Package 'JSparO'

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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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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 [email protected]

Yaohua Hu [email protected]

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)

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