JSparO (version 1.5.0)

L2SoftThr: L2SoftThr - Iterative Soft Thresholding Algorithm based on \(l_{2,1}\) norm

Description

The function aims to solve \(l_{2,1}\) regularized least squares.

Usage

L2SoftThr(A, B, X, s, maxIter = 200)

Value

The solution of proximal gradient method with \(l_{2,1}\) regularizer.

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

maxIter

maximum iteration

Author

Xinlin Hu

Yaohua Hu

Details

The L2SoftThr function aims to solve the problem: $$\min \|AX-B\|_F^2 + \lambda \|X\|_{2,1}$$ 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_L21 <- L2SoftThr(A0, B0, X0, s = 10, maxIter = maxIter0)