Title: Joint Sparse Optimization via Proximal Gradient Method for Cell Fate Conversion
Version: 1.5.0
Author: Xinlin Hu [aut, cre], Yaohua Hu [cph, aut]
Description: Implementation of joint sparse optimization (JSparO) to infer the gene regulatory network for cell fate conversion. The proximal gradient method is implemented to solve different low-order regularization models for JSparO.
Maintainer: Xinlin Hu <thompson-xinlin.hu@connect.polyu.hk>
License: GPL (≥ 3)
Encoding: UTF-8
Depends: R (≥ 4.0.0)
RoxygenNote: 7.1.1
Imports: pracma
NeedsCompilation: no
Packaged: 2022-08-17 11:09:41 UTC; Thompson
Repository: CRAN
Date/Publication: 2022-08-18 08:40:08 UTC

L1HalfThr - Iterative Half Thresholding Algorithm based on l_{1,1/2} norm

Description

The function aims to solve l_{1,1/2} regularized least squares.

Usage

L1HalfThr(A, B, X, s, maxIter = 200)

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

Details

The L1HalfThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{1,1/2}

to obtain s-joint sparse solution.

Value

The solution of proximal gradient method with l_{1,1/2} regularizer.

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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_L1half <- L1HalfThr(A0, B0, X0, s = 10, maxIter = maxIter0)

L1HardThr - Iterative Hard Thresholding Algorithm based on l_{1,0} norm

Description

The function aims to solve l_{1,0} regularized least squares.

Usage

L1HardThr(A, B, X, s, maxIter = 200)

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

Details

The L1HardThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{1,0}

to obtain s-joint sparse solution.

Value

The solution of proximal gradient method with l_{1,0} regularizer.

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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_L10 <- L1HardThr(A0, B0, X0, s = 10, maxIter = maxIter0)

L1SoftThr - Iterative Soft Thresholding Algorithm based on l_{1,1} norm

Description

The function aims to solve l_{1,1} regularized least squares.

Usage

L1SoftThr(A, B, X, s, maxIter = 200)

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

Details

The L1SoftThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{1,1}

to obtain s-joint sparse solution.

Value

The solution of proximal gradient method with l_{1,1} regularizer.

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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_L11 <- L1SoftThr(A0, B0, X0, s = 10, maxIter = maxIter0)

L1normFun

Description

The function aims to compute the l_1 norm.

Usage

L1normFun(x)

Arguments

x

vector

Details

The L1normFun aims to compute the l_1 norm: \sum_i^n |x_i|

Value

The l_1 norm of vector x

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

L1twothirdsThr - Iterative Thresholding Algorithm based on l_{1,2/3} norm

Description

The function aims to solve l_{1,2/3} regularized least squares.

Usage

L1twothirdsThr(A, B, X, s, maxIter = 200)

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

Details

The L1twothirdsThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{1,2/3}

to obtain s-joint sparse solution.

Value

The solution of proximal gradient method with l_{1,2/3} regularizer.

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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_L1twothirds <- L1twothirdsThr(A0, B0, X0, s = 10, maxIter = maxIter0)

L2HalfThr - Iterative Half Thresholding Algorithm based on l_{2,1/2} norm

Description

The function aims to solve l_{2,1/2} regularized least squares.

Usage

L2HalfThr(A, B, X, s, maxIter = 200)

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

Details

The L2HalfThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{2,1/2}

to obtain s-joint sparse solution.

Value

The solution of proximal gradient method with l_{2,1/2} regularizer.

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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_L2half <- L2HalfThr(A0, B0, X0, s = 10, maxIter = maxIter0)

L2HardThr - Iterative Hard Thresholding Algorithm based on l_{2,0} norm

Description

The function aims to solve l_{2,0} regularized least squares.

Usage

L2HardThr(A, B, X, s, maxIter = 200)

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

Details

The L2HardThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{2,0}

to obtain s-joint sparse solution.

Value

The solution of proximal gradient method with l_{2,0} regularizer.

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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_L20 <- L2HardThr(A0, B0, X0, s = 10, maxIter = maxIter0)

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

Description

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

Usage

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

Details

The L2NewtonThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{2,q}

to obtain s-joint sparse solution.

Value

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

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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)

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)

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

Details

The L2SoftThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{2,1}

to obtain s-joint sparse solution.

Value

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

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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)

L2twothirdsThr - Iterative Thresholding Algorithm based on l_{2,2/3} norm

Description

The function aims to solve l_{2,2/3} regularized least squares.

Usage

L2twothirdsThr(A, B, X, s, maxIter = 200)

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

Details

The L2twothirdsThr function aims to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{2,2/3}

to obtain s-joint sparse solution.

Value

The solution of proximal gradient method with l_{2,2/3} regularizer.

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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_L2twothirds <- L2twothirdsThr(A0, B0, X0, s = 10, maxIter = maxIter0)

demo_JSparO - The demo of JSparO package

Description

This is the main function of JSparO aimed to solve the low-order regularization models with l_{p,q} norm.

Usage

demo_JSparO(A, B, X, s, p, q, maxIter = 200)

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

p

value for l_{p,q} norm (i.e., p = 1 or 2)

q

value for l_{p,q} norm (i.e., 0 <= q <= 1)

maxIter

maximum iteration

Details

The demo_JSparO function is used to solve joint sparse optimization problem via different algorithms. Based on l_{p,q} norm, functions with different p and q are implemented to solve the problem:

\min \|AX-B\|_F^2 + \lambda \|X\|_{p,q}

to obtain s-joint sparse solution.

Value

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

Author(s)

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

Yaohua Hu mayhhu@szu.edu.cn

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)
res_JSparO <- demo_JSparO(A0, B0, X0, s = 10, p = 2, q = 'half', maxIter = maxIter0)