- function(Y, L, R) { sum((Y - L %*% R)^2) }
objective(Y,real_L,real_R)
L_0 <- randmat(nr,dm)
R_0 <- randmat(dm,nc)
objective(Y,L_0,R_0)
out1 <- murnmf(Y, L_0, R_0, max_iterations=5e3L)
objective(Y,out1$L,out1$R)
# with L1 regularization on one side
out2 <- murnmf(Y, L_0, R_0, max_iterations=5e3L,lambda_1L=0.1)
# objective does not suffer because all mass is shifted to R
objective(Y,out2$L,out2$R)
list(L1=sum(out1$L),R1=sum(out1$R),L2=sum(out2$L),R2=sum(out2$R))
sum(out2$L)
# with L1 regularization on both sides
out3 <- murnmf(Y, L_0, R_0, max_iterations=5e3L,lambda_1L=0.1,lambda_1R=0.1)
# with L1 regularization on both sides, raw objective suffers
objective(Y,out3$L,out3$R)
list(L1=sum(out1$L),R1=sum(out1$R),L3=sum(out3$L),R3=sum(out3$R))
# example showing how to use the on_iteration_end callback to save iterates.
max_iterations <- 1e3L
it_history <<- rep(NA_real_, max_iterations)
quadratic_objective <- function(Y, L, R) { sum((Y - L %*% R)^2) }
on_iteration_end <- function(iteration, Y, L, R, ...) {
it_history[iteration] <<- quadratic_objective(Y,L,R)
}
out1b <- murnmf(Y, L_0, R_0, max_iterations=max_iterations, on_iteration_end=on_iteration_end)
# should work on sparse matrices too, but beware zeros in the initial estimates
if (require(Matrix)) {
real_L <- randmat(nr,dm,min=-1)
real_R <- randmat(dm,nc,min=-1)
Y <- as(real_L %*% real_R, "sparseMatrix")
L_0 <- randmat(nr,dm)
R_0 <- randmat(dm,nc)
out1 <- murnmf(Y, L_0, R_0, max_iterations=1e2L)
}