cp_apr: Compute nonnegative CP with alternating Poisson...

In RDFTensor: Different Tensor Factorization (Decomposition) Techniques for RDF Tensors (Three-Mode-Tensors)

Description

computes an estimate of the best rank-R CP model of a nonnegative tensor X using an alternating Poisson regression. This is most appropriate for sparse count data (i.e., nonnegative integer values) because it uses Kullback-Liebler divergence.

Usage

cp_apr(X, R, opts = list())

Arguments

X	is a sparse tensor (a LIST containing subs, vals and size)
R	The rank of the factorization
opts	a list containing the options for the algorithm like maxiters:maximum iterations, tol:tolerance .. etc.

Details

Different algorithm variants are available (selected by the 'alg' parameter): 'pqnr' - row subproblems by projected quasi-Newton (default) 'pdnr' - row subproblems by projected damped Hessian 'mu' - multiplicative update Additional input parameters for algorithm 'mu': 'kappa' - Offset to fix complementary slackness 100 'kappatol' - Tolerance on complementary slackness 1.0e-10

Additional input parameters for algorithm 'pdnr': 'epsActive' - Bertsekas tolerance for active set 1.0e-8 'mu0' - Initial damping parameter 1.0e-5 'precompinds' - Precompute sparse tensor indices TRUE 'inexact' - Compute inexact Newton steps TRUE

Additional input parameters for algorithm 'pqnr': 'epsActive' - Bertsekas tolerance for active set 1.0e-8 'lbfgsMem' - Number vector pairs to store for L-BFGS 3 'precompinds' - Precompute sparse tensor indices TRUE

Value

M	the factorization of X as a LIST representing Kruskal Tensor (lambda and u)
Minit	the initial solution
output	statistics about the solution like the running time of each step and the error.

Author(s)

Abdelmoneim Amer Desouki

References

-Brett W. Bader, Tamara G. Kolda and others. MATLAB Tensor Toolbox, Version [v3.0]. Available online at https://www.tensortoolbox.org, 2015.

-E. C. Chi and T. G. Kolda. On Tensors, Sparsity, and Nonnegative Factorizations, SIAM J. Matrix Analysis, 33(4):1272-1299, Dec. 2012, http://dx.doi.org/10.1137/110859063 -S. Hansen, T. Plantenga and T. G. Kolda, Newton-Based Optimization for Kullback-Leibler Nonnegative Tensor Factorizations, Optimization Methods and Software, 2015, http://dx.doi.org/10.1080/10556788.2015.1009977

See Also

cp_nmu serial_parCube rescal cp_als

Examples

subs=matrix(c(5,1,1,
              3,1,2,
              1,1,3,
              2,1,3,
              4,1,3,
              6,1,3,
              1,1,4,
              2,1,4,
              4,1,4,
              6,1,4,
              1,2,1,
              3,2,1,
              5,2,1),byrow=TRUE,ncol=3)

    X=list(subs=subs,vals=rep(1,nrow(subs)),size=c(6,2,4))
    set.seed(12345)#for reproducability
    P1=cp_apr(X,2,opts=list(alg='mu'))
    print(P1$M)
    set.seed(12345)#for reproducability
    P2=cp_apr(X,2,opts=list(alg='pdnr'))
    print(P2$M)

RDFTensor documentation built on Jan. 16, 2021, 5:19 p.m.