softSVD: penalized SVD

In mengchen18/omic3plus: Different methods for the integrative analysis multiple omics data

Description

SVD with sparsity, non-negative and weight constrants

Usage

softSVD(x, nf = 1, kv = Inf, ku = Inf, wv = 1, wu = 1, pos = FALSE,
  init = c("svd", "average")[2], maxiter = 50,
  tol = sqrt(.Machine$double.eps), verbose = FALSE)

Arguments

x	the matrix to be decomposed
nf	the number of components want to computed
kv	the number of nonzero coefficients for the right regularized sigular vectors
ku	the number of nonzero coefficients for the left regularized sigular vectors
wv	the weight for columns of x
wu	the weight for rows of of x
pos	Logical value, if only retain non-negative values in the
init	how to initialize the algorithm. if no sparsity, svd is fast.
maxiter	the maximum number of iteration
tol	the tolerance of error
verbose	print progress of calulation

Details

The algorithm use a generalized version of NIPALS algorithm to allow sparsity, force non-negative values on both left and rigth singular vectors. In addition, different weghted could be introduced, the columns/rows with bigger weights are more likely to be selected.

Value

the same as svd, list of three components, d, u, v

Author(s)

Chen Meng

See Also

svd

Examples

library(corpcor)

#' a random matrix
x <- matrix(rnorm(50), 5, 10)
ss <- svd(x)
ss2 <- softSVD(x, nf = 5)
ss$d
ss2$d
all.equal(abs(ss$u), abs(ss2$u))
all.equal(abs(ss$v), abs(ss2$v))

#' NCI60 data
data("NCI60_4arrays")
#
d <- as.matrix(NCI60_4arrays$agilent)

###' compare with svd
ss <- svd(d, nu = 5, nv = 5)
ss2 <- softSVD(d, nf = 5)
ss$d
ss2$d
all.equal(abs(ss$u), abs(ss2$u))
all.equal(abs(ss$v), abs(ss2$v))

#' normalize the data
dt <- scale(t(d), scale = FALSE)
pp <- softSVD(x = dt, nf = 5, kv = 30, ku = 6, maxiter = 100)
barplot(pp$u[, 1], col = as.factor(substr(colnames(d), 1, 2)))
barplot(pp$v[, 1])

#' change sparsity
dt <- scale(t(d), scale = FALSE)
pp <- softSVD(x = dt, nf = 5, kv = 30, ku = 9, maxiter = 1000, pos = TRUE)
i <- 2
barplot(pp$u[, i], col = as.factor(substr(colnames(d), 1, 2)), las=2, names.arg = rownames(dt))
barplot(pp$v[, i])

#' change sparsity
pp <- softSVD(x = dt, nf = 5, kv = Inf, ku = 9, maxiter = 1000, pos = TRUE)
i <- 1
barplot(pp$u[, i], col = as.factor(substr(colnames(d), 1, 2)), las=2, names.arg = rownames(dt))
barplot(pp$v[, i])

#' change sparsity
pp <- softSVD(x = dt, nf = 5, kv = 30, ku = Inf, maxiter = 1000, pos = FALSE)
i <- 1
barplot(pp$u[, i], col = as.factor(substr(colnames(d), 1, 2)), las=2, names.arg = rownames(dt))
barplot(pp$v[, i])

#' use weight
w <- rowSums(d - min(d))
w <- w + max(w) #' prefer to select high intensity genes

pw <- softSVD(x = dt, nf = 6, kv = 30, ku = Inf, wv = w, maxiter = 1000, pos = FALSE, verbose = TRUE)
i <- 6
barplot(pw$u[, i], col = as.factor(substr(colnames(d), 1, 2)), las=2, names.arg = rownames(dt))
barplot(pw$v[, i])


i1 <- apply(pp$v, 1, function(x) any(x!=0))
i2 <- apply(pw$v, 1, function(x) any(x!=0))
plot(pw$u[, 1], pp$u[, 1])
layout(matrix(1:2, 1, 2))
hist(d[i1 & !i2, ], main = "No weight")
hist(d[i2 & !i1, ], main = "Weight")

mengchen18/omic3plus documentation built on May 6, 2019, 4:59 p.m.