| 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 |
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 |
q |
value for |
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)