generate.matrix {abess} | R Documentation |
Generate simulated matrix that is the superposition of a low-rank component and a sparse component.
generate.matrix(
n,
p,
rank = NULL,
support.size = NULL,
beta = NULL,
snr = Inf,
sigma = NULL,
seed = 1
)
n |
The number of observations. |
p |
The number of predictors of interest. |
rank |
The rank of low-rank matrix. |
support.size |
The number of nonzero coefficients in the underlying regression
model. Can be omitted if |
beta |
The coefficient values in the underlying regression model.
If it is supplied, |
snr |
A positive value controlling the signal-to-noise ratio (SNR).
A larger SNR implies the identification of sparse matrix is much easier.
Default |
sigma |
A numerical value supplied the variance of the gaussian noise.
Default |
seed |
random seed. Default: |
The low rank matrix L
is generated by L = UV
, where
U
is an n
-by-rank
matrix and
V
is a rank
-by-p
matrix.
Each element in U
(or V
) are i.i.d. drawn from N(0, 1/n)
.
The sparse matrix S
is an n
-by-rank
matrix.
It is generated by choosing a support set of size
support.size
uniformly at random.
The non-zero entries in S
are independent Bernoulli (-1, +1) entries.
The noise matrix N
is an n
-by-rank
matrix,
the elements in N
are i.i.d. gaussian random variable
with standard deviation \sigma
.
The SNR is defined as
as the variance of vectorized matrix L + S
divided
by \sigma^2
.
The matrix x
is the superposition of L
, S
, N
:
x = L + S + N.
A list
object comprising:
x |
An |
L |
The latent low rank matrix. |
S |
The latent sparse matrix. |
Jin Zhu
# Generate simulated data
n <- 30
p <- 20
dataset <- generate.matrix(n, p)
stats::heatmap(as.matrix(dataset[["S"]]),
Rowv = NA,
Colv = NA,
scale = "none",
col = grDevices::cm.colors(256),
frame.plot = TRUE,
margins = c(2.4, 2.4)
)