L2NewtonThr function

L2NewtonThr - Iterative Thresholding Algorithm based on $l_{2,q}$ norm with Newton method

The function aims to solve $l_{2,q}$ regularized least squares, where the proximal optimization subproblems will be solved by Newton method.

L2NewtonThr(A, B, X, s, q, maxIter = 200, innMaxIter = 30, innEps = 1e-06)

Arguments

• A: Gene expression data of transcriptome factors (i.e. feature matrix in machine learning). The dimension of A is m * n.
• B: Gene expression data of target genes (i.e. observation matrix in machine learning). The dimension of B is m * t.
• X: Gene expression data of Chromatin immunoprecipitation or other matrix (i.e. initial iterative point in machine learning). The dimension of X is n * t.
• s: joint sparsity level
• q: value for $l_{2,q}$ norm (i.e., 0 < q < 1)
• maxIter: maximum iteration
• innMaxIter: maximum iteration in Newton step
• innEps: criterion to stop inner iteration

Returns

The solution of proximal gradient method with $l_{2,q}$ regularizer.

Details

The L2NewtonThr function aims to solve the problem:

to obtain s-joint sparse solution.

Examples

m <- 256; n <- 1024; t <- 5; maxIter0 <- 50
A0 <- matrix(rnorm(m * n), nrow = m, ncol = n)
B0 <- matrix(rnorm(m * t), nrow = m, ncol = t)
X0 <- matrix(0, nrow = n, ncol = t)
NoA <- norm(A0, '2'); A0 <- A0/NoA; B0 <- B0/NoA
res_L2q <- L2NewtonThr(A0, B0, X0, s = 10, q = 0.2, maxIter = maxIter0)

Author(s)

Xinlin Hu thompson-xinlin.hu@connect.polyu.hk

Yaohua Hu mayhhu@szu.edu.cn