dSVD: Discretized Singular Value Decomposition (dSVD)

In dcTensor: Discrete Matrix/Tensor Decomposition

Discretized Singular Value Decomposition (dSVD)

Description

This function is the discretized version of SVD. The input data X is decomposed to a matrix product U V'. Unlike regular SVD, in dSVD, U and V are estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, U and V are estimated by adding ternary regularization so that the values are -1, 0, or 1 as much as possible.

Usage

dSVD(X, M=NULL, pseudocount=.Machine$double.eps,
    initU=NULL, initV=NULL, fixU=FALSE, fixV=FALSE,
    Ter_U=1e-10, L1_U=1e-10, L2_U=1e-10, eta=1e+10, J = 3,
    thr = 1e-10, num.iter = 100,
    viz = FALSE, figdir = NULL, verbose = FALSE)

Arguments

X	The input matrix which has N-rows and M-columns.
M	The mask matrix which has N-rows and M-columns. If the input matrix has missing values, specify the element as 0 (otherwise 1).
pseudocount	The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon).
initU	The initial values of factor matrix U, which has N-rows and J-columns (Default: NULL).
initV	The initial values of factor matrix V, which has M-rows and J-columns (Default: NULL).
fixU	Whether the factor matrix U is updated in each iteration step (Default: FALSE).
fixV	Whether the factor matrix V is updated in each iteration step (Default: FALSE).
Ter_U	Paramter for terary (-1,0,1) regularitation (Default: 1e-10).
L1_U	Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0.
L2_U	Paramter for L2 regularitation (Default: 1e-10).
eta	Stepsize of gradient descent algorithm (Default: 1e+10).
J	The number of low-dimension (J < {N, M}, Default: 3)
thr	When error change rate is lower than thr, the iteration is terminated (Default: 1E-10).
num.iter	The number of interation step (Default: 100).
viz	If viz == TRUE, internal reconstructed matrix can be visualized.
figdir	The directory for saving the figure, when viz == TRUE.
verbose	If verbose == TRUE, Error change rate is generated in console window.

Value

U : A matrix which has N-rows and J-columns (J < {N, M}). V : A matrix which has M-rows and J-columns (J < {N, M}). RecError : The reconstruction error between data tensor and reconstructed tensor from U and V. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error.

Author(s)

Koki Tsuyuzaki

Examples

# Test data
matdata <- toyModel(model = "dSVD")

# Simple usage
out <- dSVD(matdata, J=2, num.iter=2)

dcTensor documentation built on June 22, 2024, 6:57 p.m.