dSVD | R Documentation |
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.
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)
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. |
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.
Koki Tsuyuzaki
# Test data
matdata <- toyModel(model = "dSVD")
# Simple usage
out <- dSVD(matdata, J=2, num.iter=2)
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